Numerical inversion of heat exchange coefficient and source sink term for a thermal-fluid coupled model in porous medium

Abstract

In this paper, we focus on three inverse problems for a coupled model from temperature-seepage field in high-dimensional spaces. These inverse problems aim to determine an unknown heat transfer coefficient and a source sink term in seepage continuity equation with specified initial-boundary conditions and additional measurements. Some finite difference schemes of coupled equations are presented and analyzed.Three algorithms for these inverse problems are proposed. Some numerical experiments are provided to assert the accuracy and efficiency of proposed algorithms.

Keywords:

• Inverse problems
• thermal-fluid coupled model
• numerical approximation
• finite difference scheme

AMS Subject Classifications:

• 35R30
• 65M30
• 65M32

Acknowledgements

The authors thank the editor and the reviews for their valuable comments and useful suggestions.

Additional information

Funding

This study was financially supported by grants from the National Natural Science Foundation of China [grant number 11561003], [grant number 11471287]; Science and Technology Foundation of Education Office of Jiangxi Province [grant number GJJ150590]; Opening Fund from Fundamental Science on Radioactive Geology and Exploration Technology Laboratory of ECUT [grant number REGT1210].