Volume 31, Issue 6
A Remapping Method Based on Multi-Point Flux Corner Transport Upwind Advection Algorithm

J. Comp. Math., 31 (2013), pp. 592-619.

Published online: 2013-12

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• Abstract

A local remapping algorithm for scalar function on quadrilateral meshes is described. The remapper from a distorted grid to a rezoned grid is usually regarded as a conservative interpolation problem. The present paper introduces a pseudo time to transform the interpolation into an initial value problem on a moving grid, and construct a moving mesh method to solve it. The new feature of the algorithm is the introduction of multi-point information on each edge, which leads to the numerical flux consistent with grid node motion. During the procedure of deriving scheme, we illustrate a framework about how the algorithms on a rectangular mesh are easily generated to those on a moving mesh. The basic ideas include: (i) introducing coordinate transformation, which maps the irregular domain in physical space to a perfectly regular computational domain, and (ii) deriving finite volume methods in the physical domain, which can be viewed as a discretization of the transformed equation. The resulting scheme is second-order accurate, conservative and monotonicity preserving. Numerical examples are carried out to show the good performance of our schemes.

65D05, 76M12, 34M25.

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@Article{JCM-31-592, author = {}, title = {A Remapping Method Based on Multi-Point Flux Corner Transport Upwind Advection Algorithm}, journal = {Journal of Computational Mathematics}, year = {2013}, volume = {31}, number = {6}, pages = {592--619}, abstract = {

A local remapping algorithm for scalar function on quadrilateral meshes is described. The remapper from a distorted grid to a rezoned grid is usually regarded as a conservative interpolation problem. The present paper introduces a pseudo time to transform the interpolation into an initial value problem on a moving grid, and construct a moving mesh method to solve it. The new feature of the algorithm is the introduction of multi-point information on each edge, which leads to the numerical flux consistent with grid node motion. During the procedure of deriving scheme, we illustrate a framework about how the algorithms on a rectangular mesh are easily generated to those on a moving mesh. The basic ideas include: (i) introducing coordinate transformation, which maps the irregular domain in physical space to a perfectly regular computational domain, and (ii) deriving finite volume methods in the physical domain, which can be viewed as a discretization of the transformed equation. The resulting scheme is second-order accurate, conservative and monotonicity preserving. Numerical examples are carried out to show the good performance of our schemes.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1307-m4182}, url = {http://global-sci.org/intro/article_detail/jcm/9756.html} }
TY - JOUR T1 - A Remapping Method Based on Multi-Point Flux Corner Transport Upwind Advection Algorithm JO - Journal of Computational Mathematics VL - 6 SP - 592 EP - 619 PY - 2013 DA - 2013/12 SN - 31 DO - http://doi.org/10.4208/jcm.1307-m4182 UR - https://global-sci.org/intro/article_detail/jcm/9756.html KW - Remapping, Advection, Multi-point flux, Coordinate transformation, Geometric conservation law. AB -

A local remapping algorithm for scalar function on quadrilateral meshes is described. The remapper from a distorted grid to a rezoned grid is usually regarded as a conservative interpolation problem. The present paper introduces a pseudo time to transform the interpolation into an initial value problem on a moving grid, and construct a moving mesh method to solve it. The new feature of the algorithm is the introduction of multi-point information on each edge, which leads to the numerical flux consistent with grid node motion. During the procedure of deriving scheme, we illustrate a framework about how the algorithms on a rectangular mesh are easily generated to those on a moving mesh. The basic ideas include: (i) introducing coordinate transformation, which maps the irregular domain in physical space to a perfectly regular computational domain, and (ii) deriving finite volume methods in the physical domain, which can be viewed as a discretization of the transformed equation. The resulting scheme is second-order accurate, conservative and monotonicity preserving. Numerical examples are carried out to show the good performance of our schemes.

Zhijun Shen & Guixia Lv. (1970). A Remapping Method Based on Multi-Point Flux Corner Transport Upwind Advection Algorithm. Journal of Computational Mathematics. 31 (6). 592-619. doi:10.4208/jcm.1307-m4182
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