Open Access

ARTICLE

Numerical Shock Viscosity for Impact Analysis Using ALE Formulation

Souli Mhamed¹, Paul Du Bois², Essam Al-Bahkali^3,*

1 Université de Lille1 Unité de Mécanique de Lille, UMR CNRS 8107.
2 Consulting Engineer, Troy Michigan, USA.
3 Mechanical Engineering Department, King Saud University, P.O. Box 800, 11421 Riyadh, Saudi Arabia.

*Corresponding Author: Essam Al-Bahkali. Email: .

Computer Modeling in Engineering & Sciences 2018, 117(1), 91-107. https://doi.org/10.31614/cmes.2018.03888

Abstract

When the simulation takes account of dissipative mechanisms, e.g. heat conduction and viscosity, the shocks become smeared out to produce thin layers of rapidly and continuously varying energy, density, pressure and velocity rather than discrete surfaces of mathematical discontinuity. In the mid twentieth century, Von Neumann and Richtmyer suggested the use of a viscous pressure term (bulk viscosity) in the equilibrium equations for ideal gases in order to examine the shock while avoiding numerical oscillations at the shock front. When the bulk viscosity is included in the conservation equations, the comprehensive physics present a continuous solution satisfying the Rankine-Hugoniot conditions. Nevertheless, the published literature includes few engineering and research studies presenting the novel equilibrium equations in which the incorporation of bulk viscosity generates a continuous solution in keeping with conservation laws. The present work is aimed at demonstrating that the artificial bulk viscosity defined by Von Neumann and Richtmyer is also applicable to fluids described by a density-linear equation of state, that the novel equations present a continuous solution, and that a shock layer of the same order as the computational grid is generated. Although the method has been employed and mathematically proven for one-dimensional flow, it would seem to be just as relevant to the analysis of more complex flow dynamics and fluid structure interactions via an application of the Arbitrary Lagrangian Eulerian (ALE) formulation.

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