Implementation of Artificial Compressibility Method for Steady and Unsteady Incompressible Flows Based on Finite Volume Method of Unstructured Grids

Abstract

The development of a new computational fluid dynamics solver for simulating incompressible flows is described. Unlike traditional pressure-based solvers, the artificial compressibility method simulates both steady and unsteady states. Some classical numerical examples are used to validate the solvers. These findings show that the artificial compressibility method’s LES/DNS and steady flow simulations are competitive with the best previously reported methods. The following characteristics make this paper unique: (1) We implement the artificial compression method in OpenFOAM for the first time and show the detailed mathematical process of the algorithm so that readers can easily reproduce and improve it; (2) steady flow simulation case, the convergence time of the present method is 52% of the pressure base solver; (3) to accelerate the convergence rate of each time step to the incompressible state, the L-stable Singly Diagonal Implicit Runge-Kutta method is introduced into the pseudo-time advance, which enlarges the limit of maximum Courant number to accelerate convergence.