Artificial Compressibility Method

Abstract

The artificial compressibility method is quite different from the pressure projection approach in both the nature of the formulation and the subsequent numerical algorithm. In an artificial compressibility method, a fictitious time derivative of pressure is added to the continuity equation so that the set of equations modified from the incompressible Navier-Stokes equations can be solved implicitly by marching in pseudo time. When a steady-state solution is reached, the original equations are recovered. To obtain time accuracy, an iterative technique can be employed at each time level, which is equivalent to solving the governing equations for steady state at each time level. Using a large, artificial compressibility parameter to spread artificial waves quickly throughout the computational domain, and allowing some residual level of the mass conservation equation, the computing time requirement for time accurate solutions may be controlled within approximately one order-of-magnitude higher than the steady-state computations. In the artificial compressibility approach, the mass conservation does not have to be strictly enforced at each time step, and this gives robustness during iteration.