A modification of the artificial compressibility algorithm with improved convergence characteristics

Abstract

SUMMARYThe artificial compressibility algorithm has a significant drawback in the difficulty of choosing the artificial compressibility parameter, improper choice of which leads either to slow convergence or divergence. A simple modification of the equation for pressure in the artificial compressibility algorithm which removes the difficulty of choosing the artificial compressibility parameter is proposed. It is shown that the choice of the relaxation parameters for the new algorithm is relatively straightforward, and that the same values can be used to provide robust convergence for a range of application problems. This new algorithm is easily parallelized making it suitable for computations such as direct numerical simulation (DNS) which require the use of distributed memory machines. Two key benchmark problems are studied in evaluating the new algorithm: DNS of a fully developed turbulent channel flow, and DNS of a driven-cavity flow, using both explicit and implicit time integration schemes. The new algorithm is also validated for a more complex flow configuration of turbulent flow over a backward-facing step, and the computed results are shown to be in good agreement with experimental data and previous DNS work.

CFD Optimization of a Vegetation Barrier

“…The choice of the parameter β is discussed e.g. in [10], here we have used β = 1000. The resulting set of equations is discretized using the finite volume method on unstructured grid.…”

Analysis of artificial pressure equations in numerical simulations of a turbulent channel flow

“…In that case, the system is for each physical timestep iterated in pseudo-time until convergence. This approach has been followed by various authors [42,31,48,39,1,41,36]. A review on the error analysis of artificial compressibility methods is given by Shen [57].…”