Efficient exact solution procedure for quasi-one-dimensional nozzle flows with stiffened-gas equation of state

2019 ◽  
Vol 137 ◽  
pp. 523-533
Author(s):  
Geum-Su Yeom ◽  
Jung-Il Choi
Keyword(s):  
Exact Solution ◽  
Equation Of State ◽  
Solution Procedure ◽  
One Dimensional ◽  
Nozzle Flows

scholarly journals Exact solution of one-dimensional relativistic jet with relativistic equation of state

2021 ◽  
Vol 502 (4) ◽  
pp. 5227-5244
Author(s):  
Raj Kishor Joshi ◽  
Indranil Chattopadhyay ◽  
Dongsu Ryu ◽  
Lallan Yadav
Keyword(s):  
Exact Solution ◽  
Equation Of State ◽  
Cross Section ◽  
Ambient Medium ◽  
Propagation Speed ◽  
Relativistic Equation ◽  
Flat Space ◽  
Propagation Direction ◽  
Reverse Shock ◽  
One Dimensional

ABSTRACT We study the evolution of one-dimensional relativistic jets, using the exact solution of the Riemann problem for relativistic flows. For this purpose, we solve equations for the ideal special relativistic fluid composed of dissimilar particles in flat space-time and the thermodynamics of fluid is governed by a relativistic equation of state. We obtain the exact solution of jets impinging on denser ambient media. The time variation of the cross-section of the jet-head is modelled and incorporated. We present the initial condition that gives rise to a reverse shock. If the jet-head cross-section increases in time, the jet propagation speed slows down significantly and the reverse-shock may recede opposite to the propagation direction of the jet. We show that the composition of jet and ambient medium can affect the jet solution significantly. For instance, the propagation speed depends on the composition and is maximum for a pair-dominated jet, rather than a pure electron-positron or electron-proton jet. The propagation direction of the reverse-shock may also strongly depend on the composition of the jet.

Real Gas Effects for Compressible Nozzle Flows

1993 ◽  
Vol 115 (1) ◽  
pp. 115-120 ◽  
Author(s):  
D. Drikakis ◽  
S. Tsangaris
Keyword(s):  
Equation Of State ◽  
Solution Procedure ◽  
Curvilinear Coordinates ◽  
Axisymmetric Nozzle ◽  
Specific Internal Energy ◽  
Real Gas ◽  
Real Gas Effects ◽  
Flow Variables ◽  
Nozzle Flows

Numerical simulation of compressible nozzle flows of real gas with or without the addition of heat is presented. A generalized real gas method, using an upwind scheme and curvilinear coordinates, is applied to solve the unsteady compressible Euler equations in axisymmetric form. The present method is an extension of a previous 2D method, which was developed to solve the problem for a gas having the general equation of state in the form p = p(ρ, i). In the present work the method is generalized for an arbitrary P-V-T equation of state introducing an iterative procedure for the determination of the temperature from the specific internal energy and the flow variables. The solution procedure is applied for the study of real gas effects in an axisymmetric nozzle flow.

scholarly journals On a Generalization of One-Dimensional Kinetics

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1264
Author(s):  
Vladimir V. Uchaikin ◽  
Renat T. Sibatov ◽  
Dmitry N. Bezbatko
Keyword(s):  
Exact Solution ◽  
Asymptotic Behavior ◽  
Constant Velocity ◽  
Telegraph Equation ◽  
Material Derivative ◽  
Symmetric Random Walk ◽  
One Dimensional ◽  
Special Cases ◽  
Fractional Telegraph Equation ◽  
Asymmetric Case

One-dimensional random walks with a constant velocity between scattering are considered. The exact solution is expressed in terms of multiple convolutions of path-distributions assumed to be different for positive and negative directions of the walk axis. Several special cases are considered when the convolutions are expressed in explicit form. As a particular case, the solution of A. S. Monin for a symmetric random walk with exponential path distribution and its generalization to the asymmetric case are obtained. Solution of fractional telegraph equation with the fractional material derivative is presented. Asymptotic behavior of its solution for an asymmetric case is provided.

On Approximate Large Deviations for 1D Diffusion

2003 ◽  
Vol 10 (2) ◽  
pp. 381-399
Author(s):  
A. Yu. Veretennikov
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Large Deviations ◽  
Stochastic Differential Equation ◽  
Approximation Scheme ◽  
Sufficient Conditions ◽  
Rate Function ◽  
Euler Approximation ◽  
One Dimensional

Abstract We establish sufficient conditions under which the rate function for the Euler approximation scheme for a solution of a one-dimensional stochastic differential equation on the torus is close to that for an exact solution of this equation.

An exact solution for one-dimensional unsteady nonlinear groundwater flow

Meccanica ◽  
1991 ◽  
Vol 26 (2-3) ◽  
pp. 129-133
Author(s):  
Vittorio di Federico
Keyword(s):  
Exact Solution ◽  
Groundwater Flow ◽  
One Dimensional

A time-dependent model for high-pressure discharges in narrow ablative capillaries

1993 ◽  
Vol 50 (1) ◽  
pp. 51-70 ◽  
Author(s):  
D. Zoler ◽  
S. Cuperman ◽  
J. Ashkenazy ◽  
M. Caner ◽  
Z. Kaplan
Keyword(s):  
High Pressure ◽  
Equation Of State ◽  
Time Dependent ◽  
Dimensional Model ◽  
Plasma Sources ◽  
One Dimensional ◽  
Space And Time ◽  
Dependent Model ◽  
Energy Equations ◽  
Time Dependent Model

A time-dependent quasi-one-dimensional model is developed for studying high- pressure discharges in ablative capillaries used, for example, as plasma sources in electrothermal launchers. The main features of the model are (i) consideration of ablation effects in each of the continuity, momentum and energy equations; (ii) use of a non-ideal equation of state; and (iii) consideration of space- and time-dependent ionization.

scholarly journals EXACT SOLUTION OF AN IRREVERSIBLE ONE-DIMENSIONAL MODEL WITH FULLY BIASED SPIN EXCHANGES

1996 ◽  
Vol 10 (25) ◽  
pp. 3451-3459 ◽  
Author(s):  
ANTÓNIO M.R. CADILHE ◽  
VLADIMIR PRIVMAN
Keyword(s):  
Exact Solution ◽  
Domain Wall ◽  
Nearest Neighbor ◽  
Spin Exchange ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Zero Temperature ◽  
Dimensional Model ◽  
One Dimensional ◽  
Temperature Dynamics

We introduce a model with conserved dynamics, where nearest neighbor pairs of spins ↑↓ (↓↑) can exchange to assume the configuration ↓↑ (↑↓), with rate β(α), through energy decreasing moves only. We report exact solution for the case when one of the rates, α or β, is zero. The irreversibility of such zero-temperature dynamics results in strong dependence on the initial conditions. Domain wall arguments suggest that for more general, finite-temperature models with steady states the dynamical critical exponent for the anisotropic spin exchange is different from the isotropic value.

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