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

MARIO A. STORTI; BRUNO A. STORTI; GARELLI, LUCIANO; JORGE D'ELIA

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 acomputational domain and then using a coupling strategy, link all these objects in order to obtain the solution of thesystem. The method has appealing characteristics that are convenient for applications like simplified meshgeneration, moving components or boundaries, local refinement, etc. In this work a Chimera method is presentedand validated in the finite element context for structured and unstructured meshes by solving the system iterativelywith BiCGStab (BiConjugate Gradient Stabilized method). A Dirichlet-Dirichlet coupling imposes the continuity of theunknown on overlapping sub domains and to transfer these values between the multiples domains, a third-orderinterpolation 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 andcomputational cost of the method. Also, a convergence rate analysis is carried out for the proposed interpolationmethod. Finally, an advection-diffusion problem involving multiple moving boundaries is solved in order to show thepotential of the presented scheme. The selected benchmark problems are well documented, both experimentallyand numerically.