A Multigrid preconditioner for Discontinuous Galerkin Methods Applied to Numerical Weather Prediction
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High fidelity fluid simulations have many important applications in science and engineering, with examples including numerical weather prediction and simulation aided design. Discontinuous Galerkin (DG) methods are high order discretizations, promising for simulation of unsteady compressible fluid flow in three dimensions. Systems arising from such discretizations of turbulent fluid motion are often stiff, and require implicit time integration. This requires fast, parallel, low-memory solvers for the algebraic equation systems that arise. For (low order) finite volume (FV) methods, multigrid (MG) methods have been successfully applied for this purpose. But for high order DG such solver are currently lacking. This deficiency inhibit wider adoption of DG methods, and motivates our research to construct a matrix free preconditioner for high order DG discretizations. The preconditioner is based on a multigrid method constructed for a low order finite volume discretization defined on a subgrid of the DG mesh. Numerical experiments on atmospheric flow problems show the benefit of this approach.
