Efficient $p$-multigrid method based on an exponential time discretization for compressible steady flows

Shu-Jie Li

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arXiv · 1807.01151

Efficient $p$-multigrid method based on an exponential time discretization for compressible steady flows

Shu-Jie Li

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Abstract

An efficient multigrid framework is developed for the time marching of steady-state compressible flows with a spatially high-order ($p$-order polynomial) modal discontinuous Galerkin method. The core algorithm that based on a global coupling, exponential time integration scheme provides strong damping effects to accelerate the convergence towards the steady state, while high-frequency, high-order spatial error modes are smoothed out with a $s$-stage preconditioned Runge-Kutta method. Numerical studies show that the exponential time integration substantially improves the damping and propagative efficiency of Runge-Kutta time-stepping for use with the $p$-multigrid method, yielding rapid and $p$-independent convergences to steady flows in both two and three dimensions.

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physics.comp-ph cs.NA math.NA physics.flu-dyn

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BibTeX RIS

Shu-Jie Li. 2018-06-30. Efficient $p$-multigrid method based on an exponential time discretization for compressible steady flows. https://arxiv.org/abs/1807.01151

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