Compact Discontinuous Galerkin Methods for Fluids

Finite element methods, while low order, naturally work on unstructured meshes, and can compute physics inside and around complex, moving boundaries. Discontinuous Galerkin methods, which use high order polynomials within mesh elements, are significantly more accurate, but suffer because the complexity of linking the influence of the elements results in very slow methods. Compact DG Methods, which change the numerical fluxes in LDG schemes to achieve stencils that are compact (only connects neighboring elements) and sparse(few connections between the elements), are now the most efficient of all discontinuous Galerkin methods, and rapidly gaining use in compressible/incompressible Navier-Stokes solvers, linear/nonlinear elasticity, heat transfer, etc.