Numerical Solution of Partial Differential Equations in Arbitrary Shaped Domains Using Cartesian Cut-Stencil Finite Difference Method.Part II:Higher-Order Schemes  

作　　者：M.Esmaeilzadeh R.M.Barron 

机构地区：[1]Department of Mechanical,Automotive&Materials Engineering,University of Windsor,Windsor,Ontario,N9B 3P4,Canada [2]Department of Mathematics&Statistics,University of Windsor,Windsor,Ontario,N9B 3P4,Canada [3]Department of Mechanical Engineering,South Tehran Branch,Islamic Azad University,Tehran,P.C:1777613651,Iran

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2022年第3期819-850,共32页高等学校计算数学学报（英文版）

基　　金：support from the Natural Sciences and Engineering Research Council of Canada through the Discovery Grants program.

摘　　要：Compact higher-order(HO)schemes for a new finite difference method,referred to as the Cartesian cut-stencil FD method,for the numerical solution of the convection-diffusion equation in complex shaped domains have been addressed in this paper.The Cartesian cut-stencil FD method,which employs 1-D quadratic transformation functions to map a non-uniform(uncut or cut)physical stencil to a uniform computational stencil,can be combined with compact HO Pad´e-Hermitian formulations to produce HO cut-stencil schemes.The modified partial differential equation technique is used to develop formulas for the local truncation error for the cut-stencil HO formulations.The effect of various HO approximations for Neumann boundary conditions on the solution accuracy and global order of convergence are discussed.The numerical results for second-order and compact HO formulations of the Cartesian cut-stencil FD method have been compared for test problems using the method of manufactured solutions.

关 键 词：Cartesian cut-stencil finite difference method compact higher-order formulation irregular domain Neumann boundary conditions local truncation error 

分 类 号：O17[理学—数学]