High Performance Scientific Computing in Applications with Direct Finite Element Simulation
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Our simulation methodology is referred to as Direct FEM Simulation (DFS), or General Galerkin (G2) and uses a finite element method (FEM) with piecewise linear approximation in space and time, and with numerical stabilization in the form of a weighted least squares method based on the residual. The incompressible Navier-Stokes Equations (NSE) are discretized directly, without applying any filter. Thus, the method does not result in Large Eddy Simulation (LES) filtered solutions, but is instead an approximation of a weak solution satisfying the weak form of the NSE. In G2 we have a posteriori error estimates for quantities of interest that can be expressed as functionals of a weak solution. These a posteriori error estimates, which form the basis for our adaptive mesh refinement algorithm, are based on the solution of an associated adjoint problem with a goal quantity (the aerodynamic forces in this work) as data, similarly to an optimal control problem. We provide references to related work below. The methodology and software have been previously validated for a number of turbulent flow benchmark problems, including one of the HiLiftPW-2 high Reynolds number cases. The DFS method is implemented in the Unicorn solver, which uses the open source software framework FEniCS-HPC, designed for automated solution of partial differential equations on massively parallel architectures using the FEM. In this chapter we present adaptive results from the Third AIAA High Lift Prediction Workshop in Denver, Colorado based on our DFS methodology and Unicorn/FEniCS-HPC software. We show that the methodology quantitavely and qualitatively captures the main features of the experiment - aerodynamic forces and the stall mechanism with a novel numerical tripping, with a much coarser mesh resolution and cheaper computational cost than the standard in the field.