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\(p\)-multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. (English) Zbl 1177.76194

Summary: We present a \(p\)-multigrid solution algorithm for a high-order discontinuous Galerkin finite element discretization of the compressible Navier-Stokes equations. The algorithm employs an element line Jacobi smoother in which lines of elements are formed using coupling based on a \(p = 0\) discretization of the scalar convection-diffusion equation. Fourier analysis of the two-level \(p\)-multigrid algorithm for convection-diffusion shows that element line Jacobi presents a significant improvement over element Jacobi especially for high Reynolds number flows and stretched grids. Results from inviscid and viscous test cases demonstrate optimal \(h^{p + 1}\) order of accuracy as well as \(p\)-independent multigrid convergence rates, at least up to \(p = 3\). In addition, for the smooth problems considered, \(p\)-refinement outperforms \(h\)-refinement in terms of the time required to reach a desired high accuracy level.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids

Software:

Wesseling
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References:

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