A Scale-Invariant Fifth Order WCNS Scheme for Hyperbolic Conservation Laws  

作　　者：Zixuan Zhang Yidao Dong Huaibao Zhang Shichao Zheng Xiaogang Deng 

机构地区：[1]College of Aerospace Science and Engineering,National University of Defense Technology,Changsha,Hunan 410073,China [2]School of Physics,Sun Yat-sen University,Guangzhou,Guangdong 510275,China [3]Institute of Systems Engineering,Chinese Academy of Military Science,Beijing 100071,China

出　　处：《Advances in Applied Mathematics and Mechanics》2023年第5期1256-1289,共34页应用数学与力学进展（英文）

基　　金：supported by the Hunan Provincial Natural Science Foundation of China(No.2022JJ40539);National Natural Science Foundation of China(No.11972370);National Key Project(No.GJXM92579).

摘　　要：In this article,a robust,effective,and scale-invariant weighted compact nonlinear scheme(WCNS)is proposed by introducing descaling techniques to the nonlinear weights of the WCNS-Z/D schemes.The new scheme achieves an essentially non-oscillatory approximation of a discontinuous function(ENO-property),a scaleinvariant property with an arbitrary scale of a function(Si-property),and an optimal order of accuracy with smooth function regardless of the critical point(Cp-property).The classical WCNS-Z/D schemes do not satisfy Si-property intrinsically,which is caused by a loss of sub-stencils’adaptivity in the nonlinear interpolation of a discontinuous function when scaled by a small scale factor.A new nonlinear weight is devised by using an average of the function values and the descaling function,providing the new WCNS schemes(WCNS-Zm/Dm)with many attractive properties.The ENO-property,Si-property and Cp-property of the new WCNS schemes are validated numerically.Results show that the WCNS-Zm/Dm schemes satisfy the ENO-property and Si-property,while only the WCNS-Dm scheme satisfies the Cp-property.In addition,the Gaussian wave problem is solved by using successively refined grids to verify that the optimal order of accuracy of the new schemes can be achieved.Several one-dimensional shock tube problems,and two-dimensional double Mach reflection(DMR)problem and the Riemann IVP problem are simulated to illustrate the ENOproperty and Si-property of the scale-invariant WCNS-Zm/Dm schemes.

关 键 词：WCNS descaling function scale-invariant ENO-property Cp-property 

分 类 号：O17[理学—数学]