相关论文: Global Solutions of a Two-Dimensional Riemann Prob…

The dynamical behavior resulting from an initial discontinuity in focusing media is investigated using a combination of numerical simulations and Whitham modulation theory for the focusing nonlinear Schrodinger equation. Initial conditions…

We study the immersed boundary problem in 2-D. It models a 1-D elastic closed string immersed and moving in a fluid that fills the entire plane, where the fluid motion is governed by the 2-D incompressible Navier-Stokes equation with a…

This paper analyzes the vanishing pressure limit of solutions to the Aw-Rascle model and the perturbed Aw-Rascle model for modified Chaplygin gas. Firstly, the Riemann problem of the Aw-Rascle model is solved constructively. A special delta…

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,…

We introduce a second-order, central-upwind finite volume method for the discretization of nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. The semi-discrete version of the proposed method is based on a technique…

In this paper, we prove the existence of two-dimensional solutions to the steady Euler-Poisson system with continuous transonic transitions across sonic interfaces of codimension 1. First, we establish the well-posedness of a boundary value…

In this paper, two kinds of occurrence mechanism on the phenomenon of concentration and the formation of delta shock wave in the flux approximation limit of Riemann solutions to the extended Chaplygin gas equations are analyzed and…

The paper is concerned with the free boundary problem for 2D current-vortex sheets in ideal incompressible magneto-hydrodynamics near the transition point between the linearized stability and instability. In order to study the dynamics of…

Corrugation instabilities occurring for solutions of the Riemann problem in relativistic hydrodynamics in which the fluid moves with a non-zero velocity tangent to the initial discontinuity are studied numerically. We perform simulations…

For a two-dimensional steady supersonic Euler flow past a convex cornered wall with right angle, a characteristic discontinuity (vortex sheet and/or entropy wave) is generated, which separates the supersonic flow from the gas at rest (hence…

Nonlinear deformations of a two-dimensional gas bubble are investigated in the framework of a Hamiltonian formulation involving surface variables alone. The Dirichlet--Neumann operator is introduced to accomplish this dimensional reduction…

Supersonic-sonic patches are ubiquitous in regions of transonic flows and they boil down to a family of degenerate hyperbolic problems in regions surrounded by a streamline, a characteristic curve and a possible sonic curve. This paper…

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…

A 2D problem of acoustic wave scattering by a segment bearing impedance boundary conditions is considered. In the current paper (the first part of a series of two) some preliminary steps are made, namely, the diffraction problem is reduced…

In this note, we discuss a poorly known alternative boundary condition to the usual Neumann or `stress-free' boundary condition typically used to weaken boundary layers when diffusion is present but very small. These `diffusion-free'…

When a plane shock hits a two-dimensional wedge head on, it experiences a reflection-diffraction process, and then a self-similar reflected shock moves outward as the original shock moves forward in time. The experimental, computational,…

In this paper we introduce some new concepts for second-order hyperbolic equations: two-point boundary value problem, global exact controllability and exact controllability. For several kinds of important linear and nonlinear wave equations…

We consider FPU-type atomic chains with general convex potentials. The naive continuum limit in the hyperbolic space-time scaling is the p-system of mass and momentum conservation. We systematically compare Riemann solutions to the p-system…

We are concerned with the stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. In this paper, we focus on the stability of steady four-wave configurations that are the solutions of the…

This paper studies the expansion into vacuum of a wedge of gas at rest. This problem catches several important classes of wave interactions in the context of 2D Riemann problems. When the gas at rest is a nonideal gas, the gas away from the…