Higher order methods for convection-diffusion 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 second-order finite difference scheme and a splined-cubic 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