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Volume 1, Issue 1
The Error-Minimization-Based Strategy for Moving Mesh Methods

K. Lipnikov & M. Shashkov

Commun. Comput. Phys., 1 (2006), pp. 53-80.

Published online: 2006-01

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  • Abstract

The typical elements in a numerical simulation of fluid flow using moving meshes are a time integration scheme, a rezone method in which a new mesh is defined, and a remapping (conservative interpolation) in which a solution is transferred to the new mesh. The objective of the rezone method is to move the computational mesh to improve the robustness, accuracy and eventually efficiency of the simulation. In this paper, we consider the one-dimensional viscous Burgers' equation and describe a new rezone strategy which minimizes the L2 norm of error and maintains mesh smoothness. The efficiency of the proposed method is demonstrated with numerical examples.

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COPYRIGHT: © Global Science Press

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@Article{CiCP-1-53, author = {K. Lipnikov and M. Shashkov}, title = {The Error-Minimization-Based Strategy for Moving Mesh Methods}, journal = {Communications in Computational Physics}, year = {2006}, volume = {1}, number = {1}, pages = {53--80}, abstract = {

The typical elements in a numerical simulation of fluid flow using moving meshes are a time integration scheme, a rezone method in which a new mesh is defined, and a remapping (conservative interpolation) in which a solution is transferred to the new mesh. The objective of the rezone method is to move the computational mesh to improve the robustness, accuracy and eventually efficiency of the simulation. In this paper, we consider the one-dimensional viscous Burgers' equation and describe a new rezone strategy which minimizes the L2 norm of error and maintains mesh smoothness. The efficiency of the proposed method is demonstrated with numerical examples.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7950.html} }
TY - JOUR T1 - The Error-Minimization-Based Strategy for Moving Mesh Methods AU - K. Lipnikov & M. Shashkov JO - Communications in Computational Physics VL - 1 SP - 53 EP - 80 PY - 2006 DA - 2006/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7950.html KW - AB -

The typical elements in a numerical simulation of fluid flow using moving meshes are a time integration scheme, a rezone method in which a new mesh is defined, and a remapping (conservative interpolation) in which a solution is transferred to the new mesh. The objective of the rezone method is to move the computational mesh to improve the robustness, accuracy and eventually efficiency of the simulation. In this paper, we consider the one-dimensional viscous Burgers' equation and describe a new rezone strategy which minimizes the L2 norm of error and maintains mesh smoothness. The efficiency of the proposed method is demonstrated with numerical examples.

K. Lipnikov and M. Shashkov. (2006). The Error-Minimization-Based Strategy for Moving Mesh Methods. Communications in Computational Physics. 1 (1). 53-80. doi:
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