ABSTRACT
The term finite volume method appears to have been coined in the early 1970’s for discretisations of the full potential equation of gas dynamics which is given by Bernoulli’s equation. Various techniques for adapting a difference scheme according to the solution have been developed for both unsteady hyperbolic conservation laws and also for the steady convection-diffusion problems with which we are presently concerned. There is much in common between the two situations; yet there seems to have been relatively little interaction between the two fields. In finite volume methods, difficulties in imposing or proving coercivity properties are often attributed to the presence of spurious solution modes, or inadequate control of them. Artificial dissipation terms are normally used to control these spurious modes. A. Jameson has studied the use of Runge-Kutta methods in conjunction with multigrid methods where their damping properties are particularly important.
