Research papersA domain decomposed finite element method for solving Darcian velocity in heterogeneous porous media

- DDFEM is a combination of domain decomposition technique and Yeh's FEM model.
- DDFEM breaks velocity computation down to subproblems, so it has high efficiency.
- DDFEM can effectively deal with arbitrarily oriented or intersected interface.
- DDFEM is more efficient than classical methods, and it is mass balance.
- DDFEM can ensure the velocities satisfy the refraction law at material interfaces.

This paper proposes a domain decomposed finite element method (DDFEM) for groundwater flow velocity simulation, which can effectively and efficiently deal with arbitrarily oriented or intersected material interfaces in heterogeneous porous media. The main idea of this problem is to employ domain decompose technique to break the velocity problem down to subproblems by material interfaces, thereby achieving high accuracy at interface nodes and improving the velocity computation efficiency. By solving the global flow field by FEM before velocity computation, this method can capture the global information of the whole study region so as to ensure the subproblem solution accuracy by Yeh's model. After one subproblem has been solved, the DDFEM employs refraction law to obtain the Dirichlet boundary velocities of the adjacent subdomains. Numerical examples have been done to demonstrate the applicability and accuracy of the proposed method. Comparison between the DDFEM and two classical methods shows that the DDFEM can indeed save much computational cost, while achieving high accuracy.