Mass residuals in implicit finite volume models for overland and groundwater flow

Abstract

Summary A primary advantage in using the finite volume method for simulating groundwater flow and overland flow is the conservation property or the ability to conserve mass. However, when implicit finite volume methods are used with large time steps, small cell areas, or parameters with extreme value ranges, the conservation of mass equation becomes slightly unbalanced with a residual. Problems with large mass residuals can be predicted using the condition number of the solution matrix, and the convergence criterion used in the sparse matrix solver. The amount of practical guidance available on how to manage the magnitude of the mass residual or the matrix condition number is limited. To address this need, the current paper shows the usefulness of the mesh ratio. The mesh ratio is a dimensionless number that is a function of the mesh resolution and the temporal resolution. It is directly related to the condition number of the matrix, which in turn affects the mass residual and the model run time. During the current study, several numerical experiments are carried out to determine how the mesh ratio and the water level are related to the condition number, how the critical mesh ratio is related to the number of cells, how the run time is related to the mesh ratio, and how the mass residual is related to the mesh ratio. The results are useful in creating guidelines for mesh design during large-scale model applications. These guidelines can be applied to reducing the mass residual and the run time. The usefulness of the mesh ratio is illustrated using a Regional Simulation Model (RSM) (Lal, A.M.W., Van Zee, Randy, Belnap, Mark, 2005. Case study: model to simulate regional flow in South Florida. Journal of Hydraulic Engineering 131 (4), 247–258) application in south Florida.