Math @ Duke

Publications [#243616] of Anita T. Layton
Papers Published
 Li, Y; Sgouralis, I; Layton, AT, Computing viscous flow in an elastic tube,
Numerical Mathematics: Theory, Methods and Applications (NMTMA), vol. 7 no. 4
(2014),
pp. 555574, ISSN 10048979 [doi]
(last updated on 2018/10/14)
Abstract: ©2014 GlobalScience Press. We have developed a numerical method for simulating viscous flow through a compliant closed tube, driven by a pair of fluid source and sink. As is natural for tubular flow simulations, the problem is formulated in axisymmetric cylindrical coordinates, with fluid flow described by the NavierStokes equations. Because the tubular walls are assumed to be elastic, when stretched or compressed they exert forces on the fluid. Since these forces are singularly supported along the boundaries, the fluid velocity and pressure fields become unsmooth. To accurately compute the solution, we use the velocity decomposition approach, according to which pressure and velocity are decomposed into a singular part and a remainder part. The singular part satisfies the Stokes equations with singular boundary forces. Because the Stokes solution is unsmooth, it is computed to secondorder accuracy using the immersed interface method, which incorporates known jump discontinuities in the solution and derivatives into the finite difference stencils. The remainder part, which satisfies the NavierStokes equations with a continuous body force, is regular. The equations describing the remainder part are discretized in time using the semiLagrangian approach, and then solved using a pressurefree projection method. Numerical results indicate that the computed overall solution is secondorder accurate in space, and the velocity is secondorder accurate in time.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

