Previous work has shown that the one-dimensional (1D) inviscid compressible flow (Euler) equations admit a wide variety of scale-invariant solutions (including famous Noh, Sedov, and Guderley shock solutions) when included equation state (EOS) closure model assumes certain form. However, this EOS class does not include even simple models used for compression crystalline solids, including many broadly applicable representations Mie-Gr\"uneisen EOS. Intuitively, incompatibility naturally...

The problem of a one-dimensional (1D) cylindrically or spherically symmetric shock wave converging into an inviscid, ideal gas was first investigated by Guderley[Starke kugelige und zylinrische verdichtungsstosse in der nahe des kugelmitterpunktes bzw. Der zylinderachse,” Luftfahrtforschung 19, 302 (1942)]. In the time since, many authors have discussed practical notion how Guderley-like flows might be generated. One candidate is constant velocity, “cylindrical spherical piston,” giving rise...

We extend Guderley's problem of finding a self-similar scaling solution for converging cylindrical or spherical shock wave from the ideal gas case to generalized class equation state closure models, giving necessary conditions existence solution. The condition is thermodynamic one, namely that adiabatic bulk modulus, |$K_S$|⁠, fluid be form |$pf(\rho)$| where |$p$| pressure, |$\rho$| mass density, and |$f$| any function. Although this has appeared in literature before, here we give more...

As UO 2 is easily oxidized during the nuclear fuel cycle it important to have a detailed understanding of structures and properties oxidation products. Experimental work over years has revealed many stable uranium oxides including , U 4 O 9 (UO 2.25 ), 3 7 2.33 5 2.5 8 2.67 all with number different polymorphs. These are broadly split into two categories, fluorite-based stoichiometries in range less dense layered-type . While well characterized, both experimentally computationally, there...

Nonstandard analysis is an area of modern mathematics that studies abstract number systems containing both infinitesimal and infinite numbers. This article applies nonstandard to derive jump conditions for one-dimensional, converging shock waves in a compressible, inviscid, perfect gas. It assumed the thickness occurs on interval functions thermodynamic fluid dynamic parameters occur smoothly across this interval. Predistributions Heaviside function Dirac delta measure are introduced model...

Although they are polymorphic (multiphase) materials, both copper and silver reliable Hugoniot standards, thus it is necessary to establish an accurate analytic model of their principal Hugoniots. Here we present forms Hugoniots, as well those iridium platinum, two “pusher” standards for shock-ramp experiments, over a wide range pressures. They based on our new the [Burakovsky et al., J. Appl. Phys. 132, 215109 (2022)]. Comparison four Hugoniots with experimental independent theoretical data...

We present the analytic form of principal Hugoniot at all pressures. It is constructed by interpolating smoothly between three pressure (P) regimes. Specifically, (i) low-P regime in which described Us=C+BUp+AUp2, where Up and Us are particle shock velocities, respectively, values C B come from experiment, a small non-linearity (A∼10−2 s/km) added to otherwise common linear Us=C+BUp match next regime; (ii) intermediate-P quantum-statistical model Kalitkin Kuzmina, Us=c+bUp+aUp2, with c, b,...

A brief review of the theory exterior differential systems and isovector symmetry analysis methods is presented in context one-dimensional inviscid compressible flow equations. These equations are formulated as an system with equation state (EOS) closure provided terms adiabatic bulk modulus. The scaling generators—and corresponding EOS constraints—otherwise appearing existing literature recovered through application invariance under Lie derivative dragging operations.

We present the analytic forms of principal Hugoniots actinium (Ac) and lanthanide promethium (Pm), which have both never been measured or calculated before, as well those terbium (Tb), thulium (Tm), lutetium (Lu), three least studied remaining lanthanides. They are based on our new model Hugoniot. A comparison five to own independent theoretical calculations demonstrates very good agreement in every case, but each Tb, Tm, Ac from TEFIS database, ours also compared to, appear violate...

We investigate the inviscid compressible flow (Euler) equations constrained by an "isentropic" equation of state (EOS), whose functional form in pressure is arbitrary function density alone. Under aforementioned condition, we interrogate using symmetry methods scale-invariance homentropic Euler equations. find that under general conditions, can reduce into a system two coupled ordinary differential To exemplify utility these results, formulate example scale-invariant, self-similar solutions....

This paper describes a calculation technique for determining the stability of jets arbitrary cross section. In particular, elliptic and rectangular are considered. The numerical procedure involves both conformal transformation between computational domain physical plane solution transformed equation in domain. Modern, efficient, mappings used simply doubly connected domains. is based on finite difference/pseudospectral discretization equation. verified by comparison with previous...

A number of physics problems can be modeled by a set N elements, which have pair-wise interactions with one another. The use such elements for the evolution vorticity in fluid flows and calculation velocity field from evolving is well known. Fast multipole methods flow been developed past to reduce computational effort something less than O(N 2). In this paper we develop fast solver application both 3-D radiation (calculation heat flux temperature an absorbing medium) flow. This accomplished...

We investigate the two-dimensional ($2$D) inviscid compressible flow equations in axisymmetric coordinates, constrained by an ideal gas equation of state (EOS). Beginning with assumption that $2$D velocity field is space-time separable and linearly variable each corresponding spatial coordinate, we proceed to derive infinite family elliptic or hyperbolic, uniformly expanding contracting ``gas cloud'' solutions. Construction specific example solutions belonging this dependent on solution a...

This paper presents a brief historical review of G. I. Taylor’s solution the point blast wave problem which was applied to Trinity test first atomic bomb. Lie group symmetry techniques (also referred throughout this as geometric techniques) are used derive famous two-fifths law that relates position time after explosion and total energy released. The theory exterior differential systems is combined with method characteristics demonstrate directly related basic relationships exist between (or...

Abstract This paper describes a calculation technique to determine the linear instability characteristics of jets arbitrary exit geometry. In particular, elliptic and rectangular are considered. The numerical procedure involves both conformal transformation between computational domain physical plane solution transformed stability equation in domain. Modern, efficient, mappings used for simply doubly connected domains. is based on hybrid finite difference/pseudospectral discretization...

The small length scales of the dissipative processes physical viscosity and heat conduction are typically not resolved in numerical simulation high Reynolds number flows discrete geometry computational grids. Historically, simulations with shocks and/or turbulence have relied on solving Euler equations regularization. In this paper, we begin by reviewing regularization strategies used shock wave calculations both a Lagrangian an Eulerian framework. We exhibit essential similarities Large...