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, Advection, Multi-point flux, Coordinate transformation, Geometric conservation law.
AB - <p style="text-align: justify;">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.</p>