AN UNFACTORED IMPLICIT MOVING MESH METHOD FOR THE TWO-DIMENSIONAL UNSTEADY N-S EQUATIONS

AbstractThis paper extends the adaptive moving mesh method developed by Tang and Tang [36] to two-dimensional (2D) relativistic hydrodynamic (RHD) equations. The algorithm consists of two “independent” parts: the time evolution of the RHD equations and the (static) mesh iteration redistribution. In the first part, the RHD equations are discretized by using a high resolution finite volume scheme on the fixed but nonuniform meshes without the full characteristic decomposition of the governing equations. The second part is an iterative procedure. In each iteration, the mesh points are first redistributed, and then the cell averages of the conservative variables are remapped onto the new mesh in a conservative way. Several numerical examples are given to demonstrate the accuracy and effectiveness of the proposed method.

Download Full-text

A simple moving mesh method for one- and two-dimensional phase-field equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2005.01.042 ◽

2006 ◽

Vol 190 (1-2) ◽

pp. 252-269 ◽

Cited By ~ 19

Author(s):

Zhijun Tan ◽

Tao Tang ◽

Zhengru Zhang

Keyword(s):

Phase Field ◽

Moving Mesh ◽

Two Dimensional ◽

Moving Mesh Method ◽

Field Equations ◽

Mesh Method ◽

Phase Field Equations

Download Full-text

An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics

Journal of Computational Physics ◽

10.1016/j.jcp.2006.05.031 ◽

2007 ◽

Vol 220 (2) ◽

pp. 791-812 ◽

Cited By ~ 23

Author(s):

Jianqiang Han ◽

Huazhong Tang

Keyword(s):

Moving Mesh ◽

Two Dimensional ◽

Moving Mesh Method ◽

Mesh Method ◽

Adaptive Moving Mesh Method ◽

Ideal Magnetohydrodynamics

Download Full-text

Heat Conduction Simulation of 2D Moving Heat Source Problems Using a Moving Mesh Method

Advances in Mathematical Physics ◽

10.1155/2020/6067854 ◽

2020 ◽

Vol 2020 ◽

pp. 1-16

Author(s):

Zhicheng Hu ◽

Zhihui Liu

Keyword(s):

Heat Conduction ◽

Heat Source ◽

Transient Heat Conduction ◽

Moving Mesh ◽

Heat Sources ◽

Two Dimensional ◽

Moving Heat Source ◽

Moving Mesh Method ◽

Mesh Method ◽

The One

This paper focuses on efficiently numerical investigation of two-dimensional heat conduction problems of material subjected to multiple moving Gaussian point heat sources. All heat sources are imposed on the inside of material and assumed to move along some specified straight lines or curves with time-dependent velocities. A simple but efficient moving mesh method, which continuously adjusts the two-dimensional mesh dimension by dimension upon the one-dimensional moving mesh partial differential equation with an appropriate monitor function of the temperature field, has been developed. The physical model problem is then solved on this adaptive moving mesh. Numerical experiments are presented to exhibit the capability of the proposed moving mesh algorithm to efficiently and accurately simulate the moving heat source problems. The transient heat conduction phenomena due to various parameters of the moving heat sources, including the number of heat sources and the types of motion, are well simulated and investigated.

Download Full-text