The variational multiscale element free Galerkin method for the simulation of power-law fluid flows

In this work, the variational multiscale element free Galerkin method is used for the solution of incompressible generalized Newtonian fluid flow. In order to correct the lack of stability of the standard Galerkin formulation of the NavierStokes equations, the velocity field is decomposed into coarse and fine scales first, and then a model for the fine scale velocity is introduced, in the process, the stabilization parameter has appeared naturally via the solution of the fine scale problem. From the viewpoint of the application, the presented method can employ an equal order basis for pressure and velocity that is easy to implement but avoid the restriction of the Babuska-Brezzi condition. Two benchmark problems named Poiseuille flow and lid-driven cavity flow for the power-law are solved and the numerical results confirm that this method has better stability and accuracy.