HR: 1340h
AN: H33F-0536    [Abstracts]
TI: Local Discontinuous Galerkin Approximations And Variable Step Size, Variable Order Time Integration For Richards' Equation
AU: * Li, H
EM: huinali@email.unc.edu
AF: UNC, Dept. of Env. Sci. and Engr, University of North Carolina, Chapel Hill, NC 27759 United States
AU: Farthing, M W
EM: matthew_farthing@unc.edu
AF: UNC, Dept. of Env. Sci. and Engr, University of North Carolina, Chapel Hill, NC 27759 United States
AU: Dawson, C N
EM: clint@ices.utexas.edu
AF: UT-AUSTIN, Institute for Computational Engineering and Sciences, University of Texas, Austin, TX 78712 United States
AU: Miller, C T
EM: casey_miller@unc.edu
AF: UNC, Dept. of Env. Sci. and Engr, University of North Carolina, Chapel Hill, NC 27759 United States
AB: Numerical simulation of Richards' equation continues to be difficult. It is highly nonlinear under common constitutive relations and exhibits sharp fronts in both the pressure head and volume fraction for many problems of interest. For a number of multiphase flow problems, the use of variable order and variable step size temporal discretizations has shown some advantages. However, the spatial discretizations commonly used for variably saturated flow are dominated by nonadaptive, low-order finite difference and finite element methods. Discontinuous Galerkin (DG) finite element methods have received significant attention in a number of fields for hyperbolic PDE's and, more recently, for elliptic and parabolic problems. DG approaches like the local discontinuous Galerkin (LDG) method are appealing for modeling subsurface flow since they can lead to velocity fields that are locally mass-conservative without the need for auxiliary variables or alternative meshes. DG discretizations are also inherently local and so better-suited for unstructured meshes and $h$-$p$ adaption strategies than traditional methods. While some work has been done recently for multiphase subsurface flow, there are a range of issues related to the performance of DG methods for highly nonlinear parabolic problems like Richards' equation that have not been investigated fully. In this work, we consider the combination of higher order adaptive time integration with an LDG spatial discretization for Richards' equation. We compare this approach to standard low-order methods for a series of test problems and consider a number of issues including the methods' relative accuracy and computational efficiency.
DE: 1829 Groundwater hydrology
DE: 1875 Unsaturated zone
SC: Hydrology [H]
MN: 2004 AGU Fall Meeting