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%% Books
@book{fds71097,
Author = {J. Trangenstein},
Title = {Numerical Solution of Hyperbolic Partial Differential
Equations},
Publisher = {Cambridge University Press},
Year = {2007},
Month = {December},
ISBN = {052187727X},
Abstract = {Numerical Solution of Hyperbolic Partial Differential
Equations is a new type of graduate textbook, with both
print and interactive electronic components (on CD). It is a
comprehensive presentation of modern shock-capturing
methods, including both finite volume and finite element
methods, covering the theory of hyperbolic conservation laws
and the theory of the numerical methods. The range of
applications is broad enough to engage most engineering
disciplines and many areas of applied mathematics. Classical
techniques for judging the qualitative performance of the
schemes are used to motivate the development of classical
higher-order methods. The interactive CD gives access to the
computer code used to create all of the text's figures, and
lets readers run simulations, choosing their own input
parameters; the CD displays the results of the experiments
as movies. Consequently, students can gain an appreciation
for both the dynamics of the problem application, and the
growth of numerical errors.},
Key = {fds71097}
}
%% Papers Published
@article{fds28834,
Author = {J.A. Trangenstein and John A. Trangenstein and Chisup Kim},
Title = {Operator Splitting and Adaptive Mesh Refinement for the
Luo-Rudy I Model},
Journal = {Journal of Computational Physics},
Volume = {196},
Pages = {645-679},
Publisher = {Elsevier},
Year = {2004},
Keywords = {reaction-diffusion, • excitable media, • adaptive
mesh refinement, • operator splitting, • finite
elements, • multigrid, • domain
decomposition},
Abstract = {We apply second-order operator splitting to the Luo-Rudy I
model for electrical wave propagation in the heart. The
purpose of the operator splitting is to separate the
nonlinear but local reaction computations from the linear
but globally coupled diffusion computations. This approach
allows us to use {\em local nonlinear} iterations for the
stiff nonlinear reactions, and to solve {\em global linear}
systems for the implicit treatment of diffusion. For
computational efficiency, we use dynamically adaptive mesh
refinement (AMR), involving hierarchies of unions of grid
patches on distinct levels of refinement. The linear system
for the discretization of the diffusion on the composite AMR
grid is formulated via standard conforming finite elements
on unions grid patches within a level of refinement, and
aligned mortar elements along interfaces between levels of
refinement. The linear systems are solved iteratively by
preconditioned conjugate gradients. Our preconditioner uses
multiplicative domain decomposition between levels of
refinement; the smoother involves algebraic additive domain
decomposition between patches within a level of refinement,
and Gauss-Seidel iteration within grid patches. Numerical
results are presented in 1D and 2D, including spiral
waves.},
Key = {fds28834}
}
@article{fds9499,
Author = {X. Garaizar and John Trangenstein},
Title = {Adaptive Mesh Refinement and Front Tracking for shear bands
in Granular Flow},
Journal = {SIAM Journal on Scientific Computing, vol. 20, (1999), pp.
750-779},
Key = {fds9499}
}
@article{fds9037,
Author = {G. Christakos and P.T. Imhoff and John F. McBride and C.T. Miller and Joseph A. Pedit and John Trangenstein},
Title = {Multiple Flow and Transport Modeling in Heterogeneous Porous
Media: Challenges and Approaches},
Journal = {Advances in Water Resources 21(1998), 77-120.},
Key = {fds9037}
}
@article{fds9498,
Author = {F. X. Garaizar and John Trangenstein},
Title = {Front Tracking for Shear Bands in an Antiplane Shear
Model},
Journal = {J. Comp. Phys., vol.131, (1998), pp. 54-69},
Key = {fds9498}
}
@article{fds9018,
Author = {R. Hornung and John Trangenstein},
Title = {Adaptive Mesh Refinement and Multilevel Iteration for Flow
in Porous Media},
Journal = {Journal of Computational Physics, 136, 522-545.},
Key = {fds9018}
}
@article{fds9024,
Author = {S. A. Khan and G.A. Pope and John Trangenstein},
Title = {Micellar/Polymer Physical Property Models for Contaminant
Cleanup Problems and Enhanced Oil Recovery},
Journal = {Transport in Porous Media 24(1996), 35-79.},
Key = {fds9024}
}
@article{fds9021,
Author = {John Trangenstein},
Title = {Adaptive Mesh Refinement for Wave Propagation in Nonlinear
Solids},
Journal = {SIAM J. Sci. Comput. 16(1995), 819-839.},
Key = {fds9021}
}
@article{fds9022,
Author = {F. Xabier Garaizar and John Trangenstein},
Title = {Tracking of Shear Bands in an Antiplane Shear
Model},
Journal = {Proceedings of the International Conference on Hyperbolic
Equations, SUNY Stony Brook.},
Key = {fds9022}
}
@article{fds9023,
Author = {S. A. Khan and K. Holing and R.D. Hornung and B.E.R. Schilling and John
Trangenstein},
Title = {Application of Adaptive Mesh-Refinement with a New
Higher-Order Method in Simulation of a North Sea
Micellar/Polymer Flood, SPE 29145},
Journal = {Proceedings of the SPE Symposium on Reservoir
Simulation},
Key = {fds9023}
}
@article{fds9020,
Author = {John Trangenstein},
Title = {A Second-Order Godunov Algorithm for Two-Dimensional Solid
Mechanics},
Journal = {Computational Mechanics, 13(1994) pp. 343-359.},
Key = {fds9020}
}
@article{fds9492,
Author = {Richard Pember and John Trangenstein},
Title = {Numerical Algorithms for Strong Discontinuities in
Elastic-Plastic Solids},
Journal = {J. Comp. Phys., vol. 103, (1992), pp. 63-89},
Key = {fds9492}
}
@article{fds9487,
Author = {Philip Colella and John Trangenstein},
Title = {A Higher-Order Godunov Method for Modeling Finite
Deformation in Elastic-Plastic Solids},
Journal = {Comm. Pure Appl. Math., vol. XLIV, (1991), pp.
41-100},
Key = {fds9487}
}
@article{fds9488,
Author = {Richard Pember and John Trangenstein},
Title = {The Riemann Problem for Longitudinal Motion in an
Elastic-Plastic Bar},
Journal = {SIAM J. Sci. Stat. Comput., vol. 12, (1991), pp.
180-207},
Key = {fds9488}
}
@article{fds9497,
Author = {John Trangenstein},
Title = {A Comparison of Two Numerical Methods for Shocks in
One-Dimensional Elastic-Plastic Solids},
Journal = {Viscous Profiles and Numerical Methods for Shock Waves,
Michael Shearer (editor), SIAM (1991).},
Key = {fds9497}
}
@article{fds9489,
Author = {John Trangenstein},
Title = {A Second-Order Algorithm for the Dynamic Response of
Soils},
Journal = {IMPACT of Computing in Science and Engineering, vol. 2,
(1990), pp. 1-39},
Key = {fds9489}
}
@article{fds9491,
Author = {Kent Holing and Birgitte Schilling and John
Trangenstein},
Title = {The Use of Second-Order Godunov-Type Methods for Simulating
EOR Processes in Realistic Reservoir Models},
Journal = {Second European Conference on the Mathematics of Oil
Recovery, E. Guerillot and O. Guillon (ed.) (1990),
101-111},
Key = {fds9491}
}
@article{fds9480,
Author = {John B. Bell and John Trangenstein},
Title = {Mathematical Structure of the Black-Oil Model for Petroleum
Reservoir Simulation},
Journal = {SIAM J. Appl. Math., vol.49, (1989), pp.
749-783},
Key = {fds9480}
}
@article{fds9481,
Author = {John B. Bell and John Trangenstein},
Title = {Mathematical Structure of Compositional Reservoir
Simulation},
Journal = {SIAM J. Sci. Stat. Comput., vol. 10, (1989), pp.
817-845},
Key = {fds9481}
}
@article{fds9483,
Author = {John B. Bell and Philip Colella and John Trangenstein},
Title = {Higher-Order Godunov Methods for General Systems of
Hyperbolic Conservation Laws},
Journal = {J. Comp. Phys., vol.82, (1989), pp. 362-397},
Key = {fds9483}
}
@article{fds9485,
Author = {Michael Shearer and John Trangenstein},
Title = {Loss of Real Characteristics for Models of Three-Phase Flow
in a Porous Medium},
Journal = {Transport in Porous Media, vol. 4, (1989), pp.
499-525},
Key = {fds9485}
}
@article{fds9486,
Author = {John Trangenstein},
Title = {Three-Phase Flow with Gravity},
Journal = {Contemporary Mathematics, vol.100, (1989), pp.
147-160},
Key = {fds9486}
}
@article{fds9490,
Author = {John Trangenstein},
Title = {Analysis of a Model and Sequential numerical Method for
Thermal Reservoir Simulation},
Journal = {Second European Conference on the Mathematics of Oil
Recovery, P.R. King (ed.), Institute for Mathematics and Its
Applications, Cambridge University, 1989},
Key = {fds9490}
}
@article{fds9496,
Author = {I.I. Glass and J. Kaca and D.L. Zhang and H.M. Glaz and J. Trangenstein and J.B. Bell and},
Title = {Diffraction of Planar Shock Waves over Half-Diamond and
Semicircular Cyliners: an Experimental and Numerical
Comparisond},
Journal = {Proceedings of the Seventeenth International Symposium on
Shock Waves and Shock Tubes, July 17-21,
1989.},
Key = {fds9496}
}
@article{fds9479,
Author = {Myron B. Allen and Alda Behie and John Trangenstein},
Title = {Multiphase Flow in Porous Media: Mechanics, Mathematics and
Numerics},
Journal = {Springer-Verlag Lecture Notes in Engineering 34,
(1988)},
Key = {fds9479}
}
@article{fds9495,
Author = {J. Bell and P. Colella and John Trangenstein and M.
Welcome},
Title = {Godunov Methods and Adaptive Algorithms for Unsteady Fluid
Dynamics},
Journal = {Eleventh International Conference on Numerical Methods in
Fluid Dynamics, Williamsburg, Virginia, 1988.},
Key = {fds9495}
}
@article{fds9478,
Author = {John Trangenstein},
Title = {Customized Minimization Techniques for Phase Equilibrium
Computations in Reservoir Simulation},
Journal = {Chemical Engineering Science, vol.42, (1987), pp.
2847-2863},
Key = {fds9478}
}
@article{fds9494,
Author = {John Bell and Phillip Colella and John Trangenstein and Michael
Welcome},
Title = {Adaptive Methods for High Mach Number Reacting
Flow},
Journal = {AIAA Eighth Computational Fluid Dynamics Conference,
Honolulu, Hawaii, 1987.},
Key = {fds9494}
}
@article{fds9476,
Author = {John B. Bell and Gregory R. Shubin and John
Trangenstein},
Title = {a Method for Reducing Numerical Dispersion in Two-Phase
Black-Oil Reservoir Simulation},
Journal = {J. Comp. Phys., vol. 65, (1986), pp. 71-106},
Key = {fds9476}
}
@article{fds9477,
Author = {John B. Bell and Gregory R. Shubin and John
Trangenstein},
Title = {Conservation Laws of Mixed Type Describing Three-Phase Flow
in Porous Media},
Journal = {SIAM J. Applied Math., vol. 46, (1986), pp.
1000-1017},
Key = {fds9477}
}
@article{fds9475,
Author = {John Trangenstein},
Title = {Minimization of Gibbs Free Energy in Compositional Reservoir
Simulation},
Journal = {Eighth SPE Symposium on Reservoir Simulation, SPE 13520,
Dallas, 1985},
Key = {fds9475}
}
@article{fds9474,
Author = {H.E. Read and John Trangenstein},
Title = {The Inelastic Response Characteristics of the New
Endochronic Theory with Singular Kernel},
Journal = {International Journal of Solids and Structures, vol. 18,
(1982), pp. 947-956},
Key = {fds9474}
}
@article{fds9473,
Author = {W.B. Gragg and R.J. LeVeque and John Trangenstein},
Title = {Numerically Stable Methods for Updating Regressions},
Journal = {J. American Statistical Association, vol. 74, (1979), pp.
161-168},
Key = {fds9473}
}
@article{fds9472,
Author = {John Trangenstein},
Title = {Finite Element Method for the Tricomi Problem in the
Elliptic Region},
Journal = {SIAM J. Num. Anal., vol. 14, (1977), pp.
1066-1077},
Key = {fds9472}
}
@article{fds9471,
Author = {J. J. More and John Trangenstein},
Title = {On the Global Convergence of Broyden's Method},
Journal = {Mathematics of Computation, vol. 30, (1976), pp.
523-540},
Key = {fds9471}
}
%% Papers Published
@article{fds287423,
Author = {Trangenstein, JA and Kim, C},
Title = {Operator splitting and adaptive mesh refinement for the
Luo-Rudy I model},
Journal = {Journal of Computational Physics},
Volume = {196},
Number = {2},
Pages = {645-679},
Publisher = {Elsevier BV},
Year = {2004},
Month = {May},
ISSN = {0021-9991},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000221400700010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Abstract = {We apply second-order operator splitting to the Luo-Rudy I
model for electrical wave propagation in the heart. The
purpose of the operator splitting is to separate the
nonlinear but local reaction computations from the linear
but globally coupled diffusion computations. This approach
allows us to use local nonlinear iterations for the stiff
nonlinear reactions and to solve global linear systems for
the implicit treatment of diffusion. For computational
efficiency, we use dynamically adaptive mesh refinement
(AMR), involving hierarchies of unions of grid patches on
distinct levels of refinement. The linear system for the
discretization of the diffusion on the composite AMR grid is
formulated via standard conforming finite elements on unions
grid patches within a level of refinement and aligned mortar
elements along interfaces between levels of refinement. The
linear systems are solved iteratively by preconditioned
conjugate gradients. Our preconditioner uses multiplicative
domain decomposition between levels of refinement; the
smoother involves algebraic additive domain decomposition
between patches within a level of refinement, and
Gauss-Seidel iteration within grid patches. Numerical
results are presented in 1D and 2D, including spiral waves.
© 2003 Elsevier Inc. All rights reserved.},
Doi = {10.1016/j.jcp.2003.11.014},
Key = {fds287423}
}
@article{fds287424,
Author = {Trangenstein, JA},
Title = {Multi-scale iterative techniques and adaptive mesh
refinement for flow in porous media},
Journal = {Advances in Water Resources},
Volume = {25},
Number = {8-12},
Pages = {1175-1213},
Publisher = {Elsevier BV},
Year = {2002},
Month = {August},
ISSN = {0309-1708},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000180073300015&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Abstract = {Multi-component flow in porous media involves localized
phenomena that could be due to several features, such as
concentration fronts, wells or geometry of the media. Our
approach to treating the localized phenomena is to use
high-resolution discretization methods in combination with
adaptive mesh refinement (AMR). The purpose of AMR is to
concentrate the computational work near the regions of
interest in the flow. When properly designed, AMR can
significantly reduce the computational effort required to
obtain a desired level of accuracy in the simulation.
Necessarily, AMR requires appropriate techniques for
communication between length scales in a hierarchy. The
selection of appropriate scaling rules as well as
computationally efficient data structures is essential to
the success of the overall method. However, the emphasis
here is on the development of e.cient techniques for solving
linear systems that arise in the numerical discretization of
an elliptic equation for the incompressible pressure field.
In this paper, the combined AMR technique has been applied
to a two-component single-phase model for miscible flooding.
Numerical results are discussed in one-dimensional and
two-dimensional. © 2002 Elsevier Science Ltd. All rights
reserved.},
Doi = {10.1016/S0309-1708(02)00053-2},
Key = {fds287424}
}
@article{04068006912,
Author = {Trangenstein, John A. and Bi, Zhuoxin},
Title = {Multi-Scale Iterative Techniques and Adaptive Mesh
Refinement for Miscible Displacement Simulation},
Journal = {Proceedings - SPE Symposium on Improved Oil
Recovery},
Pages = {924 - 936},
Address = {Tulsa, OK, United States},
Year = {2002},
Keywords = {Petroleum reservoirs;Solubility;Object oriented
programming;Radioactive tracers;Aquifers;Vectors;Linear
systems;Computer simulation;},
Abstract = {Many enhanced oil recovery processes in reservoir
engineering involve localized phenomena that could be due to
several features, such as injection fronts, wells or
reservoir heterogeneity. In order to reach sufficient
accuracy in field-scale simulation, the localized phenomena
need to be resolved and modeled in appropriate
scale-dependent ways. Our approach to treating the localized
phenomena is to use high-resolution discretization methods
in combination with dynamically adaptive mesh refinement
(AMR). The purpose of adaptive mesh refinement is to
concentrate the computational work near the regions of
interest in the displacement processes, which may evolve
constantly in space. Adaptive mesh refinement requires
appropriate techniques for data communication in a hierarchy
of dynamically adaptive mesh. The selection of appropriate
scaling rules as well as computationally efficient data
structures is essential to the success of the overall
method. We have exploited the object-oriented features of
C++ for the AMR program structure and data management, while
numerically intensive routines are implemented in FORTRAN.
It turned out that adaptive mesh refinement can
significantly reduce the computational cost required to
obtain a desired level of accuracy in the simulation.
However, the emphasis here is on the development of
efficient techniques for solving linear systems that arise
in the numerical discretization of an elliptic equation for
the incompressible pressure field. We use a conjugate
gradient algorithm preconditioned by multiplicative domain
decomposition between refinement levels, in which additive
domain decomposition and incomplete Cholesky factorization
were employed as "smoothers". In this paper, the combined
adaptive mesh refinement technique has been applied to a
single-phase tracer transport model for miscible flooding.
Numerical results demonstrating the effectiveness of the
method are presented and discussed.},
Key = {04068006912}
}
@article{fds287425,
Author = {Bi, Z and Higdon, D and Lee, H and Trangenstein, J},
Title = {Upscaling Tensorial Permeability Fields Based on {G}Gaussian
Markov Random Field Models and the Hybrid Mixed Finite
Element Method},
Journal = {SPE Journal},
Year = {2002},
url = {http://www.math.duke.edu/~johnt/spepaper2002.ps},
Key = {fds287425}
}
@article{6216174,
Author = {Garaizar, FX and Trangenstein, J},
Title = {Adaptive mesh refinement and front-tracking for shear bands
in an antiplane shear model},
Journal = {SIAM J. Sci. Comput. (USA)},
Volume = {20},
Number = {2},
Pages = {750-779},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {1998},
url = {http://dx.doi.org/10.1137/S1064827597319271},
Keywords = {granular flow;granular materials;mesh generation;physics
computing;plastic deformation;tracking;},
Abstract = {We describe a numerical algorithm for the study of
shear-band formation and growth in a 2D antiplane shear of
granular materials. The algorithm combines front-tracking
techniques and adaptive mesh refinement. Tracking provides a
more careful evolution of the band when coupled with special
techniques to advance the ends of the shear band in the
presence of a loss of hyperbolicity. The adaptive mesh
refinement allows the computational effort to be
concentrated in important areas of the deformation, such as
the shear band and the elastic relief wave. The main
challenges are the problems related to shear bands that
extend across several grid patches and the effects that a
nonhyperbolic growth rate of the shear bands has in the
refinement process. We give examples of the success of the
algorithm for various levels of refinement},
Doi = {10.1137/S1064827597319271},
Key = {6216174}
}
@article{98013996894,
Author = {Miller, CT and Christakos, G and Imhoff, PT and McBride, JF and Pedit,
JA and Trangenstein, JA},
Title = {Multiphase flow and transport modeling in heterogeneous
porous media: Challenges and approaches},
Journal = {Advances in Water Resources},
Volume = {21},
Number = {2},
Pages = {77-120},
Publisher = {Elsevier BV},
Year = {1998},
ISSN = {0309-1708},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000071536500002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Keywords = {Porous materials;Pressure;Transport properties;Hydraulic
conductivity;Mass transfer;Random processes;Computational
methods;Mathematical models;Saturation (materials
composition);Phase interfaces;},
Abstract = {We review the current status of modeling multiphase systems,
including balance equation formulation, constitutive
relations for both pressure-saturation-conductivity and
interphase mass transfer, and stochastic and computational
issues. We discuss weaknesses and inconsistencies of current
approaches based on theoretical, computational, and
experimental evidence. Where possible, we suggest new or
evolving approaches.},
Doi = {10.1016/S0309-1708(96)00036-X},
Key = {98013996894}
}
@article{97113919459,
Author = {Hornung, RD and Trangenstein, JA},
Title = {Adaptive mesh refinement and multilevel iteration for flow
in porous media},
Journal = {Journal of Computational Physics},
Volume = {136},
Number = {2},
Pages = {522-545},
Publisher = {Elsevier BV},
Year = {1997},
Month = {September},
ISSN = {0021-9991},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1997XZ45000020&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Abstract = {An adaptive local mesh refinement algorithm originally
developed for unsteady gas dynamics by M. J. Berger is
extended to incompressible flow in porous media. Multilevel
iteration and domain decomposition methods are introduced to
accommodate the elliptic/parabolic aspects of the flow
equations. The algorithm is applied to a two-phase polymer
flooding model consisting of a system of nonlinear
hyperbolic mass conservation equations coupled to an
elliptic pressure equation. While the various numerical
methods used have been presented previously, our emphasis is
on their consistent combination within the adaptive mesh
refinement framework to treat important problems in porous
media flow. To achieve efficient, easily maintainable code,
we have exploited the features of object-oriented
programming for the overall program structure and data
management. Examples of algorithmic performance and
computational results are provided. © 1997 Academic
Press.},
Doi = {10.1006/jcph.1997.5779},
Key = {97113919459}
}
@article{97043606580,
Author = {Garaizar, FX and Trangenstein, J},
Title = {Front Tracking for Shear Bands in an Antiplane Shear
Model},
Journal = {Journal of Computational Physics},
Volume = {131},
Number = {1},
Pages = {54},
Publisher = {Elsevier BV},
Year = {1997},
url = {http://dx.doi.org/10.1006/jcph.1996.5456},
Doi = {10.1006/jcph.1996.5456},
Key = {97043606580}
}
@article{96083296598,
Author = {Khan Sameer and A and Pope Gary and A and Trangenstein John,
A},
Title = {Micellar/polymer physical-property models for contaminant
cleanup problems and enhanced oil recovery},
Journal = {Transport in Porous Media},
Volume = {24},
Number = {1},
Pages = {35-79},
Publisher = {Springer Nature},
Year = {1996},
ISSN = {0169-3913},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1996UZ43900002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Keywords = {Mathematical models;Micelles;Polymers;Flow of
fluids;Impurities;Enhanced recovery;Computer
simulation;Calculations;Surface active agents;},
Abstract = {Previous pseudo-phase representations of micellar/polymer
phase behavior have been highly successful in simulating
enhanced oil recovery processes using conventional numerical
methods. These models allowed for a variety of physical
phenomena, such as the formation of one to three phases, the
effect of salinity and co-solvents on the phase behavior,
adsorption of several of the chemical species, capillary
desaturation, and polymer shear thinning and permeability
reduction. In order to extend these models to either
higher-order simulation techniques or to contaminant
transport problems, it is necessary to remove previous
discontinuities in the model behavior and to improve the
predictions as concentrations become infinitesimal. In this
paper, we provide a complete description of a revised model
that avoids the problems of the previous model, and we show
how to implement the computations in a numerically stable
fashion. Computational results from a North Sea pilot study
are presented.},
Doi = {10.1007/BF00175603},
Key = {96083296598}
}
@article{5033123,
Author = {Trangenstein, JA},
Title = {Adaptive Mesh Refinement for Wave Propagation in Nonlinear
Solids},
Journal = {SIAM Journal on Scientific Computing},
Volume = {16},
Number = {4},
Pages = {819-839},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {1995},
Month = {July},
ISSN = {1064-8275},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1995RF58400004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Keywords = {equations of state;finite difference methods;fluid
dynamics;wave propagation;},
Abstract = {The adaptive mesh refinement algorithm for unsteady gas
dynamics is extended to nonlinear solids. Several
modifications to the original algorithm are forced by the
dissimilarities in the forms of the gas and solid equations
of state. The variety of forms of the solid constitutive
laws motivates the development of several abstractions that
are implemented through object-oriented programming.
Examples of the performance of the scheme are provided by
two numerical examples},
Doi = {10.1137/0916048},
Key = {5033123}
}
@article{95032624249,
Author = {Khan, S.A. and Trangenstein, J.A. and Horning, R.D. and Holing, Kent and Schilling, B.E.R.},
Title = {Application of adaptive mesh-refinement with a new
higher-order method in simulation of a north sea
micellar/polymer flood},
Journal = {Proceedings of the SPE Symposium on Reservoir
Simulation},
Pages = {531 - 543},
Address = {San Antonio, TX, USA},
Year = {1994},
Keywords = {Petroleum reservoir evaluation;Computational
methods;Micelles;Polymers;Finite difference
method;Costs;Surface active agents;Simulators;},
Abstract = {This paper demonstrates the application of a higher-order
Godunov method and adaptive mesh-refinement to a
three-phase, seven-component, micellar/polymer (MP) model
and use in the simulation of an MP flood designed for North
Sea conditions. Conventional one-point upstream weighting
with globally fine mesh is too expensive for obtaining a
reasonable level of accuracy for field-scale simulations.
The use of higher-order Godunov method with adaptive
mesh-refinement not only results in significant reduction in
computational times but also reveals more numerical details
of the displacement process due to higher-order accuracy.
Comparisons are also made between the first- and
second-order Godunov methods under field-scale design
conditions with and without adaptive mesh-refinement.},
Key = {95032624249}
}
@article{94041255724,
Author = {Trangenstein John and A},
Title = {Second-order Godunov algorithm for two-dimensional solid
mechanics},
Journal = {Computational Mechanics},
Volume = {13},
Number = {5},
Pages = {343-359},
Publisher = {Springer Nature},
Year = {1994},
url = {http://dx.doi.org/10.1007/BF00512588},
Keywords = {Solids;Mechanics;Wave transmission;Deformation;Equations of
motion;Convergence of numerical methods;Finite element
method;Approximation theory;Computational
complexity;Equations of state;},
Abstract = {The second-order Godunov method is extended to dynamic wave
propagation in two-dimensional solids undergoing nonlinear
finite deformation. It is shown that this explicit method is
linearly stable for timesteps satisfying the standard CFL
condition, does not support the development of hourglass
modes, and handles non-reflecting boundaries very naturally.
The computational cost is essentially one evaluation of the
kinetic equation of state per cell and timestep, the same as
explicit finite element methods employing reduced
quadrature.},
Doi = {10.1007/BF00512588},
Key = {94041255724}
}
@article{4294599,
Author = {Trangenstein, JA and Pember, RB},
Title = {Numerical algorithms for strong discontinuities in
elastic-plastic solids},
Journal = {Journal of Computational Physics},
Volume = {103},
Number = {1},
Pages = {63-89},
Publisher = {Elsevier BV},
Year = {1992},
Month = {January},
ISSN = {0021-9991},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1992JV66900004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Keywords = {elastic waves;elastoplasticity;numerical
analysis;},
Abstract = {In this paper the implementation of second-order Godunov
methods for dynamic wave propagation in one-dimensional
elastic-plastic solids is investigated. First, the
Lagrangian form of the algorithm is reviewed, and then the
algorithm is extended to the Eulerian frame of reference.
This extension requires additional evolution equations to
handle the history of the material along particle paths.
Both the Lagrangian and Eulerian versions of the algorithm
require appropriately accurate approximations to the
solution of Riemann problems, in order to represent the
interaction of waves at cell boundaries. Two inexpensive
approximations to the solution of the Riemann problem are
constructed, and the resulting algorithms are tested against
the analytic solution of the Riemann problem for
longitudinal motion in an elastic-plastic bar. These
approximations to the Riemann problem are shown to work
well, even for strong discontinuities. Finally, the
numerical experience gained from the simple longitudinal bar
problem is used to design an algorithm for strong shocks
predicted by a realistic soil model. © 1992.},
Doi = {10.1016/0021-9991(92)90326-T},
Key = {4294599}
}
@article{92121461002,
Author = {Trangenstein, J.A.},
Title = {Analysis of a model and sequential numerical method for
thermal reservoir simulation},
Journal = {Proceedings of the Conference on the Mathematics of Oil
Recovery},
Pages = {359 -},
Address = {Cambridge, Engl},
Year = {1992},
Key = {92121461002}
}
@article{3865816,
Author = {Trangenstein, JA and Pember, RB},
Title = {The Riemann Problem for Longitudinal Motion in an
Elastic-Plastic Bar},
Journal = {SIAM Journal on Scientific and Statistical
Computing},
Volume = {12},
Number = {1},
Pages = {180-207},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {1991},
Month = {January},
ISSN = {0196-5204},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1991EW35600010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Keywords = {elasticity;elastoplasticity;},
Abstract = {The analytical solution to the Riemann problem for the
Antman-Szymczak model of longitudinal motion in an
elastic-plastic bar is constructed. The model involves two
surfaces corresponding to plastic yield in tension and
compression, and exhibits the appropriate limiting behavior
for total compressions. The solution of the Riemann problem
involves discontinuous changes in characteristic speeds due
to transitions from elastic to plastic response.
Illustrations are presented, in both state-space and
self-similar coordinates, of the variety of possible
solutions to the Riemann problem for possible use with
numerical algorithms},
Doi = {10.1137/0912010},
Key = {3865816}
}
@article{3704156,
Author = {Trangenstein, JA},
Title = {A second-order algorithm for the dynamic response of
soils},
Journal = {IMPACT of Computing in Science and Engineering},
Volume = {2},
Number = {1},
Pages = {1-39},
Publisher = {Elsevier BV},
Year = {1990},
Month = {January},
url = {http://dx.doi.org/10.1016/0899-8248(90)90002-R},
Keywords = {civil engineering computing;deformation;differential
equations;geophysics computing;soil;},
Abstract = {In this paper we describe a formally second-order algorithm
for the dynamic response of one-dimensional soils and rock.
There are two kinds of equations describing the motion of
the material: the partial differential equations expressing
conservation of momentum, and the kinetic equation of state
relating the stress to the deformation. The stress-rate
equations for the kinetic equation of state are formulated
as a constrained system of ordinary differential equations
and are integrated implicitly in time, both for stability
and for satisfaction of the yield constraints. The equations
of motion are formulated as a first-order system of
hyperbolic conservation laws and integrated explicitly by
means of a second-order version of Godunov's method. Because
the motion can develop both smooth waves and shocks, special
care has been taken to design a numerical method that is
second-order in smooth waves and yet reduces to a stable
low-order method near discontinuities. We present numerical
results for both the integration of the equation of state
and the equations of motion, in order to demonstrate the
features of the method. © 1990.},
Doi = {10.1016/0899-8248(90)90002-R},
Key = {3704156}
}
@article{3834403,
Author = {Glass, I.I. and Kaca, J. and Zhang, D.L. and Glaz, H.M. and Bell, J.B. and Trangenstein, J.A. and Collins,
J.P.},
Title = {Diffraction of planar shock waves over half-diamond and
semicircular cylinders: an experimental and numerical
comparison},
Journal = {AIP Conf. Proc. (USA)},
Number = {208},
Pages = {246 - 51},
Address = {Bethlehem, PA, USA},
Year = {1990},
Keywords = {diffraction;electromagnetic wave interferometry;shock
waves;},
Abstract = {The problem of an incident planar shock interacting with a
downstream obstacle is studied; half-diamond and
semicircular cylinders are chosen for the obstacles.
Experimental data is taken from the UTIAS shock tube
facility; in particular; infinite-fringe interferograms are
analyzed which provides full flowfield data. Numerical
results are obtained using a new unsplit version of the
second-order Eulerian Godunov scheme for inviscid gas
dynamics which is capable of computing on general, body
conforming meshes. Detailed comparisons of the two
techniques are offered, and excellent agreement is
confirmed},
Key = {3834403}
}
@article{3547392,
Author = {Trangenstein, JA and Bell, JB},
Title = {Mathematical Structure of Compositional Reservoir
Simulation},
Journal = {SIAM Journal on Scientific and Statistical
Computing},
Volume = {10},
Number = {5},
Pages = {817-845},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {1989},
Month = {September},
ISSN = {0196-5204},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1989AM02600001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Keywords = {chemical technology;numerical methods;petroleum
industry;two-phase flow;},
Abstract = {Multicomponent two-phase isothermal fluid flow in petroleum
reservoirs is described. The fluid-flow model consists of
component conservation equations. Darcy's law for the
volumetric flow rates, balance between the fluid volume and
the rock void, and the conditions of thermodynamic
equilibrium that determine the distribution of the chemical
components into phases. Thermodynamic equilibrium is
described by means of a mathematical model for the chemical
potentials of each component in each phase of the fluid. The
flow equations are manipulated to form a pressure equation
and a modified component-conservation equation: these form
the basis for the sequential method. It is shown that the
pressure equation is parabolic under reasonable assumptions
on the thermodynamic equilibrium model, and that the
component-conservation equations are hyperbolic in the
absence of diffusive forces such as capillary pressure and
mixing. A numerical method based on the sequential
formulation of the flow equations is outlined and used to
illustrate the kinds of flow behavior that occur during
miscible gas injection},
Doi = {10.1137/0910049},
Key = {3547392}
}
@article{88040048974,
Author = {Trangenstein, JA},
Title = {Customized minimization techniques for phase equilibrium
computations in reservoir simulation},
Journal = {Chemical Engineering Science},
Volume = {42},
Number = {12},
Pages = {2847-2863},
Publisher = {Elsevier BV},
Year = {1987},
Month = {January},
ISSN = {0009-2509},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1987L461100004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Keywords = {COMPUTER PROGRAMMING - Algorithms;FLOW OF FLUIDS - Computer
Simulation;OIL WELL PRODUCTION - Enhanced
Recovery;},
Abstract = {This paper discusses a minimization algorithm for the
solution of the Gibbs free energy minimization problem
involving at most two phases. There are three major aspects
to this paper. The first is the selection of descent
directions and step lengths in order to handle the poorly
scaled phase equilibrium problems associated with mixtures
near bubble points and critical points. The second is the
prevention of convergence to trivial solutions in both the
Gibbs free energy minimization problem for two-phase
mixtures and the associated phase stability test for
single-phase mixtures. The third is the use of effective
convergence criteria to obtain either the desired level of
accuracy in the solution or the maximum accuracy allowed by
the problem and the computer. © 1987.},
Doi = {10.1016/0009-2509(87)87051-3},
Key = {88040048974}
}
@article{87050080444,
Author = {Subramanian, G and Trangenstein, JA and Mochizuki, S and Shen,
EIC},
Title = {EFFICIENT FLUID BEHAVIOR COMPUTATIONS IN A SEQUENTIAL
COMPOSITIONAL RESERVOIR SIMULATOR.},
Journal = {Society of Petroleum Engineers of AIME, (Paper)
SPE},
Pages = {321-327},
Address = {San Antonio, TX, USA},
Year = {1987},
Keywords = {OIL WELLS;OIL WELL PRODUCTION;FLOW OF FLUIDS -
Multiphase;},
Abstract = {A compositional reservoir simulator using a sequential
formulation of the fluid flow and phase equilibrium
equations requires that the phase equilibrium and associated
derivatives of the dependent phase equilibrium variables
with respect to the pressure and moles of individual
components be computed every time step for all the grid
blocks in the system. The phase equilibrium calculations are
computation intensive, since they solve a nonlinear system
of equations and are thus iterative in nature. This paper
describes techniques for implementing the phase equilibrium
and the associated derivative calculations in a sequential
compositional reservoir simulator designed for large
reservoir models.},
Key = {87050080444}
}
@article{87020024439,
Author = {Bell, JB and Trangenstein, JA and Shubin, GR},
Title = {Conservation Laws of Mixed Type Describing Three-Phase Flow
in Porous Media},
Journal = {SIAM Journal on Applied Mathematics},
Volume = {46},
Number = {6},
Pages = {1000-1017},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {1986},
Month = {December},
ISSN = {0036-1399},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1986F083900004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Keywords = {MATHEMATICAL TECHNIQUES;PETROLEUM RESERVOIR ENGINEERING -
Computer Simulation;},
Abstract = {In this paper we examine the mathematical structure of a
model for three-phase, incompressible flow in a porous
medium. We show that, in the absence of diffusive forces,
the system of conservation laws describing the flow is not
necessarily hyperbolic. We present an example in which there
is an elliptic region in saturation space for reasonable
relative permeability data. A linearized analysis shows that
in nonhyperbolic regions solutions grow exponentially.
However, the nonhyperbolic region, if present, will be of
limited extent which inherently limits the exponential
growth. To examine these nonlinear effects we resort to fine
grid numerical experiments with a suitably dissipative
numerical method. These experiments indicate that the
solutions of Riemann problems remain well behaved in spite
of the presence of a linearly unstable elliptic region in
saturation space. These results are relevant to modeling
fluid flow in petroleum reservoirs.},
Doi = {10.1137/0146059},
Key = {87020024439}
}
@article{85110169321,
Author = {Trangenstein John and A},
Title = {MINIMIZATION OF GIBBS FREE ENERGY IN COMPOSITIONAL RESERVOIR
SIMULATION.},
Journal = {Society of Petroleum Engineers of AIME, (Paper)
SPE},
Pages = {233-246},
Address = {Dallas, TX, USA},
Year = {1985},
Keywords = {FLOW OF FLUIDS - Two Phase;MATHEMATICAL TECHNIQUES - Phase
Space Methods;},
Abstract = {This paper describes the formulation of vapor-liquid phase
equilibrium as a linearly constrained minimization problem.
It also describes a second minimization problem designed to
test for local phase stability. Vectorized unconstrained
minimization techniques can be used to solve this pair of
constrained minimization problems. The methods of this paper
are applied to liquid-vapor equilibria for mixtures both far
from and near to the phase boundary. Significant
improvements over the standard successive substitution
algorithm are demonstrated.},
Key = {85110169321}
}
@article{83020003109,
Author = {TRANGENSTEIN, J. A. and READ, H. E.},
Title = {INELASTIC RESPONSE CHARACTERISTICS OF THE NEW ENDOCHRONIC
THEORY WITH SINGULAR KERNEL.},
Volume = {18},
Number = {11},
Pages = {947 - 956},
Year = {1982},
Keywords = {STRESSES - ANALYSIS;},
Abstract = {THE CONSTITUTIVE RESPONSE PREDICTED BY THE NEW ENDOCHRONIC
THEORY WITH SINGULAR KERNEL FOR NON-PROPORTIONAL LOADING
INVOLVING AN ABRUPT CHANGE IN THE LOADING DIRECTION IN
STRESS SPACE IS INVESTIGATED ANALYTICALLY. FOR SUCH LOADING,
THE RESPONSE IS DETERMINED, AS A FUNCTION OF THE ANGLE
BETWEEN THE ORIGINAL AND THE REVISED LOADING DIRECTIONS, FOR
INFINITESIMAL LOADING INCREMENTS IN THE REVISED DIRECTION.
IT IS SHOWN THAT THE NEW ENDOCHRONIC THEORY DIFFERS IN
IMPORTANT AND FUNDAMENTAL WAYS FROM CLASSICAL PLASTICITY
WITH HARDENING. FOR INFINITESIMAL DEFORMATIONS, THE TWO
THEORIES EXHIBIT SIMILARRESPONSE CHARACTERISTICS ONLY UNDER
VERY SPECIALIZED CONDITIONS. FOR FINITE DEFORMATIONS, THE
NEW ENDOCHRONIC THEORY LEADS TO PLASTIC FLOW FOR ALL LOADING
DIRECTIONS, WHILE THE TYPE OF RESPONSE PREDICTED BY
CLASSICAL PLASTICITY THEORY DEPENDS UPON THE DIRECTION OF
LOADING.},
Key = {83020003109}
}
@article{1158810,
Author = {Trangenstein, JA},
Title = {A Finite Element Method for the Tricomi Problem in the
Elliptic Region},
Journal = {SIAM Journal on Numerical Analysis},
Volume = {14},
Number = {6},
Pages = {1066-1077},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {1977},
Month = {December},
ISSN = {0036-1429},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1977EC70900009&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Keywords = {finite element analysis;},
Abstract = {The Tricomi problem is divided into an elliptic problem,
involving a nonlocal boundary condition on a line of
parabolic degeneracy, and a hyperbolic problem. The author
converts the elliptic problem into an equivalent variational
form, shows it to be well-posed, and applies the finite
element method. Error estimates in weighted Sobolev spaces
are proved},
Doi = {10.1137/0714073},
Key = {1158810}
}
@article{972653,
Author = {More, JJ and Trangenstein, JA},
Title = {On the global convergence of Broyden's method},
Journal = {Math. Comput. (USA)},
Volume = {30},
Number = {135},
Pages = {523-540},
Publisher = {American Mathematical Society (AMS)},
Year = {1976},
url = {http://dx.doi.org/10.1090/S0025-5718-1976-0418451-2},
Keywords = {convergence of numerical methods;nonlinear
equations;},
Abstract = {Considers Broyden's 1965 method for solving nonlinear
equations. If the mapping is linear, then a simple
modification of this method guarantees global and
Q-superlinear convergence. For nonlinear mappings it is
shown that the hybrid strategy for nonlinear equations due
to Powell leads to R-superlinear convergence provided the
search directions form a uniformly linearly independent
sequence. The authors then explore this last concept and its
connection with Broyden's method. Finally, the authors point
out how the above results extend to Powell's symmetric
version of Broyden's method},
Doi = {10.1090/S0025-5718-1976-0418451-2},
Key = {972653}
}
%% Preprints
@article{fds10153,
Author = {John Trangenstein and Zhuoxin Bi},
Title = {Multi_Scale Iterative Techniques and Adaptive Mesh
Refinement for Miscible Displacement Simulation},
url = {http://www.math.duke.edu/~johnt/spe75232.ps},
Abstract = {Accepted for presentation at SPE spring meeting,
2002},
Key = {fds10153}
}
@article{fds9028,
Author = {Bill Allard and John Trangenstein},
Title = {On the Performance of a Distributed Object Oriented Adaptive
Mesh Refinement Code},
Key = {fds9028}
}
|
