Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations

被引：50
作者：
Baines, M. J. [1 ]
Hubbard, M. E. [2 ]
Jimack, P. K. [2 ]
机构：
[1] Univ Reading, Dept Math, Reading RG6 6AX, Berks, England
[2] Univ Leeds, Sch Comp, Leeds LS2 9JT, W Yorkshire, England
来源：
COMMUNICATIONS IN COMPUTATIONAL PHYSICS | 2011年 / 10卷 / 03期
关键词：
Time-dependent nonlinear diffusion; moving boundaries; finite element method; Lagrangian meshes; conservation of mass; FINITE-ELEMENT-METHOD; GEOMETRIC CONSERVATION LAW; FLUID-STRUCTURE INTERACTION; ONE-DIMENSIONAL INFILTRATION; FREE-SURFACE FLOWS; NUMERICAL-SOLUTION; INCOMPRESSIBLE FLUIDS; EVOLUTIONARY PROBLEMS; GRID ADAPTATION; GALERKIN METHOD;
D O I：
10.4208/cicp.201010.040511a
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
This article describes a number of velocity-based moving mesh numerical methods for multidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.
引用
收藏
页码：509 / 576
页数：68
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