Evaluation of hopscotch method for transient ground-water flow

The hopscotch finite-difference technique is shown to be a fast and accurat e way to simulate transient, saturated, ground-water flow in relatively typ ical but heterogeneous 2D and 3D domains. The odd-even hopscotch (OEH) and line hopscotch methods are reviewed, and their implementation for saturated groundwater flow is presented. The OEH scheme, which is a second-order acc urate explicit process, is efficient, requiring only six floating point ope rations per mesh node and time step, and is unconditionally stable (for sat urated ground-water flow). Numerical experiments on typical 2D meshes (2,50 0 nodes) with synthetic, randomly heterogeneous hydraulic conductivity, sug gest that the OEH process is approximately 1.5 times faster than the altern ating direction implicit method and 3-4 times faster than the Crank-Nicolso n implicit method using preconditioned conjugate gradient iteration. Simila r 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 precondit ioned conjugate gradient method. Although the numerical results presented i llustrate only typical test problem performance, they nevertheless clearly indicate promise for using OEH to simulate transient ground-water flow in 2 D and, especially, 3D heterogeneous domains requiring fine spatial meshes.