Temporal and spatial discretization on quasi-3-D groundwater finite element modelling to avoid spurious oscillation

In this article, the finite element solution of quasi-three-dimensional (quasi-3-D) groundwater flow was mathematically analyzed. The research shows that the spurious oscillation solution to the Finite Element Model (FEM) is the results choosing the small time step Δt or the large element size L and using the non-diagonal storage matrix. The mechanism for this phenomenon is explained by the negative weighting factor of implicit part in the discretized equations. To avoid spurious oscillation solution, the criteria on the selection of Δt and L for quasi-3-D groundwater flow simulations were identified. An application example of quasi-3-D groundwater flow simulation was presented to verify the criteria. The results indicate that temporal discretization scale has significant impact on the spurious oscillations in the finite-element solutions, and the spurious oscillations can be avoided in solving practical quasi-3D groundwater flow problems if the criteria are satisfied.