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  1. Abstract

    We study a second order ensemble method for fast computation of an ensemble of magnetohydrodynamics flows at small magnetic Reynolds number. Computing an ensemble of flow equations with different input parameters is a common procedure for uncertainty quantification in many engineering applications, for which the computational cost can be prohibitively expensive for nonlinear complex systems. We propose an ensemble algorithm that requires only solving one linear system with multiple right‐hands instead of solving multiple different linear systems, which significantly reduces the computational cost and simulation time. Comprehensive stability and error analyses are presented proving conditional stability and second order in time convergent. Numerical tests are provided to illustrate theoretical results and demonstrate the efficiency of the proposed algorithm.

     
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  2. Summary

    We propose and analyze an efficient ensemble algorithm with artificial compressibility (AC) for fast decoupled computation of multiple realizations of the stochastic Stokes‐Darcy model with random hydraulic conductivity (including the one in the interface conditions), source terms, and initial conditions. The solutions are found by solving three smaller decoupled subproblems with two common time‐independent coefficient matrices for all realizations, which significantly improves the efficiency for both assembling and solving the matrix systems. The fully coupled Stokes‐Darcy system can be first decoupled into two smaller subphysics problems by the idea of the partitioned time stepping, which reduces the size of the linear systems and allows parallel computing for each subphysics problem. The AC further decouples the velocity and pressure which further reduces storage requirements and improves computational efficiency. We prove the long time stability and the convergence for this new ensemble method. Three numerical examples are presented to support the theoretical results and illustrate the features of the algorithm, including the convergence, stability, efficiency, and applicability.

     
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  3. Free, publicly-accessible full text available October 1, 2024