A Hybrid Petrov-Galerkin Method for Optimal Output Prediction

We present a new Boundary Discontinuous Petrov-Galerkin (BDPG) method for Computational Fluid Dynamics (CFD) simulations. The method represents a modication of the standard Hybrid Discontinuous Galerkin (HDG) scheme, and uses locally-computed optimal test functions to achieve enhanced accuracy along the domain boundaries. This leads to improved accuracy in relevant boundary outputs such as lift and drag. Results demonstrate that, for linear problems in both one and two dimensions, exact boundary outputs are obtained if the test functions and uxes are well-represented. Furthermore, for nonlinear problems such as the Navier-Stokes equations, the method can achieve 2p + 2 output convergence rates, which represents an improvement over the 2p + 1 rates of standard HDG.