A variable timestepping algorithm for the unsteady Stokes/Darcy model

2020/07/07 by Yi Qin, Qin, Yi, Yanren Hou +3 · 3 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2007.03801

openalex publication_date 2020/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This report considers a variable step time discretization algorithm proposed by Dahlquist, Liniger and Nevanlinna and applies the algorithm to the unsteady Stokes/Darcy model. Although long-time forgotten and little explored, the algorithm performs advantages in variable timestep analysis of various fluid flow systems, including the coupled Stokes/Darcy model. The paper proves that the approximate solutions to the unsteady Stokes/Darcy model are unconditionally stable due to the G-stability of the algorithm. Also variable time stepping error analysis follows from the combination of G-stability and consistency of the algorithm. Numerical experiments further verify the theoretical results, demonstrating the accuracy and stability of the algorithm for time-dependent Stokes/Darcy model.

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