A Fully Implicit Method for Fluid Flow Based on Vectorial Operator Splitting

摘要

A fully implicit finite difference method for the incompressible Navier-Stokes equations is presented that conserves mass, momentum, the square of velocity components, and, in the inviscid limit, kinetic energy.The method uses a staggered arrangement of velocity and pressure on a structured Cartesian grid and retains its conservation properties for both uniform and non-uniform grids.The convergence properties of the method are confirmed via numerical experiments.