Long time stability of four methods for splitting the evolutionary Stokes–Darcy problem into Stokes and Darcy subproblems

摘要

This report analyzes the long time stability of four methods for non-iterative, sub-physics, uncoupling for the evolutionary Stokes–Darcy problem. The four methods uncouple each timestep into separate Stokes and Darcy solves using ideas from splitting methods. Three methods uncouple sequentially while one is a parallel uncoupling method. We prove long time stability of four splitting based partitioned methods under timestep restrictions depending on the problem parameters. The methods include those that are stable uniformly in S0, the storativity coefficient, for moderate kmin, the minimum hydraulic conductivity, uniformly in kmin for moderate S0 and with no coupling between the timestep and the spacial meshwidth.