Math @ Duke

Publications [#246947] of JianGuo Liu
Papers Published
 Degond, P; Jin, S; Liu, JG, Machnumber uniform asymptotic preserving Gauge schemes for compressible flows,
Bulletin of the Institute of Mathematics Academia Sinica (New Series), vol. 2
(2007),
pp. 851892
(last updated on 2019/02/20)
Abstract: We present novel algorithms for compressible flows that are
efficient for all Mach numbers. The approach is based on several
ingredients: semiimplicit schemes, the gauge decomposition of the
velocity field and a second order formulation of the density
equation (in the isentropic case) and of the energy equation (in the
full NavierStokes case). Additionally, we show that our approach
corresponds to a micromacro decomposition of the model, where the
macro field corresponds to the incompressible component satisfying a
perturbed low Mach number limit equation and the micro field is the
potential component of the velocity. Finally, we also use the
conservative variables in order to obtain a proper conservative
formulation of the equations when the Mach number is order unity. We
successively consider the isentropic case, the full NavierStokes
case, and the isentropic NavierStokesPoisson case. In this work,
we only concentrate on the question of the time discretization and
show that the proposed method leads to Asymptotic Preserving
schemes for compressible flows in the low Mach number limit.
Keywords: Mach number uniform method • Euler equations • NavierStokes equations • Asymptotic Preserving schemes • gauge schemes • compressible fluids • LowMach number limit • macromicro decomposition • semiimplicit scheme • EulerPoisson system • NavierStokesPoisson system


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