摘要
This article describes developing and improving sixth-order characteristicwise Weighted Essentially Non-Oscillatory(WENO)finite difference schemes.These schemes are specially designed to solve scalar and system hyperbolic conservation laws with high accuracy/resolution and robustness.The schemes have been enhanced by using a new reference global smoothness indicator,which ensures the optimal order of accuracy for smooth solutions.The schemes also incorporate affine-invariant nonlinear Ai-weights that are independent of the scaling of solution and the choice of sensitivity parameter.The improved nonlinear weights enhance the essentially nonoscillatory(ENO)capturing of discontinuities and minimize the numerical dissipation,especially for long-time simulations.The study also introduces the positivitypreserving limiter to ensure that the numerical solution of Euler equations is physically valid.The effectiveness of improved schemes is demonstrated through one-and twodimensional benchmark shock-tube problems,such as the Sod,Lax,and Woodward-Colella problems.The improved schemes are compared with other WENO schemes in terms of accuracy,resolution,ENO,and robustness.
基金
support provided for this research by the National Natural Science Foundation of China(No.12301530)
the China Postdoctoral Science Foundation(No.2023M733348)
the Shandong Provincial Natural Science Foundation(No.ZR2022MA012).
