A Triangular Finite Volume Approach With High‐Resolution Upwind Terms for the Solution of Groundwater Transport Equations

A finite volume approach is developed for the solution of the contaminant transport equation in groundwater. By defining a triangular control volume over which the dependent variable of the governing equation is averaged, the scheme combines the flexibility in handling complex geometries intrinsic to finite element methods with the simplicity of finite difference techniques. High‐resolution upwind schemes are employed for the discretization of the advective terms. The technique is based on the concept of “monotone interpolation” to ensure the monotonicity preserving property of the scheme, and on the exact solution of local Riemann problems at the interface between neighboring control volumes. In this way, numerical oscillations are completely avoided for a full range of cell Peclet numbers. Together with the discretization of the dispersive fluxes, an approximation is obtained that is locally first order, but globally of second‐order accuracy. As compared to usual upwind schemes, much smaller amounts of numerical viscosity are introduced when sharp concentration fronts occur. A number of numerical tests show good agreement with analytical solutions. A hypothetical problem involving nonequilibrium reaction terms is solved to illustrate the applicability and robustness of the proposed formulation for solving the groundwater transport equations.