Evaluation of Hopscotch Method for Transient Ground-Water Flow

Abstract

The hopscotch finite-difference technique is shown to be a fast and accurate way to simulate transient, saturated, ground-water flow in relatively typical but heterogeneous 2D and 3D domains. The odd-even hopscotch (OEH) and line hopscotch methods are reviewed, and their implementation for saturated ground-water flow is presented. The OEH scheme, which is a second-order accurate explicit process, is efficient, requiring only six floating point operations per mesh node and time step, and is unconditionally stable (for saturated ground-water flow). Numerical experiments on typical 2D meshes (2,500 nodes) with synthetic, randomly heterogeneous hydraulic conductivity, suggest that the OEH process is approximately 1.5 times faster than the alternating direction implicit method and 3–4 times faster than the Crank-Nicolson implicit method using preconditioned conjugate gradient iteration. Similar experiments on medium-sized 3D meshes (87,500 nodes) suggest that the OEH process is between 7 and 10 times faster than the Crank-Nicolson preconditioned conjugate gradient method. Although the numerical results presented illustrate only typical test problem performance, they nevertheless clearly indicate promise for using OEH to simulate transient ground-water flow in 2D and, especially, 3D heterogeneous domains requiring fine spatial meshes.