Numerical modeling with a moving coordinate system: Application to flow through porous media
Abstract
A numerical technique for solving convective diffusive equations is developed. Convective diffusive equations arise from mass conservation relations in flow through porous media. An analysis and comparison of numerical methods are performed. Criteria are given for the spatial mesh size to eliminate the oscillations for weighted residual methods. The solution technique developed minimizes the oscillations. The differential equations are transformed into a moving coordinate system with a time dependent velocity, which eliminates the influence of the convective term, but makes the boundary location change in time. Both linear and nonlinear, one and two dimensional equations are solved with physically realistic parameters. Methods for determining the moving coordinate system velocity and changing the location of the boundary conditions are described. Orthogonal collocation on finite elements, finite difference, and the Galerkin finite element method are applied. Several integration schemes including variable timestep schemes are used. Comparisons of the accuracy and the solution cost to exact solutions and schemes with a fixed coordinate system are made.
 Publication:

Ph.D. Thesis
 Pub Date:
 1980
 Bibcode:
 1980PhDT........21J
 Keywords:

 Convective Flow;
 Diffusion;
 Mathematical Models;
 Oil Recovery;
 Porous Materials;
 Finite Difference Theory;
 Flow Velocity;
 Fluid Boundaries;
 Numerical Analysis;
 Fluid Mechanics and Heat Transfer