Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) method in computation of non-Newtonian fluid flow and heat transfer with moving boundaries

This work presents an extension of the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) method to non-Newtonian fluid flow and heat transfer with moving boundaries. In this method, the variational formulation is written over the space-time domain. Three sets of stabilization parameters are used for the continuity, momentum and thermal energy equations. The more efficient solution for highly non-linear problems is achieved by using the Newton-Raphson iterative method for non-linear terms and the generalized minimal residual method for algebraic equations. This work makes the computations feasible with third-order accuracy in time, which is higher then most versions of the FEM. To validate this method, it is used to solve the well-known benchmark problems such as channel-confined flow, lid-driven cavity, flow around a cylinder, and flow in channel with wavy wall, where the non-Newtonian fluid rheological behaviour is incorporated. In particular, the results in terms of the Nusselt number, wall shear stress (WSS), vorticity fields and streamlines are discussed. It shows that the flow and heat transfer characteristics are quite different if the moving boundaries are taken into account. In summary, this work provides an effective extension of the DSD/SST method to hydrodynamics and heat transfer problems involving complex fluids and moving boundaries.