Related papers: Gas Dynamics Equations: Computation
Non-classical non-linear waves exist in dense gases for large specific heats at pressures and temperatures of the order of critical point values. These waves behave precisely opposite to the classical non-linear waves, with inverted…
To date it has not been possible to prove whether or not the three-dimensional incompressible Euler equations develop singular behaviour in finite time. Some possible singular scenarios, as for instance shock-waves, are very important from…
In recent years, stochastic effects have become increasingly relevant for describing fluid behaviour, particularly in the context of turbulence. The most important model for inviscid fluids in computational fluid dynamics are the Euler…
The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure, the spatial part of the dimensionless four-velocity and the particle density. Radially symmetric solutions of these equations are studied in two…
This paper considers one-dimensional equations of acoustics equations of inhomogeneous media and the system of gas dynamics equations with constant entropy. Using the Riemann approach, the gas dynamics equations are reduced to a…
Brenner has recently proposed modifications to the Navier-Stokes equations that are based on theoretical arguments but supported only by experiments having a fairly limited range. These modifications relate to a diffusion of fluid volume…
This article proposes an in-depth investigation into the emergence of thermoacoustic waves from a variational formalism rooted in non-equilibrium thermodynamics. Differing from traditional approaches based on linear simplifications, this…
We study the Cauchy problem for the compressible Euler equations in two spatial dimensions under any physical barotropic equation of state except that of a Chaplygin gas. We prove that the well-known phenomenon of shock formation in simple…
In classical continuum physics, a wave is a mechanical disturbance. Whether the disturbance is stationary or traveling and whether it is caused by the motion of atoms and molecules or the vibration of a lattice structure, a wave can be…
The process of downfall of initially homogeneous gas onto a solid ball due to the ball's gravity (relevant in astrophysical situations) is studied with a combination of analytic and numerical methods. The initial explicit solution soon…
Considering the isentropic Euler equations of compressible fluid dynamics with geometric effects included, we establish the existence of entropy solutions for a large class of initial data. We cover fluid flows in a nozzle or in spherical…
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…
We consider Einstein's equations coupled to the Euler equations in plane symmetry, with compact spatial slices and constant mean curvature time. We show that for a wide variety of equations of state and a large class of initial data,…
We show that equations of Newtonian hydrodynamics and gravity describing one-dimensional steady gas flow possess nonlinear periodic solutions. In the case of a zero-pressure gas the solution exhibits hydrodynamic similarity and is…
By analogy with the kinetic theory of gases, most turbulence modeling strate- gies rely on an eddy viscosity to model the unresolved turbulent fluctuations. How- ever, the ratio of unresolved to resolved scales - very much like a degree of…
I review the basic physics of ultracold dilute trapped atomic gases, with emphasis on Bose-Einstein condensation and quantized vortices. The hydrodynamic form of the Gross-Pitaevskii equation (a nonlinear Schr{\"o}dinger equation)…
Acoustic perturbations to stellar envelopes can lead to the formation of weak shock waves via nonlinear wave-steepening. Close to the stellar surface, the weak shock wave increases in strength and can potentially lead to the expulsion of…
Entropy weak solutions with bounded periodic initial data are considered for the system of weakly nonlinear gas dynamics. Through a modified Glimm scheme, an approximate solution sequence is constructed, and then a priori estimates are…
The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge…
Upcoming large-scale-structure surveys can shed new light on the properties of dark energy. In particular, if dark energy is a dynamical component, it must have spatial perturbations. Their behaviour is regulated by the speed of sound…