Staggered finite element and finite volume method for suffusion simulation based on local conservation

Simulating suffusion involves computing both the seepage flow of pore water in soil and the transport of fine particles with pore water flow. Since the conventional finite element method (FEM) exhibits instability when used to solve the pure transport equations, a staggered method that employs FEM to solve the seepage equation and the finite volume method (FVM) for the particle transport equation is proposed. As conventional FEM cannot provide a locally conservative velocity field that satisfies the input requirement of FVM, an algorithm, based on the global re-balance of the element residual fluxes, is employed to correct the flow velocity at element boundaries. With this algorithm, the local conservation of the flow velocity computed by FEM at the element boundary is achieved. This enables FVM to solve the particle transport equation on the same FEM mesh, facilitating the convenient integration of FVM with existing FEM codes. Case studies demonstrate that the proposed local conservation algorithm and the staggered method exhibit high computational efficiency and acceptable accuracy, offering a straightforward and practical approach to simulating suffusion problems.