Abstract:We develop and analyze high-order ensemble schemes for the unsteady Navier--Stokes--Darcy system with uncertain initial conditions, forcing terms, hydraulic conductivity tensors, and Lions-Beavers-Joseph-Saffman interface conditions. The proposed schemes which are called GSAV-GBDF$k$-Ensemble schemes integrate a partitioned decoupling strategy, the generalized scalar auxiliary variable (GSAV) approach, and generalized BDF$k$ discretizations. This framework achieves high-order temporal accuracy and long-time stability, permits explicit treatment of the nonlinear term, and facilitates an efficient ensemble implementation for multiple parameter realizations by sharing a single, unified coefficient matrix at each time step. Moreover, the numerical solutions are shown to satisfy uniform-in-time bounds without time-step restrictions. Owing to the ensemble formulation, the resulting linear systems share common coefficient matrices, which significantly improves computational efficiency. We further establish optimal-order error estimates for the proposed high-order schemes. Numerical results are included to confirm the theoretical analysis and to illustrate the accuracy, stability, and efficiency of the proposed methods.
From: Weiwei Han [view email]
[v1]
Fri, 22 May 2026 07:03:19 UTC (777 KB)
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