Spatial-Temporal Adaptive-Order Positivity-Preserving WENO Finite Difference Scheme with Relaxed CFL Condition for Euler Equations with Extreme Conditions: Spatial-temporal adaptive-order positivity-preserving WENO finite difference scheme with relaxed CFL condition for Euler equations with extreme conditions
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| Titel: | Spatial-Temporal Adaptive-Order Positivity-Preserving WENO Finite Difference Scheme with Relaxed CFL Condition for Euler Equations with Extreme Conditions: Spatial-temporal adaptive-order positivity-preserving WENO finite difference scheme with relaxed CFL condition for Euler equations with extreme conditions |
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| Autoren: | Li, Jia-Le, Don, Wai-Sun, Wang, Cai-Feng, Wang, Bao-Shan |
| Quelle: | Advances in Applied Mathematics and Mechanics. 17:804-839 |
| Verlagsinformationen: | Global Science Press, 2025. |
| Publikationsjahr: | 2025 |
| Schlagwörter: | relaxed CFL condition, WENO, Hyperbolic equations on manifolds, Hyperbolic conservation laws, Finite difference methods for initial value and initial-boundary value problems involving PDEs, positivity-preserving, adaptive-CFL and adaptive-order method, extreme problems |
| Beschreibung: | Summary: 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 \(\mathrm{CFL} \leq 0.5\) 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 \(0.5 < \mathrm{CFL} < 1\) if desired. The AT-PP method detects negative cells after each RK3 stage posteriori and computes a new solution with the PP-Limiter (\(\mathrm{CFL} < 0.5\)) for that step. The AO-PP method progressively lowers the WENO operator's order and terminates with the first-order HLLC solver, proven positivity-preserving with \(\mathrm{CFL} < 1\), only at negative cells at that RK3 stage. A single numerical flux enforces conservation at neighboring interfaces. Extensive 1D and 2D shock-tube problems were conducted to illustrate the performance of AT-PP and AO-PP with \(\mathrm{CFL} = 0.9\). Both methods outperformed the classical PP-Limiter in accuracy and resolution, while AO-PP performed better computationally in some cases. The AO-PP method is globally conservative and accurate, adaptiveness, and robustness while resolving fine-scale structures in smooth regions, capturing strong shocks and gradients with ENO-property, improving computational efficiency, and preserving the positivity, all without imposing a restrictive limit on the CFL condition. |
| Publikationsart: | Article |
| Dateibeschreibung: | application/xml |
| ISSN: | 2075-1354 2070-0733 |
| DOI: | 10.4208/aamm.oa-2023-0306 |
| Zugangs-URL: | https://zbmath.org/8033903 https://doi.org/10.4208/aamm.oa-2023-0306 |
| Dokumentencode: | edsair.doi.dedup.....2ae63dd473e08d173f5adfa064d0f484 |
| Datenbank: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstract: | Summary: 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 \(\mathrm{CFL} \leq 0.5\) 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 \(0.5 < \mathrm{CFL} < 1\) if desired. The AT-PP method detects negative cells after each RK3 stage posteriori and computes a new solution with the PP-Limiter (\(\mathrm{CFL} < 0.5\)) for that step. The AO-PP method progressively lowers the WENO operator's order and terminates with the first-order HLLC solver, proven positivity-preserving with \(\mathrm{CFL} < 1\), only at negative cells at that RK3 stage. A single numerical flux enforces conservation at neighboring interfaces. Extensive 1D and 2D shock-tube problems were conducted to illustrate the performance of AT-PP and AO-PP with \(\mathrm{CFL} = 0.9\). Both methods outperformed the classical PP-Limiter in accuracy and resolution, while AO-PP performed better computationally in some cases. The AO-PP method is globally conservative and accurate, adaptiveness, and robustness while resolving fine-scale structures in smooth regions, capturing strong shocks and gradients with ENO-property, improving computational efficiency, and preserving the positivity, all without imposing a restrictive limit on the CFL condition. |
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| ISSN: | 20751354 20700733 |
| DOI: | 10.4208/aamm.oa-2023-0306 |