Showing papers by "Nils Henrik Risebro published in 1992"

Solution of the Cauchy problem for a conservation law with a discontinuous flux function

Abstract: The Cauchy problem is solved for a conservation law arising in oil reservoir simulation where the flux function may depend discontinuously on the space variable. To do this front tracking is used as a method of analysis.

A New Front-Tracking Method for Reservoir Simulation

Abstract: This paper reports on the standard nonlinear, partial-differential equations that describe flow in porous media which can be separated into a pressure equation and saturation equations. If the diffusion term is ignored, the saturation equations describe a physical problem where sharp discontinuities in the physical data are possible. Finite-difference methods used to solve these equations typically exhibit numerical dispersion. They also show numerical stability problems so that very short timesteps may be required. Use of an implicit formulation can reduce this limitation of the timestep length, but this will not solve the numerical dispersion problem. New methods in the field of hyperbolic conservation laws have led to alternative solution procedures for the saturation equations. A simulator based on an implicit pressure, explicit saturation (IMPES) formulation and these methods is under development. The goal of this development work is a 3D, three-phase simulator. In this reservoir simulator, the pressure equation is solved by a finite-element method (FEM). The grid for the pressure equation can therefore be fitted to the reservoir geometry and the geometry of the sharp discontinuities in the saturations with great flexibility. The linear equation system is solved with a preconditioned conjugate-gradient method.