In this paper, a tracking method is proposed for the expansion of gas flow into vacuum which may be combined with numerical methods for the equations of gas dynamics, the Euler equations. This tracking prevents the difficulties of the numerical approximation introduced by the vacuum as a region where the Euler equations are not valid due to the failure of the continuum assumption. The tracking algorithm is based on the exact or an approximate solution of the vacuum Riemann problem. This is the initial value problem with two constant states, one being the gas and the other the vacuum state, and a limit case of the usual Riemann problem. In this approach, the gas–vacuum boundary is sharply resolved within one mesh interval. For a test problem, the numerical results of gas flow into vacuum are presented which indicate that the gas vacuum boundary is captured very well.

A tracking method for gas flow into vacuum based on the vacuum Riemann problem

The construction of Godunov-type schemes at material interfaces is considered. The main building block of the flux calculation in a Godunov-type scheme is the exact or the approximate solution of Riemann problems. At a material interface the flux function is discontinuous due to the change of the equation of state. A regularization of this problem is introduced and a Roe linearization of the regularized Riemann problem is given. From its solution appropriate numerical fluxes at material interfaces are deduced. These can be applied directly in the framework of Godunov-type schemes for the Euler equations in the Lagrangian frame of reference or on a moving grid. In Eulerian coordinates fixed in space it must be combined with an appropriate tracking of the material interfaces.

Approximate Riemann Solvers for Fluid Flow with Material Interfaces

We present a simple approach of the tracking of a gas-vacuum interface within a fixed Eulerian grid in conjunction with a scheme in conservation form. The tracking algorithm gives an estimation of the movement of the interface. This information is used to modify the numerical flux at the vacuum boundary to prevent the numerical smearing and is used to identify the vacuum region. The numerical method is applied to grid zones containing gas only.

The Numerical Approximation of a Free Gas-Vacuum Surface

Modeling of the quenching of blast products from energetic materials by expansion into vacuum

: The modeling and simulation work in this grant was directed by Prof. D. Scott Stewart, (the Stewart-Group) and the experimental work and data collection was directed by Prof. Nick Glumac (the Glumac-group). Professors Stewart and Glumac and Drs. John Bdzil and Joseph C. Foster, collaborated on experimental designs, that benefited from the concurrent theoretical and computational modeling. The effort described in this report fully integrated modeling and experiments to study the energy release processes that thermitic and/or exothermic intermetallic reactive materials experience when they are subjected to sustained shock loading.

Integrated Modeling and Experimental Studies at the Meso Scale for Advanced Reactive Materials

An efficient algorithm is presented for solving the Riemann problem for a polytropic gas. It enables the user to compute the solution for all physically reasonable data. The convergence of the algorithm is proved. The accuracy of the solution is limited only by the accuracy of the computer. There is an a-priori estimation of the required number of iterations. The rate of convergence turns out to be much higher than that of the usual fixed point iteration scheme.

A fast solver for Riemann problems

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A fast solver for Riemann problems