TY - JOUR

T1 - A General Moving Mesh Framework in 3D and Its Application for Simulating the Mixture of Multi-Phase Flows

AU - Di, Yana

AU - Li, Ruo

AU - Tang, Tao

N1 - Funding information:
The research of Di and Li was supported in part by the Joint Applied Mathematics Research Institute of Peking University and Hong Kong Baptist University. Li was also partially supported by the National Basic Research Program of China under the grant 2005CB321701. The research of Tang was supported by CERG Grants of Hong Kong Research Grant Council, FRG grants of Hong Kong Baptist University, and NSAF Grant #10476032 of National Science Foundation of China. He was supported in part by the Chinese Academy of Sciences while visiting its Institute of Computational Mathematics.
Publisher copyright:
©2008 Global-Science Press

PY - 2008/3

Y1 - 2008/3

N2 - In this paper, we present an adaptive moving mesh algorithm for meshes of unstructured polyhedra in three space dimensions. The algorithm automatically adjusts the size of the elements with time and position in the physical domain to resolve the relevant scales in multiscale physical systems while minimizing computational costs. The algorithm is a generalization of the moving mesh methods based on harmonic mappings developed by Li et al. [J. Comput. Phys., 170 (2001), pp. 562-588, and 177 (2002), pp. 365-393]. To make 3D moving mesh simulations possible, the key is to develop an efficient mesh redistribution procedure so that this part will cost as little as possible comparing with the solution evolution part. Since the mesh redistribution procedure normally requires to solve large size matrix equations, we will describe a procedure to decouple the matrix equation to a much simpler block-tridiagonal type which can be efficiently solved by a particularly designed multi-grid method. To demonstrate the performance of the proposed 3D moving mesh strategy, the algorithm is implemented in finite element simulations of fluid-fluid interface interactions in multiphase flows. To demonstrate the main ideas, we consider the formation of drops by using an energetic variational phase field model which describes the motion of mixtures of two incompressible fluids. Numerical results on two- and three-dimensional simulations will be presented.

AB - In this paper, we present an adaptive moving mesh algorithm for meshes of unstructured polyhedra in three space dimensions. The algorithm automatically adjusts the size of the elements with time and position in the physical domain to resolve the relevant scales in multiscale physical systems while minimizing computational costs. The algorithm is a generalization of the moving mesh methods based on harmonic mappings developed by Li et al. [J. Comput. Phys., 170 (2001), pp. 562-588, and 177 (2002), pp. 365-393]. To make 3D moving mesh simulations possible, the key is to develop an efficient mesh redistribution procedure so that this part will cost as little as possible comparing with the solution evolution part. Since the mesh redistribution procedure normally requires to solve large size matrix equations, we will describe a procedure to decouple the matrix equation to a much simpler block-tridiagonal type which can be efficiently solved by a particularly designed multi-grid method. To demonstrate the performance of the proposed 3D moving mesh strategy, the algorithm is implemented in finite element simulations of fluid-fluid interface interactions in multiphase flows. To demonstrate the main ideas, we consider the formation of drops by using an energetic variational phase field model which describes the motion of mixtures of two incompressible fluids. Numerical results on two- and three-dimensional simulations will be presented.

KW - Moving mesh methods

KW - multi-phase flows

KW - unstructured tetrahedra

KW - phase field model

KW - Navier-Stokes equations

KW - finite element method

UR - http://www.scopus.com/inward/record.url?scp=41749090913&partnerID=8YFLogxK

M3 - Journal article

AN - SCOPUS:41749090913

SN - 1815-2406

VL - 3

SP - 582

EP - 602

JO - Communications in Computational Physics

JF - Communications in Computational Physics

IS - 3

ER -