Geometric Conservation Law in ALE Formulations

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

Tandil

Congreso; XVIII Congreso sobre métodos numéricos y sus aplicaciones. ENIEF 2009; 2009

Universidad Nacional del Centro de la pcia. de Bs. As. y Asociación Argentina de Mecánica Computacional

The aim of this work is to study the influence of the GeometricConservation 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 FiniteElement Method (FEM) using the PETSc-FEM code which has beendeveloped at CIMEC.Solving the problem on a moving mesh using an ALE formulation needs the computation of some geometric quantities, such as element volumes and Jacobians, which involve the nodal positions and velocities. The so-called Discrete Geometric Conservation Law (DGCL) is satisfied if the algorithm can exactly reproduce an uniform flow 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 both in 2D and 3D domains using rotations, dilatations and shear movements of the meshes, using different degrees of regularity in the mesh velocity. In these experiments different temporal integration schemes, as well as different spatial interpolation have been used (i.e, linear triangles and quadrangles in 2D and linear tetrahedra and hexaedra in 3D).