Artificial Compressibility Method Revisited: Asymptotic Numerical Method for Incompressible Flows

摘要

On the basis of the fact that the Lattice Boltzmann Method (LBM) essentially solves an artificial compressibility PDE system, an explicit numerical method for the incompressible Navier-Stokes equations without Poisson solver is developed. The scheme does not contain any kinetic ingredients, which is in contrast to LBM. By making use of the asymptotic behavior of solution of the compressible PDE system for small Mach numbers, high order accuracy (4th order in space and 2nd order in time) can be achieved, which is also demonstrated numerically.