Characteristic based split (CBS) meshfree method modeling for viscoelastic flow

A semi-implicit characteristic based split meshfree algorithm is proposed for the numerical solution of incompressible viscoelastic flow in the paper, in which the governing equations are discretized by element free Galerkin method in spatial space and the characteristic based split method is adopted in temporal space. In order to obtain stable and convergent solution at high Weissenberg number, streamline upwind method is chosen to tackle the convective terms in constitutive equations of viscoelastic flow. Meanwhile, mass lumped technique is adopted to accelerate computational efficiency. The method allows the equal order basis to approximate pressure, velocity and extra stress, especially the linear basis that is easy to implement. The planar Poiseuile flow and 4:1 planar contraction flow for an Oldroyd B fluid are investigated. Through these numerical experiments, we find that the method has good stability and the numerical results are in agreement well with those reported by other papers.