Positivity-preserving finite difference WENO scheme for Ten-Moment equations with source term

TL;DR

This paper introduces a high-order finite difference WENO scheme that preserves positivity for Ten-Moment equations with source terms, combining operator splitting, an integrating factor, and adaptive CFL strategies.

Contribution

It presents a novel positivity-preserving approach compatible with various WENO schemes, enhancing stability and efficiency in solving Ten-Moment equations with source terms.

Findings

Achieves high-order accuracy while preserving positivity.

Demonstrates effectiveness with multiple WENO schemes.

Develops an adaptive CFL strategy for improved efficiency.

Abstract

We develop a positivity-preserving finite difference WENO scheme for the Ten-Moment equations with body forces acting as a source in the momentum and energy equations. A positive forward Euler scheme under a CFL condition is first constructed which is combined with an operator splitting approach together with an integrating factor, strong stability preserving Runge-Kutta scheme. The positivity of the forward Euler scheme is obtained under a CFL condition by using a scaling type limiter, while the solution of the source operator is performed exactly and is positive without any restriction on the time step. The proposed method can be used with any WENO reconstruction scheme and we demonstrate it with fifth order accurate WENO-JS, WENO-Z and WENO-AO schemes. An adaptive CFL strategy is developed which can be more efficient than the use of reduced CFL for positivity preservation. Numerical results show that high order accuracy and positivity preservation are achieved on a range of test problems.