An ALE based iterative CBS algorithm for non-isothermal non-Newtonian flow with adaptive coupled finite element and meshfree method

This paper presents a generalized scheme of the fractional step algorithm using Characteristic Based Split (CBS) in ALE framework for the numerical simulation of incompressible non-isothermal non-Newtonian fluid flows and applies it, combined with the adaptive coupled finite element and meshfree method for spatial discretizations, to the polymer injection molding process. Based on the idea to discretize the material time derivative instead of the spatial time derivative, the characteristic Galerkin method is derived in a more general way and is used to discretize the non-Newtonian momentum and the energy conservation equations. An iterative procedure which makes the conservation equations satisfied in an implicit sense is introduced into the scheme to enhance its stability in the time domain. Numerical experiments with the power-law fluid model demonstrate and validate the performance and the capability of the proposed scheme.