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Numerical investigation of two second-order, stabilized SAV ensemble methods for the Navier–Stokes equations

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In this report we present a second-order, stabilized SAV based, Crank–Nicolson leap-frog (CNLF) ensemble method, and perform a comprehensive numerical study of it as well as the Crank–Nicolson ensemble method with a linear extrapolation (CNLE) presented in Jiang and Yang (SIAM J. Sci. Comput. 43:A2869–A2896, 2021). Both methods are extremely efficient as only one linear system with multiple right hands needs to be solved at each time for a (potentially large) number of realizations of the flow problems. In particular the coefficient matrix of the fully discretized system is a constant matrix that does not change from one time step to another. We present extensive testing of these two methods and demonstrate the advantages of each. We also present long time stability analysis for both methods.

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Funding

N. Jiang was partially supported by the US National Science Foundation grants DMS-1720001, DMS-2120413, and DMS-2143331. H. Yang was supported in part by the National Natural Science Foundation of China under grant 11801348, the key research projects of general universities in Guangdong Province (grant no. 2019KZDXM034), and the basic research and applied basic research projects in Guangdong Province (Projects of Guangdong, Hong Kong and Macao Center for Applied Mathematics, grant no. 2020B1515310018).

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Authors and Affiliations

  1. Department of Mathematics, University of Florida, Gainesville, FL, 32611, USA

    Nan Jiang

  2. Department of Mathematics, Shantou University, Guangdong, 515063, China

    Huanhuan Yang

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  1. Nan Jiang
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Correspondence to Huanhuan Yang.

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Jiang, N., Yang, H. Numerical investigation of two second-order, stabilized SAV ensemble methods for the Navier–Stokes equations. Adv Comput Math 48, 65 (2022). https://doi.org/10.1007/s10444-022-09977-9

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