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Shock-Capturing Exponential Multigrid Methods for Steady Compressible Flows

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Abstract

In this paper, a robust and efficient exponential multigrid framework is proposed for computing steady compressible flows. The algorithm based on a global coupling, exponential time integration scheme can provide 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. The resultant exponential multigrid framework is shown to be effective for smooth flows and can stabilize shock-capturing computations without limiting or adding artificial dissipation for medium-strength shock waves.

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ACKNOWLEDGMENTS

This work is funded by the National Natural Science Foundation of China (NSFC) under the Grant U1930402. Beijing Computational Science Research Center provides computing resources.

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  1. Beijing Computational Science Research Center, Beijing, China

    Shu-Jie Li

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  1. Shu-Jie Li
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Correspondence to Shu-Jie Li.

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Li, SJ. Shock-Capturing Exponential Multigrid Methods for Steady Compressible Flows. Comput. Math. and Math. Phys. 62, 1397–1412 (2022). https://doi.org/10.1134/S0965542522080085

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