SUMMARYThis paper presents a numerical study for the unsteady flow of a magnetohydrodynamic (MHD) Sisko fluid in annular pipe. The fluid is assumed to be electrically conducting in the presence of a uniform magnetic field. Based on the constitutive relationship of a Sisko fluid, the non-linear equation governing the flow is first modelled and then numerically solved. The effects of the various parameters especially the power index n, the material parameter of the non-Newtonian fluid b and the magnetic parameter B on the flow characteristics are explored numerically and presented through several graphs. Moreover, the shear-thinning and shear-thickening characteristics of the non-Newtonian Sisko fluid are investigated and a comparison is also made with the Newtonian fluid.

ABSTRACT:We investigate the accuracy aspects of weak boundary conditions for the Navier-Stokes equations. As a model problem, the linear advection-diffusion equation for a boundary layer problem is analyzed. The analysis shows that the weak boundary conditions are advantageous compared with the strong boundary conditions. We exemplify the analysis of the advection-diffusion problem by doing Navier-Stokes calculations and show that most of the conclusions for the model problem hold also for that case.

A procedure to locally change the order of accuracy of finite difference schemes is developed. The development is based on existing SummationBy-Parts operators and a weak interface treatment. The resulting scheme is proven to be accurate and stable.Numerical experiments verify the theoretical accuracy for smooth solutions. In addition, shock calculations are performed, using a scheme where the developed switching procedure is combined with the MUSCL technique.