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(R...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<CFL<1 if desired.The AT-PP method detects negative cells after each RK3 stage posteriori and computes a new solution with the PPLimiter(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 positivitypreserving with CFL<1,only at negative cells at that RK3 stage.A single numerical flux enforces conservation at neighboring interfaces.Extensive 1D and 2D shocktube problems were conducted to illustrate the performance of AT-PP and AO-PP with 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.展开更多
基金support provided by the National Natural Science Foundation of China(No.12301530)China Postdoctoral Science Foundation(No.2023M733348)for this research+1 种基金support provided by the Shandong Provincial Natural Science Foundation(No.ZR2022MA012)Hong Kong Research Grant Council GRF Grant.
文摘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<CFL<1 if desired.The AT-PP method detects negative cells after each RK3 stage posteriori and computes a new solution with the PPLimiter(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 positivitypreserving with CFL<1,only at negative cells at that RK3 stage.A single numerical flux enforces conservation at neighboring interfaces.Extensive 1D and 2D shocktube problems were conducted to illustrate the performance of AT-PP and AO-PP with 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.
