Geometric Conservation Law in 2D Advection-Diffusion Problem

LUCIANO GARELLI; RODRIGO R. PAZ; MARIO A. STORTI

Rosario, Santa Fe

Congreso; II Congreso de Matemática Aplicada, Computacional e Industrial - MACI 2009; 2009

Asociación Argentina de Matemática Aplicada, Computacional e Industrial

The aim of this work is to study the influence of the Geometric Conservation Law (GCL) when numerical simulations are performed on deforming domains with an Arbitrary Lagrangian-Eulerian (ALE) formulation. This analysis is carried out in the context of the Finite Element Method (FEM) for a model problem of a scalar advection-diffusion equation defined on a moving domain. The so-called Geometric Conservation Law (GCL) is satisfied if the algorithm can exactly reproduce a constant solution on moving grids. Not complying with the GCL means that the stability of the time integration is not assured and, thus, the order of convergence could not be preserved. To emphasize the importance of fulfilling the GCL, numerical experiments are performed in 2D using several mesh movements. In these experiments different temporal integration schemes have been used.