On several numerical strategies to solve Richards' equation in heterogeneous media with finite volumes

We propose several numerical approaches building on upstream mobility two-point flux approximation finite volumes to solve Richards' equation in domains made of several rock-types. Our study encompasses four different schemes corresponding to different ways to approximate the nonlinear transmission condition systems arising at the interface between different rocks consisting in the continuity of the pressure and the fluxes, as well as different resolution strategies based on Newton's method with variable switch. We benchmark the robustness and accuracy of the different methods on filling and drainage test cases with standard nonlinearities of Brooks-Corey and van Genuchten-Mualem type, as well as with challenging steep nonlinearities.

Automated summary

This study proposes several numerical approaches using upstream mobility two-point flux approximation finite volumes to solve Richards' equation in domains made of several rock-types. The methods are benchmarked on filling and drainage test cases with standard nonlinearities and challenging steep nonlinearities.