A hybrid penalty-pseudocompressibility method for transient incompressible fluid flow

A numerical method is described for performing time-accurate transient incompressible fluid flow calculations. The method is a hybrid or combination of the penalty (P) and pseudocompressibility (PC) methods. It therefore possesses both the parabolic (diffusional) character of the P method and the hyperbolic (wave-like) character of the PC method. The parabolic character provides rapid damping of short-wavelength disturbances, while the hyperbolic character permits rapid equilibration of long-wavelength components. The relative proportions of the P and PC methods in the hybrid method are controlled by a parameter χ which is essentially the PC:P ratio. The mathematical character of the method permits the use of purely explicit numerical schemes, which are well-suited to vector and parallel processing. Such a scheme has been used to perform systematic studies of solution error as a function of χ for several different error measures in two different test problems: (1) the driven cavity; and (2) flow past a rectangular obstacle. Minimum error is generally obtained for values of χ near unity, corresponding to a roughly equal admixture of the P and PC methods. These studies show that the hybrid method performs significantly better than either the P or PC method alone: it is more accurate for given computer time, and reduces computer time for given accuracy. The method is very simple and easy to implement, and requires only trivial modifications to existing P or PC computer programs.