An adaptive quadtree grid generation algorithm is developed and applied for tracer and multiphase flow in channelized heterogeneous porous media. Adaptivity was guided using two different approaches. In the first approach, wavelet transformation was used to generate a refinement field based on permeability variations. The second approach uses flow information based on the solution of an initial...

In an adaptive grid, the physics of the problem at hand must ultimately direct the grid points to distribute themselves so that a functional relationship on these points can represent the physical solution with sufficient accuracy. The idea is to have the grid points move as the physical solution develops, concentrating in regions of large variation in the solution as they emerge. The mathemati...

I describe an adaptive h-reenement method for solving systems of parabolic partial diierential equations in three space dimensions on hexahedral grids. These grids typically have irregular (hanging) nodes. Solutions are calculated using Galerkin's method with a piecewise trilinear basis in space and a BDF code in time. New a posteriori error indicators based on interpolation error estimates for...

Two distinct redistribution grids - adaptation techniques, spring analogy and elliptic grid generator are applied to two-dimensional steady, inviscid, shocked flows, and the ability of each technique is examined and compared. Euler equations are solved base on Roe's Reimann solver approach to simulate supersonic flow around a sphere, transonic flow about an airfoil and supersonic flow in a symm...

Composite adaptive grid (CAG) methods for solving hyperbolic partial differential equations (PDE's) are discussed in this paper. Composite grids are used at the coarsest level to deal with domains with complicated geometries. Stair step grids developed for composite grids are also used in the ner levels to cover reened regions. New data structures for stair step grids are proposed and implement...

Desktop grids are usually equipped with hundreds or thousands of desktops which use the idle cycles of desktop PCs of small enterprises and institutions. From conventional multi -site cluster grids, desktop grids vary markedly in terms of their dynamic nature. In terms of their dynamic nature such grids vary markedly from conventional grids] . This causes the need of new scheduling algorithms ,...

This paper presents a numerical entropy production (NEP) scheme for two-dimensional shallow water equations on unstructured triangular grids. We implement NEP as the error indicator for adaptive mesh refinement or coarsening in solving the shallow water equations using a finite volumemethod. Numerical simulations show thatNEP is successful to be a refinement/coarsening indicator in the adaptive...

Discretizations based on unstructured grids have been widely used in other scientific disciplines for modeling problems bounded by complex geometries. Solution-adaptive techniques are relatively easy to implement on unstructured grids and in addition they provide a convenient way to model the multi-scale spanning nature of atmospheric flows. This paper describes the implementation of a higher-o...

In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the p...