An Admissible Asymptotic-Preserving Numerical Scheme for the Electronic M1 Model in the Diffusive Limit

2018 ◽  
Vol 24 (5) ◽  
Author(s):  
Sebastien Guisset ◽  
Stephane Brull ◽  
Bruno Dubroca ◽  
Rodolphe Turpault
Keyword(s):  
Numerical Scheme ◽  
Asymptotic Preserving ◽  
Diffusive Limit

scholarly journals Asymptotic-preserving well-balanced scheme for the electronic M1 model in the diffusive limit: Particular cases

2017 ◽  
Vol 51 (5) ◽  
pp. 1805-1826 ◽  
Author(s):  
Sébastien Guisset ◽  
Stéphane Brull ◽  
Emmanuel D’Humières ◽  
Bruno Dubroca
Keyword(s):  
Diffusion Equation ◽  
Integral Form ◽  
Riemann Solver ◽  
Homogeneous Case ◽  
Asymptotic Preserving ◽  
Approximate Riemann Solver ◽  
Numerical Tests ◽  
Diffusive Regime ◽  
Diffusive Limit ◽  
Asymptotic Preserving Scheme

This work is devoted to the derivation of an asymptotic-preserving scheme for the electronic M1 model in the diffusive regime. The case without electric field and the homogeneous case are studied. The derivation of the scheme is based on an approximate Riemann solver where the intermediate states are chosen consistent with the integral form of the approximate Riemann solver. This choice can be modified to enable the derivation of a numerical scheme which also satisfies the admissible conditions and is well-suited for capturing steady states. Moreover, it enjoys asymptotic-preserving properties and handles the diffusive limit recovering the correct diffusion equation. Numerical tests cases are presented, in each case, the asymptotic-preserving scheme is compared to the classical HLL [A. Harten, P.D. Lax and B. Van Leer, SIAM Rev. 25 (1983) 35–61.] scheme usually used for the electronic M1 model. It is shown that the new scheme gives comparable results with respect to the HLL scheme in the classical regime. On the contrary, in the diffusive regime, the asymptotic-preserving scheme coincides with the expected diffusion equation, while the HLL scheme suffers from a severe lack of accuracy because of its unphysical numerical viscosity.

scholarly journals Asymptotic preserving discretization of a Jin–Xin model with implicit equilibrium manifold on a bounded domain

2019 ◽  
Vol 40 (1) ◽  
pp. 530-562
Author(s):  
Nicolas Seguin ◽  
Magali Tournus
Keyword(s):  
Linear System ◽  
Boundary Conditions ◽  
Bounded Domain ◽  
Numerical Scheme ◽  
Asymptotic Limit ◽  
Implicit Function ◽  
Asymptotic Preserving ◽  
Equilibrium Manifold

Abstract In this paper, we design and analyze a numerical scheme that approximates a Jin–Xin linear system with implicit equilibrium on a bounded domain. This scheme relaxes toward the asymptotic limit of the linear system. The main properties of the limiting scheme are that it does not require to invert the implicit function defining the manifold and that it provides an accurate discretization of the boundary conditions.

Asymptotic-Preserving Scheme for the M1-Maxwell System in the Quasi-Neutral Regime

2016 ◽  
Vol 19 (2) ◽  
pp. 301-328 ◽  
Author(s):  
S. Guisset ◽  
S. Brull ◽  
B. Dubroca ◽  
E. d'Humières ◽  
S. Karpov ◽  
...  
Keyword(s):  
Numerical Scheme ◽  
Numerical Test ◽  
Test Cases ◽  
Maxwell System ◽  
Asymptotic Preserving ◽  
Numerical Resolution ◽  
Moment Models ◽  
Asymptotic Preserving Scheme ◽  
The Stability ◽  
Limit Models

AbstractThis work deals with the numerical resolution of the M1-Maxwell system in the quasi-neutral regime. In this regime the stiffness of the stability constraints of classical schemes causes huge calculation times. That is why we introduce a new stable numerical scheme consistent with the transitional and limit models. Such schemes are called Asymptotic-Preserving (AP) schemes in literature. This new scheme is able to handle the quasi-neutrality limit regime without any restrictions on time and space steps. This approach can be easily applied to angular moment models by using a moments extraction. Finally, two physically relevant numerical test cases are presented for the Asymptotic-Preserving scheme in different regimes. The first one corresponds to a regime where electromagnetic effects are predominant. The second one on the contrary shows the efficiency of the Asymptotic-Preserving scheme in the quasi-neutral regime. In the latter case the illustrative simulations are compared with kinetic and hydrodynamic numerical results.

NUMERICAL SCHEME OF THE WAHA CODE

2008 ◽  
Vol 20 (3-4) ◽  
pp. 323-354 ◽  
Author(s):  
Iztok Tiselj ◽  
A. Horvat ◽  
J. Gale
Keyword(s):  
Numerical Scheme
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