Related papers: Relativistic Shock Reflection using Integral Conse…
We solve the relativistic Riemann problem in viscous matter using the relativistic Boltzmann equation and the relativistic causal dissipative fluid-dynamical approach of Israel and Stewart. Comparisons between these two approaches clarify…
Reflection of a normal incident matter wave by a perfectly reflecting wall moving with a constant velocity is investigated. A surprising phenomenon is found-that if the the wall moves faster than the phase velocity of the incident wave,…
The goal of this paper is to prove the existence and stability of shocks for viscous scalar conservation laws with space periodic flux, in the multi-dimensional case. Such a result had been proved by the first author in one space dimension,…
We propose a new entropy-compatible neural network method for scalar hyperbolic conservation laws and establish, to our knowledge, the first explicit \(L^1\) convergence rates in this setting that apply to piecewise smooth entropy…
Radiative shocks, behind which gas cools faster than the dynamical time, play a key role in many astrophysical transients, including classical novae and young supernovae interacting with circumstellar material. The dense layer behind high…
We review recent interest in the relativistic Riemann problem as a method for generating a non-equilibrium steady state. In the version of the problem under con- sideration, the initial conditions consist of a planar interface between two…
We present a criterion for a shock wave existence in relativistic magnetic hydrodynamics with an arbitrary (possibly non-convex) equation of state. The criterion has the form of algebraic inequality that involves equation of state of the…
Extending our earlier work on Lax-type shocks of systems of conservation laws, we establish existence and stability of curved multidimensional shock fronts in the vanishing viscosity limit for general Lax- or undercompressive-type shock…
This work derives exact solutions to the problem of interacting particle density evolution in relativistic and quasi-relativistic approximations for electromagnetic and gravitational interactions. Two types of radial symmetry for the…
Cosmic rays are charged particles that are accelerated to relativistic speeds by astrophysical shocks. Numerical models have been successful in confirming the acceleration process for (quasi-)parallel shocks, which have the magnetic field…
A main disadvantage of many high-order methods for hyperbolic conservation laws lies in the famous Gibbs-Wilbraham phenomenon, once discontinuities appear in the solution. Due to the Gibbs-Wilbraham phenomenon, the numerical approximation…
This paper examines the mechanism of internal shocks in opaque relativistic outflows, in particular in cosmological gamma-ray bursts. The shocks produce neutrino emission and affect the observed photospheric radiation from the explosion.…
Coughlin et al. (2018) (Paper I) derived and analyzed a new regime of self-similarity that describes weak shocks (Mach number of order unity) in the gravitational field of a point mass. These solutions are relevant to low energy explosions,…
This paper concerns the construction and analysis of a new family of exact general relativistic shock waves. The construction resolves the open problem of determining the expanding waves created behind a shock-wave explosion into a static…
We numerically study fast Newtonian radiation mediated shocks (RMS - v/c~0.2) in two simplified problems in the context of supernova shock breakout; (1) An RMS traveling in a uniform medium, and (2) an RMS escaping a powerlaw density…
A system of equations governing the structure of a steady, relativistic radiation dominated shock is derived, starting from the general form of the transfer equation obeyed by the photon distribution function. Closure is obtained by…
The aim of this work is to make a further step towards the understanding of the near-critical reflection of internal gravity waves from a slope in the more general and realistic context where the size of viscosity $\nu$ and the size of…
The dynamics of a shock wave impinging on a transitional high-enthalpy boundary layer out of thermochemical equilibrium is investigated for the first time by means of a direct numerical simulation. The freestream Mach number is equal to 9…
We study the effects of weak viscosity on shock formation in 1D hyperbolic conservation laws. Given an inviscid solution that forms a nondegenerate shock, we add a small viscous regularization and study the limit as the viscosity vanishes.…
In the present work the linearized problem of plasma wave reflection from a boundary of a half--space is solved analytically. Specular accommodative conditions of plasma wave reflection from plasma boundary are taken into consideration.…