A Penalty-projection based Efficient and Accurate Stochastic Collocation Method for Magnetohydrodynamic Flows
| Autor: | Mohebujjaman, Muhammad, Miranda, Julian, Mahbub, Md. Abdullah Al, Xiao, Mengying |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We propose, analyze, and test a penalty projection-based efficient and accurate algorithm for the Uncertainty Quantification (UQ) of the time-dependent Magnetohydrodynamic (MHD) flow problems in convection-dominated regimes. The algorithm uses the Els\"asser variables formulation and discrete Hodge decomposition to decouple the stochastic MHD system into four sub-problems (at each time-step for each realization) which are much easier to solve than solving the coupled saddle point problems. Each of the sub-problems is designed in a sophisticated way so that at each time-step the system matrix remains the same for all the realizations but with different right-hand-side vectors which allows saving a huge amount of computer memory and computational time. Moreover, the scheme is equipped with ensemble eddy-viscosity and grad-div stabilization terms. The stability of the algorithm is proven rigorously. We prove that the proposed scheme converges to an equivalent non-projection-based coupled MHD scheme for large grad-div stabilization parameter values. We examine how Stochastic Collocation Methods (SCMs) can be combined with the proposed penalty projection UQ algorithm. Finally, a series of numerical experiments are given which verify the predicted convergence rates, show the algorithm's performance on benchmark channel flow over a rectangular step, and a regularized lid-driven cavity problem with high random Reynolds number and magnetic Reynolds number. Comment: 28 pages, 13 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|