Consideration of artificial compressibility for explicit computational fluid dynamics simulation

In this paper, we discuss the theoretical interpretation of the artificial compressibility method (ACM) to propose a new explicit method for the unsteady numerical simulation of fluid flow. The proposed method employs the compressible continuity and Navier–Stokes equations, which facilitates the replacement of pressure as one of the major variables with density, theoretically backed by virtual particle concept. This new concept justifies the theoretical treatment assuming the speed of sound in ACM as a model parameter determined by the grid system. More importantly, the present method realizes, in a fully explicit manner, the solving of a set of equations, which prevents the solving of the Poisson equation of pressure. The new method was validated and proven by comparing the results of two-dimensional cavity flow between the proposed method, conventional incompressible method, and the Lattice–Boltzmann method with varying Reynolds numbers (100, 1000, and 10000). The results of the proposed method agree well with conventional and reference data for both steady-state and unsteady-state conditions, although slight numerical oscillations were observed for the proposed method at a Reynolds number of 10000. Thus, the numerical validation assures that the proposed method is an explicit method based on a solid theoretical ground to be a new efficient simulation framework.