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

William Layton; Hoang Tran; Xin Xiong

doi:10.1016/j.cam.2012.02.019

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

William Layton, Hoang Tran, Xin Xiong

Research output: Contribution to journal › Article › peer-review

48 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	3198-3217
Number of pages	20
Journal	Journal of Computational and Applied Mathematics
Volume	236
Issue number	13
DOIs	https://doi.org/10.1016/j.cam.2012.02.019
State	Published - Jul 2012
Externally published	Yes

Funding

The author WL had a stimulating E-mail exchange with Professor Jan Verwer in January 2011 on the Stokes–Darcy coupling. This exchange led to the consideration of splitting methods and the development of the ideas herein. We gratefully acknowledge our discussion with Professor Verwer which inspired our work. The work of WL, HT and XX was partially supported by NSF grant DMS 0810385 .

Funders	Funder number
National Science Foundation	DMS 0810385
Directorate for Mathematical and Physical Sciences	0810385

Keywords

Partitioned methods
Splitting methods
Stokes-Darcy coupling

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10.1016/j.cam.2012.02.019

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AU - Tran, Hoang

AU - Xiong, Xin

PY - 2012/7

Y1 - 2012/7

N2 - 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.

AB - 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.

KW - Partitioned methods

KW - Splitting methods

KW - Stokes-Darcy coupling

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JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 13

ER -

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

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