Uma formulação multiescala não linear e descontínua para problemas de convecção-difusão-reação

Enéas Mendes de Jesus; Isaac Pinheiro dos Santos

doi:10.35819/remat2024v10iespecialid7088

Authors

Enéas Mendes de Jesus Instituto Federal de Educação, Ciência e Tecnologia do Espírito Santo (IFES), Campus Piúma, Piúma, ES; Universidade Federal do Espírito Santo (UFES), Vitória, ES, Brasil https://orcid.org/0000-0002-2384-3831
Isaac Pinheiro dos Santos Universidade Federal do Espírito Santo (UFES), Campus de São Mateus, São Mateus, ES, Brasil https://orcid.org/0000-0001-8524-0393

DOI:

https://doi.org/10.35819/remat2024v10iespecialid7088

Keywords:

discontinuous Galerkin, artificial diffusion, convection-diffusion-reaction, bubble functions, multiscale methods

Abstract

This work presents a formulation of discontinuous multiscale and nonlinear Galerkin method aiming to solve convection-diffusion-reaction problems. Considering a decomposition of the approximation space into two scales, macro and micro, the new method introduces a nonlinear artificial diffusion operator at both discretization scales, while employing the discontinuous approach only at the macro scale. The micro scale is modeled through bubble functions (polynomial functions that vanish at the boundary of the elements), allowing the application of the static condensation process in each element. The discretization of the numerical model results in a global system of equations associated with nodal points only at the macro scale. To assess the stability and convergence properties of the proposed scheme, several numerical experiments were conducted and compared with the classical discontinuous Galerkin method. The proposed formulation proved to be efficient in eliminating spurious oscillations that appear in regions of high gradients in problems with dominant convection/reaction. Furthermore, the method exhibited optimal convergence rates.

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Author Biographies

Enéas Mendes de Jesus, Instituto Federal de Educação, Ciência e Tecnologia do Espírito Santo (IFES), Campus Piúma, Piúma, ES; Universidade Federal do Espírito Santo (UFES), Vitória, ES, Brasil

http://lattes.cnpq.br/4180558774113196
Isaac Pinheiro dos Santos, Universidade Federal do Espírito Santo (UFES), Campus de São Mateus, São Mateus, ES, Brasil

http://lattes.cnpq.br/3793156690673506

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