A local rezoning and remapping method for unstructured mesh

This paper presents explicit description of the rezoning and remapping method for unstructured mesh. The rezoning and remapping constitute two of the three phases of Arbitrary Lagrangian–Eulerian (ALE) methods, while the other one is Lagrangian phase. Our method is local (vs. global) in order that the majority of mesh remains unchanged, and that the error caused by remapping can be confined within the changed areas. This is achieved by specifying the local worse areas of mesh based on the mesh-closure and mesh-union concepts. After the computing of worse areas, they are rezoned and united with the remaining areas to compose the new mesh. Then within the new mesh only the worse areas are remapped using four methods with different orders of accuracy, including linear interpolation, particle remapping, first order integral remapping and high order ENO (essentially non-oscillatory) remapping. (However, our program only uses the first order integral remapping method for the moment.) Our methodʼs application in the inertial confinement fusion (ICF) simulation is introduced at the end.Program summaryProgram title: MaxisCatalogue identifier: AEIP_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIP_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 285 253No. of bytes in distributed program, including test data, etc.: 13 384 369Distribution format: tar.gzProgramming language: MatlabComputer: PCOperating system: Windows/Linux/UnixRAM: 50 MBWord size: 32 bitsClassification: 12, 19.7Subprograms used:Cat IdTitleReferenceAECV_v1_0MULTI2DCPC 180 (2009) 977Full-size tableTable optionsView in workspaceDownload as CSVNature of problem: Although the great deformation of mesh elements moved with the fluid, which causes the severe shortening of computing time step and the increasing of computing error, makes it indispensable that the rezoning of distorted mesh and the remapping of physical variables such as density or velocity are performed, it still bothers people that the rezoning and remapping also bring in the loss of Lagrangian motion information of old mesh. Therefore the essential problem is how to minimize the error caused by remapping while improving the mesh quality.Solution method: The best method would be based on the remapping error estimation. Unfortunately, in practice, this method would be quite intricate. Instead of the error estimation we adopt the local rezoning and remapping technique to confine the error within the worse or ʼnot very importantʼ areas, that is, only the worse areas are rezoned and remapped which are determined by the mesh-closure or mesh-union method.Restrictions: It is sometimes annoying that there is no uniform criterion to distinguish the worse mesh elements from the good ones.Additional comments: Since MULTI2D created by R. Ramis is used to fulfill the Lagrangian phase of the simulation of the ICF process, while our programs are called to perform the rezoning and remapping phases, it is required for non-MULTI2D users that our routines should be slightly reprogrammed.Running time: 1967 seconds for my example.