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An efficient scalar auxiliary variable partitioned projection ensemble method for simulating surface-groundwater flows

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  • Jiang, Nan
  • Li, Ying

Abstract

We propose an efficient, partitioned, scalar auxiliary variable rotational pressure correction backward Euler (SAV-RPC-BE) ensemble scheme for simulating surface-groundwater flows modeled by the Stokes-Darcy equations. The rotational pressure correction method decouples the Stokes equations into one elliptic equation for the fluid velocity and one Poisson equation for the pressure at each time step. We incorporate the recently-developed SAV approach and the ensemble time-stepping method to further decouple the computation of the free flow region and the porous media region. The ensemble scheme results in only one common coefficient matrix shared by all realizations at each time step. Hence, efficient direct/iterative block solvers can be used to greatly reduce the computation cost. The stability analysis shows that the SAV-RPC-BE ensemble scheme is long-time stable under three parameter conditions without any time step constraints. Some numerical experiments are presented to support the theoretical results and show the effectiveness of the proposed scheme.

Suggested Citation

  • Jiang, Nan & Li, Ying, 2024. "An efficient scalar auxiliary variable partitioned projection ensemble method for simulating surface-groundwater flows," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 39-54.
    • Handle: RePEc:eee:matcom:v:221:y:2024:i:c:p:39-54
    DOI: 10.1016/j.matcom.2024.02.002
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