Related papers: Hugoniot Relation for Multi-Temperature Euler Equa…
Hamilton's principle plays a central role in fluid mechanics as a fundamental tool for deriving governing equations, analyzing conservation laws, and designing structure-preserving numerical schemes. However, its classical formulation is…
We prove that for the two-dimensional steady complete compressible Euler system, with given uniform upcoming supersonic flows, the following three fundamental flow patterns (special solutions) in gas dynamics involving transonic shocks are…
This paper considers the formulation of the adjoint problem in two dimensions when there are shocks in the flow solution. For typical cost functions, the adjoint variables are continuous at shocks, where they have to obey an internal…
Starting from coupled fluid-kinetic equations for the modeling of laden flows, we derive relevant viscous corrections to be added to asymptotic hydrodynamic systems, by means of Chapman-Enskog expansions and analyse the shock profile…
The equation of state and the shock Hugoniot of deuterium are calculated using a first-principles approach, for the conditions of the recent shock experiments. We use density functional theory within a classical mapping of the quantum…
In this paper, we are trying to show the uniqueness of transonic shock solutions in an expanding nozzle under certain conditions and assumptions on the boundary data and the shock solution. The idea is to compare two transonic shock…
We are concerned with geometric properties of transonic shocks as free boundaries in two-dimensional self-similar coordinates for compressible fluid flows, which are not only important for the understanding of geometric structure and…
Radial similarity flow offers a rare instance where concrete inviscid, multi-dimensional, compressible flows can be studied in detail. In particular, there are flows of this type that exhibit imploding shocks and cavities. In such flows the…
In this paper, we study the uniqueness of the steady 1-D shock solutions for the inviscid compressible Euler system in a finite nozzle via asymptotic analysis for physical parameters. The parameters for the heat conductivity and the…
A number of physical phenomena are described by nonlinear hyperbolic equations. Presence of discontinuous solutions motivates the necessity of development of reliable numerical methods based on the fundamental mathematical properties of…
It has recently been shown that the maximal kinematical invariance group of polytropic fluids, for smooth subsonic flows, is the semidirect product of SL(2,R) and the static Galilei group G. This result purports to offer a theoretical…
The effects of radiation on the structure of shocks in a fully-ionized plasma are investigated by solving the steady-state fluid equations for ions, electrons, and radiation. The electrons and ions are assumed to have the same bulk velocity…
We present some recent developments on shock capturing methods for nonlinear hyperbolic systems of balance laws, whose prototype is the Euler system of compressible fluid flows, and especially discuss {structure-preserving} techniques. The…
We present estimates of the critical properties, thermodynamic functions, and principal shock Hugoniot of hot dense aluminum fluid as predicted from a chemical model for the equation-of-state of hot dense, partially ionized and partially…
In some inertial confinement fusion hohlraum designs, the inside plasma is not sufficiently collisional to be satisfactorily described by the Euler equations implemented in hydrodynamic simulation codes, particularly in converging regions…
We study the behavior of perturbations in a compressible one-dimensional inviscid gas with an ambient state consisting of constant pressure and periodically-varying density. We show through asymptotic analysis that long-wavelength…
The research is aimed at the study of the properties of solutions for parallel MHD shock waves in collisionless plasma with heat fluxes, using 8-moment MHD approximation. Restrictions have been established on the upstream shock parameters…
In this paper we study the general relationship between the evolutionary conditions for discontinuous solutions of hyperbolic conservation laws with a concave entropy function and the existence and uniqueness of steady dissipative shock…
This work concerns the numerical approximation with a finite volume method of inviscid, nonequilibrium, high-temperature flows in multiple space dimensions. It is devoted to the analysis of the numerical scheme for the approximation of the…
In this paper, we analyze various types of critical phenomena in one-dimensional gas flows described by Euler equations. We give a geometrical interpretation of thermodynamics with a special emphasis on phase transitions. We use ideas from…