A Comparison Between the Finite Volume and the Boundary Element Methods Solving Homogeneous and Heterogeneous Two-dimensional Media Wave Problems

Resumo

This work presents a comparison between the boundary element method with direct interpolation and the finite volume method, the latter in an unstructured version, solving problems of scalar wave propagation in homogeneous and heterogeneous media in two dimensions. The objective is to evaluate the potential of the two numerical techniques in solving dynamic problems of this nature, which are known to be challenging in terms of accuracy of results. Evaluations regarding the convergence rate as a function of the mesh refinement, the numerical robustness involving the stability of the temporal advance schemes, among other particularities, are assessed by solving some classical problems and others in which analytical solutions were generated to better assess the accuracy of the results.