An efficient ensemble algorithm for numerical approximation of stochastic Stokes–Darcy equations

An artificial compressibility ensemble algorithm for a stochastic Stokes‐Darcy model with random hydraulic conductivity and interface conditions

“…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.…”

“…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.…”

“…Based on the key ideas of 45,60 which was a fundamental development of the efficient ensemble algorithm for flow equations, in this article we utilize the idea of artificial compressibility and partitioned time stepping methods to construct the decoupled ensemble algorithm for efficiently computing multiple realizations of the stochastic Stokes-Darcy interface model with a random hydraulic conductivity tensor, source terms and initial conditions. In this algorithm, the originally coupled multi-physics model is decoupled by a two-level technique.…”

“…By recalling (3.9) in 60 , the other two terms on the right hand side of (10) can be bounded as follows…”

A stochastic collocation method based on sparse grids for a stochastic Stokes-Darcy model

“…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].…”