Higher order methods for convectiondiffusion problems
Abstract
This paper applies C1 cubic Hermite polynomials embedded in an orthogonal collocation scheme to the spatial discretization of the unsteady nonlinear Burgers equation as a model of the equations of fluid mechanics. The temporal discretization is carried out by means of either a noniterative finite difference or an iterative finite difference procedure. Results of this method are compared with those of a secondorder finite difference scheme and a splinedcubic Taylor's series scheme. Stability limits are derived and the matrix structure of the several schemes are compared.
 Publication:

Computers and Fluids
 Pub Date:
 1985
 Bibcode:
 1985CF.....13..157M
 Keywords:

 Burger Equation;
 Computational Fluid Dynamics;
 Convective Flow;
 Diffusion Theory;
 Discrete Functions;
 Finite Difference Theory;
 Hermitian Polynomial;
 Boundary Value Problems;
 Collocation;
 Iterative Solution;
 Matrices (Mathematics);
 Orthogonality;
 Reynolds Number;
 Spline Functions;
 Taylor Series;
 Fluid Mechanics and Heat Transfer