The use of wavelet transformations in the solution of two-phase flow problems
- Lawrence Berkeley Lab., CA (United States)
- Texas A and M Univ., College Station, TX (United States)
In this paper the authors present the use of wavelets to solve the non-linear Partial Differential Equation (PDE) of two-phase flow in one dimension. The wavelet transforms allow a drastically different approach in the discretization of space. In contrast to the traditional trigonometric basis functions, wavelets approximate a function not by cancellation but by placement of wavelets at appropriate locations. When an abrupt change, such as a shock wave or a spike, occurs in a function, only local coefficients in a wavelet approximation will be affected. The unique feature of wavelets is their Multi-Resolution Analysis (MRA) property, which allows seamless investigation at nay spatial resolution. The use of wavelets is tested in the solution of the one-dimensional Buckley-Leverett problem against analytical solutions and solutions obtained from standard numerical models. Two classes of wavelet bases (Daubechies and Chui-Wang) and two methods (Galerkin and collocation) are investigated. The authors determine that the Chui-Wang wavelets and a collection method provide the optimum wavelet solution for this type of problem. Increasing the resolution level improves the accuracy of the solution, but the order of the basis function seems to be far less important. The results indicate that wavelet transforms are an effective and accurate method which does not suffer from oscillations or numerical smearing in the presence of steep fronts.
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 153093
- Report Number(s):
- CONF-950206-; TRN: IM9602%%185
- Resource Relation:
- Conference: Symposium on reservoir simulation, San Antonio, TX (United States), 12-15 Feb 1995; Other Information: PBD: 1995; Related Information: Is Part Of 13. Symposium on reservoir simulation: Proceedings; PB: 572 p.
- Country of Publication:
- United States
- Language:
- English
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