Tuan Anh Dao
Division of Scientific Computing, IT Department, Uppsala University
We propose a hybrid method to couple FD methods and FE methods with shock-capturing capability in a nonconforming multiblock fashion. The initiatory aim is to optimize computational efficiency when complex geometries present. While requiring minimal changes in the existing schemes, the proposed technique results in a provably stable, accurate and energy conserving unified SBP method. Shocks are efficiently captured by a Residual-based viscosity stabilization technique. Results are demonstrated on linear and nonlinear scalar conservation laws in two spatial dimensions, including a challenging shock-capturing benchmark - the KPP problem.