Related papers: Singular solutions to the Riemann problem for the …
We give a solution of the Riemann problem in relativistic hydrodynamics in the case of ultrarelativistic equation of state and nonvanishing components of the velocity tangent to the initial discontinuity. Simplicity of the…
Existence and admissibility of $\delta$-shock type solution is discussed for the following nonconvex strictly hyperbolic system arising in studues of plasmas: \pa_t u + \pa_x \big(\Sfrac{u^2+v^2}{2} \big) &=0 \pa_t v +\pa_x(v(u-1))&=0. The…
We consider the Riemann problem composed of two shocks for the 1D Euler system. We show that the Riemann solution with two shocks is stable and unique in the class of weak inviscid limits of solutions to the Navier-Stokes equations with…
In this paper we provide bound estimates for the two fastest wave speeds emerging from the solution of the Riemann problem for three well-known hyperbolic systems, namely the Euler equations of gas dynamics, the shallow water equations and…
This paper proposes a second-order accurate direct Eulerian generalized Riemann problem (GRP) scheme for the ten-moment Gaussian closure equations with source terms. The generalized Riemann invariants associated with the rarefaction waves,…
In this work we present a general strategy for constructing multidimensional Riemann solvers with a single intermediate state, with particular attention paid to detailing the two-dimensional Riemann solver. This is accomplished by…
The question of well- and ill-posedness of entropy admissible solutions to the multi-dimensional systems of conservation laws has been studied recently in the case of isentropic Euler equations. In this context special initial data were…
In this paper the new procedure for a construction of an approximated solution to initial data problem for one-dimensional pressureless gas dynamics system is introduced. The procedure is based on solving the Riemann problems and tracking…
This is the second paper in a series studying the nonlinear stability of rarefaction waves in multi-dimensional gas dynamics. We construct initial data near singularities in the rarefaction wave region and, combined with the a priori energy…
The study of spherically symmetric motion is important for the theory of explosion waves. In this paper, we construct rigorously self-similar solutions to the Riemann problem of the spherically symmetric Euler equations for general…
In this paper, we are concerned with the long time behavior of the piecewise smooth solutions to the generalized Riemann problem governed by the compressible isothermal Euler equations in two and three dimensions. Non-existence result is…
Riemann problems at geometric discontinuities are a classic and fascinating issue of hydraulics. In the present paper, the complete solution to the Riemann problem of the one-dimensional Shallow water Equations at monotonic width…
We present a waveform relaxation version of the Dirichlet-Neumann and Neumann-Neumann methods for parabolic problems. Like the Dirichlet-Neumann method for steady problems, the method is based on a non-overlapping spatial domain…
We prove the existence of ``pure tone'' nonlinear sound waves of all frequencies. These are smooth, time periodic, oscillatory solutions of the $3\times3$ compressible Euler equations satisfying periodic or acoustic boundary conditions in…
Due to the limited cell resolution in the representation of flow variables, a piecewise continuous initial reconstruction with discontinuous jump at a cell interface is usually used in modern computational fluid dynamics methods. Starting…
We have extended the procedure to find the exact solution of the Riemann problem in relativistic hydrodynamics to a particular case of relativistic magnetohydrodynamics in which the magnetic field of the initial states is tangential to the…
We introduce a new wave formulation for the relativistic Euler equations with vacuum boundary conditions that consists of a system of non-linear wave equations in divergence form with a combination of acoustic and Dirichlet boundary…
We utilize a three-dimensional manifold to solve Riemann Problems that arise from a system of two conservation laws with quadratic flux functions. Points in this manifold represent potential shock waves, hence its name wave manifold. This…
We study the domain of existence of a solution to a Riemann problem for the pressure gradient equation in two space dimensions. The Riemann problem is the expansion of a quadrant of gas of constant state into the other three vacuum…
Einstein equations are addressed with the energy-momentum tensor that appears if the equations under discussion are required to possess conformal invariance. It is proved that thus derived equations (equations of conformally invariant…