CSE Seminar
SPEAKER: Daniil Svyatskiy,
Los Alamos National Laboratory
TITLE:
Nonlinear Monotone Finite Volume Method for Anisotropic Diffusion
Problems
DATE: Wednesday, November 14, 2007
TIME: 12:00 Noon
PLACE: 2240 DCL
1304 W. Springfield Ave., Urbana, IL
ABSTRACT
Predictive numerical simulations of subsurface processes require not
only more sophisticated physical models but also more accurate and
reliable discretization methods for these models. The discretization
methods used in existing simulations fail to preserve positivity of a
continuum solution of the pressure equation when the porous media is
heterogeneous and anisotropic or the computational mesh is strongly
perturbed to resolve complex geological structures. A negative discrete
solution implies non-physical Darcy velocities and hence wrong
prediction of a contaminant transport. Also, the complexity of the
subsurface physics results in using of upscaled coefficients and coarse
meshes which only amplify problems of existing discretization methods.
In our research we study new monotone finite volume discretization
methods that guarantee positivity of the discrete solution for
unstructured meshes and strongly heterogeneous anisotropic diffusion
tensors. The methods are based on the nonlinear flux formula proposed
by C. Le Potier in 2005. We gave the first proof of monotonicity of the
new finite volume methods for a stationary diffusion problem. We also
developed new monotone methods for shape-regular polygonal meshes and
heterogeneous isotropic diffusion coefficients. All new methods are
locally conservative, second-order accurate for smooth solutions, and
have compact discretization stencils.