Related papers: An exact Riemann solver based solution for regular…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…