A Multi-State HLL Approximate Riemann Solver for Solid/Vacuum Riemann Problem

A new multi-state HLLD (‘‘D’’ stands for Discontinuities.) approximate Riemann solver for Riemann problem of nonlinear elastic solid is developed based on the assumption that a wave configuration for the solution that consists of five waves (two slow waves, two fast waves and a contact discontinuity) separating six constant states. Since the intermediate states satisfied with the Rankine-Hugoniot relations in this approximate Riemann system are analytically obtained, the HLLD Riemann solver can be constructed straightforwardly. The Piecewise Parabolic Method (PPM) is used directly to construct high-order finite-volume schemes. Numerical tests demonstrate that the scheme PPM coupled with HLLD is robust and efficient. It indicates that the scheme PPM+ HLLD can be useful in practical applications for the non-linear elasticity.

Assessment of a Shallow Water Model using a Linear Turbulence Model for Obstruction-Induced Discontinuous Flows

Assessment of the performance of a shallow water model with closure using a linear k-ε turbulence model is made for various obstruction-induced discontinuous flows. The monotone upwind scheme of conservative laws (MUSCL) - Hancock scheme is used, together with the Harten Lax van Leer (HLL) approximate Riemann solver in the discretization of the finite volume shallow water model. These kinds of models contribute to the improvement of optimized design of various processes in chemical<br />engineering and technology. Two obstructed flow applications are presented, namely, single obstruction and multiple obstruction induced discontinuous flows; and the ability of the shallow water model with the k-ε based turbulence model to predict these applications are assessed. The simulation results of the shallow water model are compared with those found by direct numerical simulation (DNS) and experimental measurements in the literature.