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Numerical investigation of dynamic capillary pressure in two-phase flow in porous medium

Radek Fučík, Jiří Mikyška (2011)

Mathematica Bohemica

In order to investigate effects of the dynamic capillary pressure-saturation relationship used in the modelling of a flow in porous media, a one-dimensional fully implicit numerical scheme is proposed. The numerical scheme is used to simulate an experimental procedure using a measured dataset for the sand and fluid properties. Results of simulations using different models for the dynamic effect term in capillary pressure-saturation relationship are presented and discussed.

On monotone and Schwarz alternating methods for nonlinear elliptic PDEs

Shiu-Hong Lui (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method...

On Monotone and Schwarz Alternating Methods for Nonlinear Elliptic PDEs

Shiu-Hong Lui (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method...

On multi-parameter error expansions in finite difference methods for linear Dirichlet problems

Ta Van Dinh (1987)

Aplikace matematiky

The paper is concerned with the finite difference approximation of the Dirichlet problem for a second order elliptic partial differential equation in an n -dimensional domain. Considering the simplest finite difference scheme and assuming a sufficient smoothness of the domain, coefficients of the equation, right-hand part, and boundary condition, the author develops a general error expansion formula in which the mesh sizes of an ( n -dimensional) rectangular grid in the directions of the individual...

Currently displaying 101 – 120 of 195