Abstract
An exponential multigrid framework is developed and assessed with a modal high-order discontinuous Galerkin method in space. The algorithm 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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Acknowledgements
This work is funded by the National Natural Science Foundation of China (NSFC) under the Grant U1930402. The computational resources are provided by Beijing Computational Science Research Center (CSRC).
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Li, SJ. (2021). Efficient Steady Flow Computations with Exponential Multigrid Methods. In: Garanzha, V.A., Kamenski, L., Si, H. (eds) Numerical Geometry, Grid Generation and Scientific Computing. Lecture Notes in Computational Science and Engineering, vol 143. Springer, Cham. https://doi.org/10.1007/978-3-030-76798-3_24
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DOI: https://doi.org/10.1007/978-3-030-76798-3_24
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