Second-order accurate monotone finite volume scheme for Richards’ equation. (English) Zbl 1284.76269
Summary: In this work we perform a theoretical and numerical analysis of Richards’ equation. For certain types of nonlinearities we provide explicit analytical solutions. These solutions are used to show that conventional unconditionally monotone finite volume schemes have only first-order accuracy. We derive necessary and sufficient conditions for the monotonicity of finite volume discretizations and use these conditions to construct a monotone finite volume discretization accurate to second-order.
MSC:
76M12 | Finite volume methods applied to problems in fluid mechanics |
65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
35D30 | Weak solutions to PDEs |
35A16 | Topological and monotonicity methods applied to PDEs |