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

TL;DR

This paper introduces a high-order WENO-based kinetic scheme for entropy-based moment models of linear kinetic equations, ensuring realizability and stability while demonstrating improved accuracy on benchmark problems.

Contribution

The paper presents a novel high-order WENO reconstruction scheme combined with a realizability-preserving time integrator for entropy-based moment models.

Findings

Scheme achieves expected convergence order on manufactured solutions.

High-order solutions demonstrate advantages on benchmark problems.

The kinetic-level limiter effectively dampens spurious oscillations.

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, and 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 converges of the expected order up to the numerical noise from the numerical optimization, 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.