A New Finite-Volume Method for Convection-Diffusion Problems in Arbitrary Triangulations

Abstract

A Finite Volume Method has been applied for many years to the solution of convection-diffusion problems. Linear shape functions have proven to be inapplicable at even moderate Peclet numbers, and particular shape functions for triangular elements have been proposed by other authors to overcome this limitation. It is shown here that these functions lead to physically unrealistic approximations, are also have poor numerical behavior, when applied to elements with obtuse angles.
A new shape function that overcomes the aformetioned difficulties is proposed. Theorical and numerical results are shown. It can be concluded that the new method produces realistic approximations whatever the shape of the elements, and shows a very good numerical behavior. It can handle successfully arbitrary triangulations, thus making very much easier the work of designing a grid.