A variable timestepping algorithm for the unsteady Stokes/Darcy model

TL;DR

This paper applies a historical variable step time discretization algorithm to the unsteady Stokes/Darcy model, demonstrating its unconditional stability and accuracy through theoretical analysis and numerical experiments.

Contribution

It introduces the use of a forgotten variable timestep algorithm for the unsteady Stokes/Darcy model, proving its stability and error properties.

Findings

The algorithm is unconditionally stable for the model.

Numerical results confirm the theoretical stability and accuracy.

Variable timestep analysis benefits fluid flow simulations.

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.