The Hopscotch Method for Simulating Transient Well Tests
Abstract
Simulating well tests in complex heterogeneous aquifers can be computationally intensive, with computer run times that try even the most patient investigator. This issue can be particularly severe where many simulations are required to solve transient inverse problems. The so-called Odd-Even Hopscotch (OEH) method is a numerical technique that may offer some significant reduction in the time required to solve transient flow problems, and so it may improve the ability to analyze transient well tests. The hopscotch method is an explicit finite difference technique that gets its name from the pattern of nodes used during execution. This method can be faster than many widely used solvers because fewer operations are required per mesh node. For example, 8 FLOPS are required per node at each time step for the hopscotch method compared to 14 FLOPS per node for the Crank-Nicolson implicit method using preconditioned conjugate gradient iteration. The hopscotch method is second-order accurate and unconditionally stable for the transient saturated ground water flow problem. Storage space is used efficiently by overwriting a single array of heads and boundary values during each time step. Transient analyses of a pumping well in 2-D and 3-D randomly heterogeneous, spatially correlated media were conducted using the odd-even hopscotch (OEH), alternating direction implicit (ADI), and Crank-Nicolson PCG methods. Time steps for the methods were adjusted so that the accuracy of the results was similar. Preliminary results for the 2-D problems indicate that the OEH method is about 1.5 times faster than the ADI method and 3 to 4 times faster than the Crank-Nicolson PCG method on an equal accuracy basis. The real payoff appears to come with 3-D problems, however. Results indicate that the hopscotch method is between 7 and 10 times faster than the Crank-Nicolson PCG method for the particular test cases used in the evaluation. The OEH technique has seen limited application in the ground water field. Preliminary evaluation suggests that this method should be well suited for adapting as a solver for MODFLOW. Including the OEH method as an option for MODFLOW should make this fast solver readily accessible for analyzing well tests and other transient ground water problems.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2001
- Bibcode:
- 2001AGUFM.H21A0283H
- Keywords:
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- 1829 Groundwater hydrology