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

Zhijun Shen & Guixia Lv

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 multipoint 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.

  • Keywords

Remapping Advection Multi-point flux Coordinate transformation Geometric conservation law

  • AMS Subject Headings

65D05 76M12 34M25.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-31-592, author = {Zhijun Shen and Guixia Lv}, 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 multipoint 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 AU - Zhijun Shen & Guixia Lv 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 KW - Advection KW - Multi-point flux KW - Coordinate transformation KW - 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 multipoint 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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