Meshfree iterative stabilized Taylor–Galerkin and characteristic-based split (CBS) algorithms for incompressible N–S equations

Abstract

This paper presents two stabilized schemes of the fractional step algorithm using characteristic-based split and Taylor–Galerkin like based split respectively in the meshfree context. An iterative procedure which makes the convective term satisfy the momentum conservation equation in an implicit sense is introduced into the two schemes to allow much larger time step sizes. A modified version of finite increment calculus process for incompressibility stabilization is developed to avoid the calculation of high order spatial derivatives. Numerical experiments demonstrate the capability and stability of the proposed schemes of the meshfree-based fractional step method in the simulation of incompressible flows.