Application of the GRP scheme to open channel flow equations

The GRP (generalized Riemann problem) scheme, originally conceived for gasdynamics, is reformulated for the numerical integration of the shallow water equations in channels of rectangular cross-section, variable width and bed profile, including a friction model for the fluid-channel shear stress. This scheme is a second-order analytic extension of the first-order Godunov-scheme, based on time-derivatives of flow variables at cell-interfaces resulting from piecewise-linear data reconstruction in cells. The second-order time-integration is based on solutions to generalized Riemann problems at cell-interfaces, thus accounting for the full governing equations, including source terms. The source term due to variable bed elevation is treated in a well-balanced way so that quiescent flow is exactly replicated; this is done by adopting the Surface Gradient Method (SGM). Several problems of steady or unsteady open channel flow are considered, including the terms corresponding to variable channel width and bed elevation, as well as to shear stress at the fluid-channel interface (using the Manning friction model). In all these examples remarkable agreement is obtained between the numerical integration and the exact or accurate solutions

Vector Image Polygon (VIP) limiters in ALE Hydrodynamics

Recently ([1, 2]) we have formulated a new frame invariant monotonicity criterion and slope limiter for vectors and applied it to the Lagrangian phase of the SMG/Q scheme. This Vector Image Polygon/Polyhedron (VIP) limiter was shown to improve symmetry preservation in a set of test problems. In this study we implement the VIP limiter also to the momentum advection phase of the SMQ/Q scheme for (Arbitrary Lagrangian Eulerian) ALE hydrodynamics. The 2D cylindrical Noh problem serves as a test case to demonstrate the effect of the VIP limiter on symmetry preservation

Vector Image Polygon (VIP) limiters in ALE Hydrodynamics

Recently ([1, 2]) we have formulated a new frame invariant monotonicity criterion and slope limiter for vectors and applied it to the Lagrangian phase of the SMG/Q scheme. This Vector Image Polygon/Polyhedron (VIP) limiter was shown to improve symmetry preservation in a set of test problems. In this study we implement the VIP limiter also to the momentum advection phase of the SMQ/Q scheme for (Arbitrary Lagrangian Eulerian) ALE hydrodynamics. The 2D cylindrical Noh problem serves as a test case to demonstrate the effect of the VIP limiter on symmetry preservation

Review of methods to attenuate shock/blast waves

International audienceQuick and reliable shock wave attenuation is the goal of every protection facility and therefore it is not surprising that achieving this has drawn much attention during the past hundred years. Different options have been suggested; their usefulness varying from a reasonable protection to the opposite, a shock enhancement. An example for a suggestion for shock mitigation that turned out to be an enhancement of the impinging shock wave was the idea to cover a protected object with a foam layer. While the pressure behind the reflected shock wave from the foam frontal surface was smaller than that recorded in a similar reflection from a rigid wall [25], the pressure on the ``protected'' surface, attached to the foam's rear-surface, was significantly higher than that recorded in a similar reflection from a bare, rigid wall [11]. In protecting humans and installations from destructive shock and/or blast waves the prime goal is to reduce the wave amplitude and the rate of pressure increase across the wave front. Both measures result in reducing the wave harmful effects. During the past six decades several approaches for achieving the desired protection have been offered in the open literature. We point out in this review that while some of the suggestions offered are practical, others are impractical. In our discussion we focus on recent schemes for shock/blast wave attenuation, characterized by the availability of reliable measurements (notably pressure and optical diagnostics) as well as high-resolution numerical simulations. (c) 2012 Elsevier Ltd. All rights reserved