Localized Collocation Method for Transport and Transport-like Equations



F. Fedele,   G.F. Pinder,   J.P. Laible,   L. Wu

Abstract

An apparently new numerical technique based upon a localized form of the collocation method executed using Lagrange quadratic polynomials exhibits the ability to very accurately solve the convection dominated transport equation. Using an unique upstream-weighting strategy, an approximating equation can be generated that exhibits remarkably little numerical dispersion or diffusion. As a result sharp fronts can be propagated more accurately than is the case with other widely used finite-element and finite-difference techniques. In spite of its enhanced accuracy, the proposed algorithm requires essentially the same computational effort as alternative classical methods.