A Chimera Method Based on Dirichlet-Dirichlet Coupling Applied to Moving Boundary Problems

LUCIANO GARELLI; JORGE D'ELÍA; BRUNO STORTI; MARIO STORTI

New York

Congreso; 13th World Congress on Computational Mechanics (WCCM XIII). 2nd Pan American Congress on Computational Mechanics (PANACM II); 2018

IACM International Association for Computational Mechanics

The main idea of the Chimera method is to generate independent and optimized meshes for the objects present in a computational domain and then using a coupling strategy, link all these objects in order to obtain the solution of the system. The method has appealing characteristics that are convenient for applications like simplified mesh generation, moving components or boundaries, local refinement, etc. In this work a Chimera method is presented and validated in the finite element context for structured and unstructured meshes by solving the system iteratively with BiCGStab (BiConjugate Gradient Stabilized method). A Dirichlet-Dirichlet coupling imposes the continuity of the unknown on overlapping sub domains and to transfer these values between the multiples domains, a third-order interpolation method is used in conjunction with a "pasting" penalization operator.Several numerical examples are shown in order to validate the solution and assessing the precision and computational cost of the method. Also, a convergence rate analysis is carried out for the proposed interpolation method. Finally, an advection-diffusion problem involving multiple moving boundaries is solved in order to show the potential of the presented scheme. The selected benchmark problems are well documented, both experimentally and numerically.