Application of the multigrid approach to the solution of 3D Navier–Stokes equations on hexahedral grids by the Galerkin method with discontinuous basis functions
Abstract:
The Galerkin method with discontinuous basis functions is adapted for solving the Euler and Navier–Stokes equations on unstructured hexahedral grids. A hybrid multigrid algorithm involving the finite element and grid stages is used as an iterative solution method. Numerical results of calculating the sphere inviscid flow, viscous flow in a bent pipe, and turbulent flow past a wing are presented. The numerical results and the computational cost are compared with those obtained using the finite volume method.
Key words:discontinuous Galerkin method, hp-multigrid method, scheme of high order of accuracy, 3D Euler and Navier–Stokes equations, unstructured hexahedral grids.
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