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

Abstract

We propose and analyze an efficient ensemble algorithm with artificial compressibility 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 sub-physics problems by the idea of the partitioned time stepping, which reduces the size of the linear systems and allows parallel computing for each sub-physics problem. The artificial compressibility 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.

A decoupled numerical method for two-phase flows of different densities and viscosities in superposed fluid and porous layers

“…In order to decouple the velocity and pressure in the Navier-Stokes equations, we follow the idea of artificial compressibility method [17,19,39,68,75] and replace the divergence-free condition by…”

“…Furthermore, it is desirable to separate the computation of velocity and pressure when solving the Navier-Stokes equations. Due to the presence of the nonlinear Lions domain interface boundary condition, we adopt a special method of artificial compressibility [19,39] which avoids boundary conditions in the update of the pressure. We rigorously establish the unconditional long-time stability of the proposed algorithm and verify numerically that the fully discrete schemes are convergent and energy-law preserving.…”

A Parallel Robin–Robin Domain Decomposition Method based on Modified Characteristic FEMs for the Time-Dependent Dual-porosity-Navier–Stokes Model with the Beavers–Joseph Interface Condition

“…In [9], the authors proved the BJ interface condition is more accurate compared with BJS interface condition from a mathematical point of view. There has been a great deal of achievements for solving such system [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The Robin-Robin domain decomposition methods, as a sense of continuous decoupling method, provides a natural and efficient means for multi-domain and multi-physics coupled problems.…”

On the solution of the coupled steady-state dual-porosity-Navier-Stokes fluid flow model with the Beavers-Joseph-Saffman interface condition

“…The authors used the dual-porosity equations over Darcy's region to describe fluid flowing through the multiple porous medium. Recently, several related research on the above model can be found in the literatures [2,3,24,29,44]. In particular, Gao and Li [24] proposed a decoupled stabilized finite element method to solve the coupled dual-porosity-Navier-Stokes fluid flow model in the numerical field.…”