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Second-order characteristic methods for advection–diffusion equations and comparison to other schemes

✍ Scribed by Mohamed Al-Lawatia; Robert C. Sharpley; Hong Wang

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 873 KB
Volume: 22
Category: Article
ISSN: 0309-1708
DOI: 10.1016/s0309-1708(98)00035-9

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✦ Synopsis

We develop two characteristic methods for the solution of the linear advection diusion equations which use a second order Runge±Kutta approximation of the characteristics within the framework of the Eulerian±Lagrangian localized adjoint method. These methods naturally incorporate all three types of boundary conditions in their formulations, are fully mass conservative, and generate regularly structured systems which are symmetric and positive de®nite for most combinations of the boundary conditions. Extensive numerical experiments are presented which compare the performance of these two Runge±Kutta methods to many other well perceived and widely used methods which include many Galerkin methods and high resolution methods from ¯uid dynamics.

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