2019
DOI: 10.1016/j.cma.2018.08.020
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An efficient ensemble algorithm for numerical approximation of stochastic Stokes–Darcy equations

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Cited by 35 publications
(35 citation statements)
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“…Furthermore, the velocity and pressure solves can be decoupled by the artificial compressibility method resulting in a simple updating step for the pressure. Therefore the storage requirements can be reduced and the computational speed is faster than traditional method and the ensemble method in 60 . The long time stability and first order accuracy in time under a time-step condition and two parameter conditions are proved for this algorithm.…”
Section: Discussionmentioning
confidence: 99%
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“…Furthermore, the velocity and pressure solves can be decoupled by the artificial compressibility method resulting in a simple updating step for the pressure. Therefore the storage requirements can be reduced and the computational speed is faster than traditional method and the ensemble method in 60 . The long time stability and first order accuracy in time under a time-step condition and two parameter conditions are proved for this algorithm.…”
Section: Discussionmentioning
confidence: 99%
“…Some recent work on the ensemble algorithm include studying numerical regularizations for high Reynolds number flows 48,49 , developing ensemble-based turbulence models 50 , incorporating model reduction techniques to further reduce computational cost 51,52 and devising ensemble algorithms to account for uncertain model parameters for various flow equations 53,54,55,56,57,58,59 . As for the Stokes-Darcy system, the first study on efficient ensemble algorithms can be found in 60 . The ensemble algorithm can be incorporated with all the aforementioned non-intrusive UQ methods to further reduce the computational cost and potentially improve the performance of the overall stochastic simulations as the ensemble algorithm makes more simulations runs possible given a limited computation capacity.…”
Section: Dfmentioning
confidence: 99%
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“…The Stokes-Darcy model describes the free flow of a liquid by the Stokes equation and the confined flow in a porous media by the Darcy equation, the two flows are coupled through interface conditions. Due to the fact that the resulting coupled Stokes-Darcy model has higher fidelity than either the Darcy or Stokes systems on their own, it is not surprising that a great deal of effort has been devoted to developing numerical methods for solving the model, such as the coupled finite element methods [21,72,85,99], domain decomposition methods [19,24,31,37,39,40,57,79,108], Lagrange multiplier methods [6,50,76], multi-grid methods [2,20,88], discontinuous Galerkin methods [33,54,71,78,96], mortar discretization [17,48,55], and many others [5,10,18,22,32,43,63,68,70,77,83,89,100,110,111,119].…”
mentioning
confidence: 99%