A realizability-preserving high-order kinetic scheme using WENO reconstruction for entropy-based moment closures of linear kinetic equations in slab geometry

Florian  Schneider; Jochen  Kall; Graham  Alldredge

doi:10.3934/krm.2016.9.193

Article Contents

2016, Volume 9, Issue 1: 193-215. Doi: 10.3934/krm.2016.9.193

This issue Previous Article Global existence and semiclassical limit for quantum hydrodynamic equations with viscosity and heat conduction Next Article A random cloud model for the Wigner equation

A realizability-preserving high-order kinetic scheme using WENO reconstruction for entropy-based moment closures of linear kinetic equations in slab geometry

1.
Fachbereich Mathematik, TU Kaiserslautern, Erwin-Schrödinger-Str, 67663 Kaiserslautern
2.
Department of Mathematics, RWTH Aachen University, Schinkelstr. 2, 52062 Aachen

Received: December 31, 2014

Revised: May 31, 2015

Published: February 2016

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Abstract

We develop a high-order kinetic scheme for entropy-based moment models of a one-dimensional linear kinetic equation in slab geometry. High-order spatial reconstructions are achieved using the weighted essentially non-oscillatory (WENO) method. For time integration we use multi-step Runge-Kutta methods which are strong stability preserving and whose stages and steps can be written as convex combinations of forward Euler steps. We show that the moment vectors stay in the realizable set using these time integrators along with a maximum principle-based kinetic-level limiter, which simultaneously dampens spurious oscillations in the numerical solutions. We present numerical results both on a manufactured solution, where we perform convergence tests showing our scheme has the expected order up to the numerical noise from the optimization routine, as well as on two standard benchmark problems, where we show some of the advantages of high-order solutions and the role of the key parameter in the limiter.

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Mathematics Subject Classification: Primary: 35L40, 35Q84, 65M08, 65M70; Secondary: 65K10, 49M15.

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