Spatial-Temporal Adaptive-Order Positivity-Preserving WENO Finite Difference Scheme with Relaxed CFL Condition for Euler Equations with Extreme Conditions

Jia-Le Li; Wai-Sun Don; Cai-Feng Wang; Bao-Shan Wang

doi:10.4208/aamm.OA-2023-0306

Spatial-Temporal Adaptive-Order Positivity-Preserving WENO Finite Difference Scheme with Relaxed CFL Condition for Euler Equations with Extreme Conditions

Authors

Jia-Le Li
Wai-Sun Don
Cai-Feng Wang
Bao-Shan Wang

DOI:

https://doi.org/10.4208/aamm.OA-2023-0306

Keywords:

Adaptive-CFL and adaptive-order method, positivity-preserving, relaxed CFL condition, WENO, extreme problems.

Abstract

In extreme scenarios, classical high-order WENO schemes may result in non-physical states. The Positivity-Preserving Limiter (PP-Limiter) is often used to ensure positivity if CFL≤0.5 with a third-order TVD Runge-Kunta (RK3) scheme. This study proposes two novel conservative WENO-Z methods: AT-PP and AO-PP to improve efficiency with 0.5