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We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave often referred to as the shock wave refraction. The refraction of a…

Pattern Formation and Solitons · Physics 2015-05-28 G. A. El , V. V. Khodorovskii , A. M. Leszczyszyn

This paper is concerned with the study of the main wave interactions in a system of conservation laws in geochemical modeling. We study the modeling of the chemical complexes on the rock surface. The presence of stable surface complexes…

Analysis of PDEs · Mathematics 2022-07-21 A. C. Alvarez , J. Bruining , D. Marchesin

We extend our approach for the exact solution of the Riemann problem in relativistic hydrodynamics to the case in which the fluid velocity has components tangential to the initial discontinuity. As in one-dimensional flows, we here show…

General Relativity and Quantum Cosmology · Physics 2009-11-07 L. Rezzolla , O. Zanotti , J. A. Pons

We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient…

Numerical Analysis · Mathematics 2013-07-18 Manuel Quezada de Luna David I. Ketcheson

The motivation of this study is to find the Riemann solutions of the Aw-Rascle model with a more realistic version of extended Chaplygin gas. Firstly, we establish the Riemann solutions with two different structures, viz., a shock wave…

Analysis of PDEs · Mathematics 2025-08-12 Priyanka , M. Zafar

Richtmyer-Meshkov instability (RMI) plays an important role in many areas of science and engineering, from supernovae and fusion to scramjets and nano-fabrication. Classical Richtmyer-Meshkov instability is induced by a steady shock and…

Fluid Dynamics · Physics 2020-07-15 Desmond Hill , Snezhana Abarzhi

Aims: In the present work we investigate the nature of the magnetic Rayleigh-Taylor instability at a density interface permeated by an oblique, homogeneous magnetic field in an incompressible limit. Methods: Using the system of linearised…

Solar and Stellar Astrophysics · Physics 2020-02-19 E. Vickers , I. Ballai , R. Erdélyi

We are concerned with a two-dimensional ($2$-D) Riemann problem for compressible flows modeled by the pressure gradient system that is a $2$-D hyperbolic system of conservation laws. The Riemann initial data consist of four constant states…

Analysis of PDEs · Mathematics 2020-08-26 Gui-Qiang G. Chen , Qin Wang , Shengguo Zhu

Shocks are ubiquitous in astrophysical sources, many of which involve relativistic bulk motions, leading to the formation of relativistic shocks. Such relativistic shocks have so far been studied mainly in one dimension, for simplicity, but…

High Energy Astrophysical Phenomena · Physics 2023-09-25 Prasanta Bera , Jonathan Granot , Michael Rabinovich , Paz Beniamini

The nonlinear convection terms in the governing equations of compressible fluid flows are hyperbolic in nature and are nontrivial for modelling and numerical simulation. Many numerical methods have been developed in the last few decades for…

Numerical Analysis · Mathematics 2021-10-26 Ramesh Kolluru , N. Venkata Raghavendra , S. V. Raghurama Rao , G. N. Sekha

This paper investigates the inverse scattering problem of time-harmonic plane waves incident on a perfectly reflecting random periodic structure. To simulate random perturbations arising from manufacturing defects and surface wear in…

Numerical Analysis · Mathematics 2025-07-29 Zhiqi Sun , Yiwen Lin

Shock flame interactions are fundamental problems in many combustion applications ranging from flame acceleration to flame control in supersonic propulsion applications. The present paper seeks to quantify the rate of deformation of the…

Fluid Dynamics · Physics 2021-09-01 Hongxia Yang , Matei Ioan Radulescu

Scattering of a plane electromagnetic wave by an anisotropic impedance right-angled concave wedge at skew incidence is analyzed. A closed-form solution is derived by reducing the problem to a symmetric order-2 vector Riemann-Hilbert problem…

Mathematical Physics · Physics 2014-01-16 Y. A. Antipov

We have developed a one-dimensional code to solve ultra-relativistic hydrodynamic problems, using the Glimm method for an accurate treatment of shocks and contact discontinuities. The implementation of the Glimm method is based on an exact…

Astrophysics · Physics 2009-10-28 L. Wen , A. Panaitescu , P. Laguna

We consider a sharp-interface approach for the inviscid isothermal dynamics of compressible two-phase flow, that accounts for phase transition and surface tension effects. To fix the mass exchange and entropy dissipation rate across the…

Fluid Dynamics · Physics 2016-11-10 Christian Rohde , Christoph Zeiler

In this article, we investigate the two-dimensional pressureless Euler equations with three constant Riemann initial data. Our primary focus is on the wave interactions involving contact discontinuities and delta shocks. A distinguishing…

Analysis of PDEs · Mathematics 2025-07-24 Anamika Pandey , T. Raja Sekhar

In the present paper, an efficient method to generate "pure" cylindrically converging shock wave without a following contact surface is proposed firstly. Then, the Richtmyer-Meshkov instabilities of two interfaces driven by the generated…

Fluid Dynamics · Physics 2021-02-09 Wei-Gang Zeng , Yu-Xin Ren , Jianhua Pan

The problem of reconstruction of an unknown refractive index $k(x)$ of an inhomogeneous solid $P$ is considered. The refractive index is assumed to be a piecewise-H\"{o}lder function The original boundary value problem for the Helmholtz…

Numerical Analysis · Mathematics 2018-03-14 Mikhail Medvedik , Yury Smirnov , Aleksei Tsupak

We investigate the shock-induced turbulent mixing between a light and heavy gas, where a Richtmyer-Meshkov instability (RMI) is initiated by a $\Ma = 1.5$ shock wave. The prescribed initial conditions define a deterministic multimode…

Fluid Dynamics · Physics 2015-06-18 V. K. Tritschler , B. J. Olson , S. K. Lele , S. Hickel , X. Y. Hu , N. A. Adams

Exact solutions describing the Rayleigh-Bloch waves for the two-dimensional Helmholtz equation are constructed in the case when the refractive index is a sum of a constant and a small amplitude function which is periodic in one direction…

Mathematical Physics · Physics 2018-06-13 A. Merzon , P. Zhevandrov , M. I. Romero Rodríguez , J. E. De la Paz Méndez