Elbridge Gerry Puckett

On the refraction of shock waves at a slow–fast gas interface

We present the results of numerical computations of the refraction of a plane shock wave at a CO 2 /CH 4 gas interface. The numerical method was an operator split version of a second-order Godunov method, with adaptive grid refinement. We solved the unsteady, two-dimensional, compressible, Euler equations numerically, assuming perfect gas equations of state, and compared our results with the experiments of Abd-El-Fattah & Henderson. Good agreement was usually obtained, especially when the contamination of the CH 4 by the CO 2 was taken into account. Remaining discrepancies were ascribed to the uncertainties in measuring certain wave angles, due to sharp curvature, poor definition, or short length of the waves at large angles of incidence. All the main features of the regular and irregular refractions were resolved numerically for shock strengths that were weak, intermediate, or strong. These include free precursor shock waves in the intermediate and strong cases, evanescent (smeared out) compressions in the weak case, and the appearance of an extra expansion wave in the bound precursor refraction (BPR). The structure of a BPR was elucidated for the first time.

A 3D adaptive mesh refinement algorithm for multimaterial gas dynamics

Abstract Adaptive mesh refinement (AMR) in conjunction with high order upwind finite difference methods has been used effectively on a variety of problems. In this paper we discuss an implementation of an AMR finite difference method that solves the equations of gas dynamics with two material species in three dimensions. An equation for the evolution of volume fractions augments the gas dynamics system. The material interface is preserved and tracked from the volume fractions using a piecewise linear reconstruction technique.

Non-convex profile evolution in two dimensions using volume of fluids

A new Volume of Fluid (VoF) method is applied to the problem of surface evolution in two dimensions (2D). The VoF technique is applied to problems that are representative of those that arise in semiconductor manufacturing, specifically photolithography and ion-milling. The types of surface motion considered are those whose etch rates vary as a function of both surface position and orientation. Functionality is demonstrated for etch rates that are non-convex in regard to surface orientation. A new method of computing surface curvature using divided differences of the volume fractions is also introduced, and applied to the advancement of surfaces as a vanishing diffusive term.

Supply-demand Diagrams and a New Framework for Analyzing the Inhomogeneous Lighthill-Whitham-Richards Model

Traditionally, the Lighthill-Whitham-Richards (LWR) models for homogeneous and inhomogeneous roads have been analyzed in flux-density space with the fundamental diagram of the flux-density relation. In this paper, we present a new framework for analyzing the LWR model, especially the Riemann problem at a linear boundary in which the upstream and downstream links are homogeneous and initially carry uniform traffic. We first review the definitions of local supply and demand functions and then introduce the so-called supply-demand diagram, on which a traffic state can be represented by its supply and demand, rather than as density and flux as on a fundamental diagram. It is well-known that the solutions to the Riemann problem at each link are self-similar with a stationary state, and that the wave on the link is determined by the stationary state and the initial state. In our new framework, there can also exist an interior state next to the linear boundary on each link, which takes infinitesimal space, and admissible conditions for the upstream and downstream stationary and interior states can be derived in supply-demand space. With an entropy condition consistent with a local supply-demand method in interior states, we show that the stationary states exist and are unique within the solution framework. We also develop a graphical scheme for solving the Riemann problem, and the results are shown to be consistent with those in the literature. We further discuss asymptotic stationary states on an inhomogeneous ring road with arbitrary initial conditions and demonstrate the existence of interior states with a numerical example. The framework developed in this study is simpler than existing ones and can be extended for analyzing the traffic dynamics in general road networks.

A study of the vortex sheet method and its rate of convergence

The subject of this study is Chorins vortex sheet method, which is used to solve the Prandtl boundary layer equations and to impose the no-slip boundary condition in the random vortex method solution of the Navier–Stokes equations. This is a particle method in which the particles carry concentrations of vorticity and undergo a random walk to approximate the diffusion of vorticity in the boundary layer. During the random walk, particles are created at the boundary in order to satisfy the no-slip boundary condition. It is proved that in each of the

Edge effects in molybdenum‐encapsulated molten silicate shock wave targets

L^1

Accurate and Robust Methods for Variable Density Incompressible Flows with Discontinuities

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A fast vortex method for computing 2D viscous flow

L^2

A General Theory of Anomalous Shock Refraction

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A Numerical Study of Shock Wave Refraction at a CO2/CH4 Interface

L^\infty