Formulações estabilizadas submalhas aplicadas às equações de Euler

Abstract

This work presents an implementation of the finite element method to solve the system of two-dimensional compressible Euler equations in conservation variables, using the Dynamic Diffusion subgrid stabilization method, considering static and transient subgrid scales. This method is based on the multiscale formalism and has been proposed to solve convection-dominant transport problems. A nonlinear dissipative operator acting isotropically in all discretization scales is added to the Galerkin method. We let the subgrid scales very in time, and thus they need to be tracked. Then, we propose a closed-form expression for them at each time step. A second order implicit predictor multicorrector scheme is used for time integration and the linear systems resulting are solved by the GMRES iterative method. We consider a set of classic experiments: normal shock, oblique shock and reflected shock. Numerical experiments shown that the method Diffusion Dynamics - with transient subgrid scales - results in more accurate solutions than the stabilized methods SUPG/CAU e SUPG/YZβ.