Characteristic Finite Difference Method Research Articles

Domain decomposition with characteristic finite difference method for two-phase displacement problems

Domain decomposition difference schemes modified with characteristic method are presented for two-phase displacement. The pressure equation is discretized by a five-point difference procedure. To compute in parallel, the saturation equation is treated by domain decomposition difference schemes with characteristic approximation, which rely on implicit procedures in subdomains and one-dimensional calculation on the inter-domain boundaries. Error analysis in discrete l 2 -norm is discussed. Finally, numerical examples illustrating the theoretical accuracy ant parallelism are shown.

Characteristic finite element scheme and analysis the three-dimensional two-phase displacement semi-definite problem

NUMERICAL simulation of the two-phase (oil and water) displacement problem is the mathematical basis of energy sources. For two-dimensional positive problem, Douglas et al. put forward the well-known characteristic finite difference method and characteristic finite element method. However, for numerical analysis there exist some difficulties. They assumed that the problem is periodic and the diffusion matrix of the concentration equation is positive difinite in

The Characteristic Finite Difference Methods for Enhanced Oil Recovery Simulation and L 2 Estimates

A 2-dimensional, multicomponent, multiphase, and incompressible compositional reservoir simulator has been developed and applied to chemical flooding (surfactants, alcohol and polymers) and convergence analysis. The characteristic finite difference methods for 2-dimensional enhanced oil recovery can be described as a coupled system of nonlinear partial differential equations. For a generic case of the cross interference and bounded region, we put forward a kind of characteristic finite difference schemes and make use of thick and thin grids to form a complete set, and of calculus of variations, the theory of prior estimates and techniques. Optimal order estimates in L 2 norm are derived for the error in the approximate solutions. Thus we have thoroughly solved the well-known theoretical problem proposed by a famous scientist, J. Douglas, Jr.

On the Convergence of Finite-Differenced Multigroup, Discrete-Ordinates Methods for Anisotropically Scattered Slab Media

A convergence analysis is provided for the multigroup, discrete-ordinates method used to numerically solve the linear transport equation for anisotropically scattering, subcritical slab media. Characteristic finite-difference methods for discretizing the spatial variable are considered. The multigroup fluxes are shown to converge in a Banach space setting under realistic smoothness conditions on the solution to the linear transport equation. This is the first thorough convergence analysis for the fully discretized multigroup slab transport equations.

A Characteristic Finite Difference Method for the Wave Equation in Two Dimensions

The equations of a hyperbolic, first order system relate derivatives tangent to characteristic surfaces in space-time. Although mesh cubes with characteristic faces have not previously been used in more than one space dimension, they do provide a natural setting for solution by difference methods. Simple centering ensures second order accuracy. Sufficient conditions for the stability of such difference approximations have been derived for the two-dimensional case. The conditions are found to restrict the relative orientations of the characteristic planes and also the values of adjustable coefficients. A one-parameter family of differential systems representing the wave equation in two dimensions and leading to a stable, explicit difference approximation is presented.