A Variational Multiscale Method with Discontinuous Subscales for Output-Based Adaptation of Aerodynamic Flows
Arthur C. Huang, Hugh A. Carson, Steven R. Allmaras, Marshall C. Galbraith, David Darmofal, Dmitry S. Kamenetskiy
Abstract
In this work, we present an adjoint consistent continuous Galerkin discretization, Varia- tional Multiscale with Discontinuous Subscales (VMSD), for the simulation of aerodynamic flows. The method uses a multi-scale solution decomposition and models the unresolved scales with a discontinuous solution field. The discontinuous subscales are used to stabilize the discretization in an adjoint consistent manner. Adjoint consistency can both improve the accu- racy of output functionals and makes VMSD suitable for mesh adaptation schemes that rely on adjoint-based output error estimates. Here, VMSD is shown to be as accurate or better than the Galerkin Least-Squares method for select advection-diffusion and RANS test cases. Mesh adapted results using the output-based Metric Optimization via Error Sampling and Synthesis (MOESS) scheme for both discontinuous Galerkin (DG) and VMSD discretizations of the 2D and 3D RANS equations are presented. For the 3D RANS hemisphere-cylinder test case, VMSD MOESS achieves one count drag error with a third of the computation time and half the memory of DG MOESS.