Space-Time Adaptive Solution of Richards' Equation
Abstract
Efficient, robust simulation of groundwater flow in the unsaturated zone remains computationally expensive, especially for problems characterized by sharp fronts in both space and time. Standard approaches that employ uniform spatial and temporal discretizations for the numerical solution of these problems lead to inefficient and expensive simulations. In this work, we solve Richards' equation using adaptive methods in both space and time. Spatial adaption is based upon a coarse grid solve and gradient-based error indicators, while the spatial step size is adjusted using a fixed-order approximation. Temporal adaption is accomplished using variable-order, variable-step-size approximations based upon the backward difference formulas up to fifth order. Since the advantages of similar adaptive methods in time are now established, we evaluate our method by comparison with a uniform spatial discretization that is adaptive in time for four different test problems. The numerical results demonstrate that the proposed method provides a robust and efficient alternative to standard approaches for simulating variably saturated flow.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2003
- Bibcode:
- 2003AGUFM.H11G0953A
- Keywords:
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- 1875 Unsaturated zone