Predictor-Multicorrector Schemes for the Multiscale Dynamic Diffusion Method to solve Compressible flow problems
Ramoni Z. Sedano1; Sérgio S. Bento1; Leonardo M. Lima2; Lucia Catabriga1
1 Universidade Federal do Espírito Santo; 2 Instituto Federal do Espírito Santo
doi:10.20906/CPS/CILAMCE2015-0463
Resumo
In this work we evaluate predictor-multicorrector integration schemes for Compressible Euler Equations using the Dynamic Diffusion (DD) two-scale method [1,4]. This multiscale finite element formulation is a free parameter method in which the subgrid scale space is defined using bubble functions whose degrees of freedom are locally eliminated in favor of the degrees of freedom that live on the resolved scales. The time advancing schemes assume that the resolved coarse scale chances in time by second order approximation and the unresolved scale can chance by first and second order approximations. The formulation is compared with the well known method SUPG considering two shock capturing operators, the Consistent Upwind Petrov-Galerkin (CAU)[3] and the YZβ [2]. Performance and accuracy comparisons are based on 2D test problems involving supersonic flows and shocks. References: [1] Arruda, N.C.B., Almeida, R.C. and Carmo, E.G.D., Dynamic diffusion formulation for advection dominated transport problems. In: MECOM - CILAMCE, 2010, Buenos Aires. [2] Catabriga L, de Souza D.F., Coutinho A.L.G.A, Tezduyar T.E., Three-Dimensional Edge-Based SUPG Computation of Inviscid Compressible Flows With YZβ Shock-Capturing. ASME. J. Appl. Mech.. 2009;76(2):021208-021208-7. doi:10.1115/1.3062968. [3] Galeão, A.C. and Carmo, E.G.D., A consistent approximate upwind petrov-galerkin method for convection-dominated problems. Computer Methods in Applied Mechanics and Engineering, 68:83-95, 1988. [4] Valli, A.M.P., Catabriga, L., Santos, I.P., Coutinho, A.L.G.A., and Almeida, R.C., Predictor-multicorretor scheme for the Dynamic Diffusion method, Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 2015.
Palavras-chave: Predictor - Multicorrector; Dynamic Diffusion Method; Compressible Euler Equations