Simple smoothness indicator WENO-Z scheme for hyperbolic conservation laws

The advantage of WENO-JS5 scheme [ J. Comput. Phys. 1996] over the WENO-LOC scheme [J. Comput. Phys.1994] is that the WENO-LOC nonlinear weights do not achieve the desired order of convergence in smooth monotone regions and at critical points. In this article, this drawback is achieved with the WENO-LOC smoothness indicators by constructing a WENO-Z type nonlinear weights which contains a novel global smoothness indicator. This novel smoothness indicator measures the derivatives of the reconstructed flux in a global stencil, as a result, the proposed numerical scheme could decrease the dissipation near the discontinuous regions. The theoretical and numerical experiments to achieve the required order of convergence in smooth monotone regions, at critical points, the essentially non-oscillatory (ENO), the analysis of parameters involved in the nonlinear weights like $\epsilon$ and $p$ are studied. From this study, we conclude that the imposition of certain conditions on $\epsilon$ and $p$, the proposed scheme achieves the global order of accuracy in the presence of an arbitrary number of critical points. Numerical tests for scalar, one and two-dimensional system of Euler equations are presented to show the effective performance of the proposed numerical scheme.Comment: 25 pages, 10 figure

Entropy analysis of the MHD Jeffrey fluid flow in an inclined porous pipe with convective boundaries

The present work deals with entropy generation analysis of a non-Newtonian Jeffrey fluid flow through an inclined pipe of circular cross section in the presence of uniform porous medium. The flow is subjected to constant pressure gradient and uniform magnetic field. The boundaries of circular pipe are assumed to be convective. Due to the presence of mixed convection, the underlying governing equations are nonlinear and coupled. The numerical solution of the system of governing equations is obtained. The analysis of roles played by the transport properties viz. fluid velocity and temperature is done to explore the thermodynamic entities like entropy generation number and Bejan number. The study of irreversibilities in the considered flow is analysed taking several sets of parameters, i.e., the Jeffrey fluid parameter, the Hartmann number, the Darcy number, the Grashof number, suction/injection parameter, the Brinkman number, the Prandtl number and the Biot number appearing in the problem