Moving mesh generation with a sequential approach for solving PDEs

Young-il Lim (Author), J. M. LeLann (Author), Xavier Joulia (Author)

Research output: Non-textual formSound/Visual production (digital)Research

Abstract

In moving mesh methods, physical PDEs and a mesh equation derived from equidistribution of an error metrics (so-called the monitor function) are simultaneously solved and meshes are dynamically concentrated on steep regions (Lim et al., 2001). However, the simultaneous solution procedure of physical and mesh equations suffers typically from long computation time due to highly nonlinear coupling between the two equations. Moreover, the extended system (physical and mesh equations) may be sensitive to the tuning parameters such as a temporal relaxation factor. It is therefore useful to design a simple and robust moving mesh algorithm in one or multidimension. In this study, we propose a sequential solution procedure including two separate parts: prediction step to obtain an approximate solution to a next time level (integration of physical PDEs) and regriding step at the next time level (mesh generation and solution interpolation). Convection terms, which appear in physical PDEs and a mesh equation, are discretized by a WENO (Weighted Essentially Non-Oscillatory) scheme under the consrvative form. This sequential approach is to keep the advantages of robustness and simplicity for the static adaptive grid method (local refinement by adding/deleting the meshes at a discrete time level) as well as of efficiency for the dynamic adaptive grid method (or moving mesh method) where the number of meshes is not changed. For illustration, a phase change problem is solved with the decomposition algorithm.
Original languageEnglish
Publication date2002
Size0
DOIs
Publication statusPublished - 2002
Event12th European Symposium on Computer Aided Process Engineering: 35th European symposium of the Working Party on Computer Aided Process Engineering - The Hague, Netherlands
Duration: 26 May 200229 May 2002
Conference number: 12, 35

Conference

Conference12th European Symposium on Computer Aided Process Engineering
Number12, 35
CountryNetherlands
CityThe Hague
Period26/05/200229/05/2002

Cite this

Lim, Y. (Author), LeLann, J. M. (Author), & Joulia, X. (Author). (2002). Moving mesh generation with a sequential approach for solving PDEs. Sound/Visual production (digital) https://doi.org/10.1016/S1570-7946(02)80179-1