相关论文: Structural stability of shock waves and current-vo…
We summarize recent progress on one- and multi-dimensional stability of viscous shock wave solutions of compressible Navier--Stokes equations and related symmetrizable hyperbolic--parabolic systems, with an emphasis on the large-amplitude…
The Kelvin-Helmholtz (KH) instability occurring in a single shear flow configuration that is embedded in a uniform flow-aligned magnetic field, is revisited by means of high resolution two-dimensional (2D) magnetohydrodynamic (MHD)…
Media composed of colliding hard disks (2D) or hard spheres (3D) serve as good approximations for the collective hydrodynamic description of gases, liquids and granular media. In the present study, the compressible hydrodynamics and shock…
Simulations of strongly stratified turbulence often exhibit coherent large-scale structures called vertically sheared horizontal flows (VSHFs). VSHFs emerge in both two-dimensional (2D) and three-dimensional (3D) stratified turbulence with…
Using two dimensional simulations, we study the formation of structures with a high-density contrast by magnetohydrodynamic waves in regions in which the ratio of thermal to magnetic pressure is small. The initial state is a uniform…
We present and test a new, special-relativistic formulation of Smoothed Particle Hydrodynamics (SPH). Our approach benefits from several improvements with respect to earlier relativistic SPH formulations. It is self-consistently derived…
We describe a high-order numerical magnetohydrodynamics (MHD) solver built upon a novel non-linear entropy stable numerical flux function that supports eight travelling wave solutions. By construction the solver conserves mass, momentum,…
A weak wave turbulence theory is developed for two-dimensional (2D) magnetohydrodynamics (MHD). We derive and analyze the kinetic equation describing the three-wave interactions of pseudo-Alfv\'en waves. Our analysis is greatly helped by…
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…
Numerical solutions of the incompressible magnetohydrodynamic (MHD) equations are reported for the interior of a rotating, perfectly-conducting, rigid spherical shell that is insulator-coated on the inside. A previously-reported spectral…
In this paper, we validate the boundary layer theory for 2D steady viscous incompressible magnetohydrodynamics (MHD) equations in a domain $\{(X, Y)\in[0, L]\times\mathbb{R}_+\}$ under the assumption of a moving boundary at $\{Y=0\}$. The…
Recently, we developed a pair of meshless finite-volume Lagrangian methods for hydrodynamics: the 'meshless finite mass' (MFM) and 'meshless finite volume' (MFV) methods. These capture advantages of both smoothed-particle hydrodynamics…
In this paper we analyze the stability of equilibrium manifolds of hyperbolic shallow water moment equations. Shallow water moment equations describe shallow flows for complex velocity profiles which vary in vertical direction and the…
Compared to the results in \cite{Shivamoggi}, using the normal mode method, we have rigorously confirmed that a transverse magnetic field reduces the stability of the system. Specifically, a larger velocity is required for stability in the…
We have studied forced turbulence of compressible magnetohydrodynamic (MHD) flows through two-dimensional simulations with different numerical resolutions. First, hydrodynamic turbulence with Mach number $<M_s >_{\rm init} \equiv < v >_{\rm…
This paper focuses on the 3D incompressible magnetohydrodynamic (MHD) equations with mixed partial dissipation and magnetic diffusion. Our main result assesses the global stability of perturbations near the steady solution given by a…
Rigorous theories of the tearing instability are mathematically quite involving. Therefore, the present note aims to demonstrate how their main results can be reproduced by a simple qualitative analysis of the respective magnetohydrodynamic…
Nonlinear and low-frequency solitary waves are investigated in the framework of the one-dimensional Hall-magnetohydrodynamic model with finite Larmor effects and a double adiabatic model for plasma pressures. The organization of these…
In this article some of the hydrodynamical (HD) aspects of steady shocks as described by the steady-state shock model are reviewed and discussed. It is found that, at least in some of the contexts in which the steady-state model is used,…
We present the theory, algorithms and implementation of a parallel finite-volume algorithm for the solution of the incompressible magnetohydrodynamic (MHD) equations using unstructured grids that are applicable for a wide variety of…