A high order accurate conservative remapping method on staggered meshes

作者：Cheng Juan^*; Shu Chi Wang

来源：Applied Numerical Mathematics, 2008, 58(7): 1042-1060.

DOI：10.1016/j.apnum.2007.04.015

• remapping
• high order accuracy
• conservation
• staggered mesh
• ENO reconstruction

An accurate remapping algorithm is an essential component of the Arbitrary Lagrangian-Eulerian (ALE) methods. Most ALE codes applied to high speed flow problems use a staggered mesh, i.e., all the solution variables except the velocities are cell-centered while the velocities are vertex-centered. In this paper, we present a high order accurate conservative remapping method on staggered meshes by using the idea of essentially non-oscillatory (ENO) schemes. The algorithm is based on the ENO reconstruction and approximate integration. On the staggered mesh, two sets of control volumes are built for the cell-centered conserved quantities including the mass and total energy and vertex-centered quantity-momentum respectively. On each rezoning step, we first reconstruct a polynomial function by the cell averages of mass, energy and momentum on their old control volumes. ENO idea is used to choose the best stencils for reconstruction to avoid oscillation. Then, we integrate the reconstructed functions of the old cells over the rezoned cell. These procedures of remapping ensure the algorithm to have the properties of conservation, high order accuracy and essentially non-oscillatory output. A suite of one and two dimensional examples are given to verify the performance of the algorithm.

• 出版日期2008-7
• 单位北京应用物理与计算数学研究所