When studying non-linear (higher order MUSCL type) nite volume approximation of a linear convection diiusion problem, one is confronted with a question whether the corresponding nonlinear discrete problem is solvable. In this contribution we note that the corresponding discrete problem L h u h = f h in two dimensions in general need not to possess a solution. However, we show that to every righ...

In this article, an algorithm for the numerical approximation of two-phase flow in porous media by adaptive mesh is presented. A convergent and conservative finite volume scheme for an elliptic equation is proposed, together with the finite difference schemes, upwind and MUSCL, for a hyperbolic equation on grids with local refinement. Hence, an IMPES method is applied in an adaptive composite g...

 Abstract—The cylindrically converging shock wave was numerically simulated by solving the Euler equations in cylindrical coordinates with TVD scheme and MUSCL [1] approach, using Roe's approximate Riemann solver [2] and super-bee nonlinear limiter [3]. The present study used the in house code developed for this purpose. The behavior of the solution in the vicinity of axis is investigated and ...