A mass-conserved domain decomposition method for the unsaturated soil flow water problem
Abstract In this paper, an efficient mass conservative domain decomposition method is developed for solving the unsaturated soil water flow over non-overlapping multiple sub-domains. In the first step, the predicted interface fluxes are computed by the semi-implicit flux scheme. In the second step,...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-07-01
|
| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2213-2 |
| Summary: | Abstract In this paper, an efficient mass conservative domain decomposition method is developed for solving the unsaturated soil water flow over non-overlapping multiple sub-domains. In the first step, the predicted interface fluxes are computed by the semi-implicit flux scheme. In the second step, the interior water content and fluxes in the interiors are computed by the coupled solution and flux implicit scheme. The interface fluxes are finally recomputed by the implicit scheme. The important features of our proposed scheme are mass conserved and unconditionally stable by defining global fluxes which contain the diffusivity and hydraulic conductivity. We prove that the scheme has the error estimate of O(Δt+(Δz)2+(Δt)2(Δz)32) $O(\Delta t+(\Delta z)^{2}+\frac{(\Delta t)^{2}}{(\Delta z)^{ \frac{3}{2}}})$ in L2 $L^{2}$-norm. |
|---|---|
| ISSN: | 1687-1847 |