2007 / December Volume 2 No.4
Mach-number uniform asymptotic-preserving gauge schemes for compressible flows
| Published Date |
2007 / December
|
|---|---|
| Title | Mach-number uniform asymptotic-preserving gauge schemes for compressible flows |
| Author | |
| Keyword |
Mach number uniform methord, Euler equations, Navier-Stokes equations, Asymptotic Preserving schemes, gauge schemes, compressible fluids, Low-Mach number limit, macro-micro decomposition, semi-implicit scheme, Euler-Poisson system, Mach number uniform method, Euler equations, Navier-Stokes equations, Asymptotic Preserving schemes, gauge schemes, compressible fluids, Low-Mach number limit, macro-micro decomposition, semi-implicit scheme, Euler-Poisson system, Navier-Stokes-Poisson system
|
| Download | |
| Pagination | 851-892 |
| Abstract | We present novel algorithms for compressible flows that are efficient for all Mach numbers. The approach is based on several
ingredients: semi-implicit 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 Navier-Stokes case). Additionally, we show that our approach
corresponds to a micro-macro 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 Navier-Stokes case, and the isentropic Navier-Stokes-Poisson
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.
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| AMS Subject Classification |
65N22, 76N15, 76R10, 76X05
|
| Received |
2007-07-13
|