Related papers: On the shock change equations
Starting with a brief introduction into the basics of relativistic fluid dynamics, I discuss our current knowledge of a relativistic theory of fluid dynamics in the presence of (mostly shear) viscosity. Derivations based on the generalized…
The continuous injection of energy in a stationary gas creates a shock wave that propagates radially outwards. We study the hydrodynamics of this disturbance using event driven molecular dynamics of a hard sphere gas in two and three…
The evolution of quantum gases, released from traps, are studied through hydrodynamics, both analytically and numerically, in one and two dimensions. In particular, we demonstrate the existence of long time self-similar solutions of the…
In this paper we develop two models for the steady states and evolution of two dimensional isothermal self gravitating and rotating incompressible gas which are based on the hydrodynamic equations for stratified fluid. The first model is…
We introduce an application of the Quasi-Gasdynamic method for a solution of ideal magnetohydrodynamic equations in the modeling of compressible conductive gas flows. A time-averaging procedure is applied for all physical parameters in…
1-D scalar conservation laws with convex flux and Markov initial data are now known to yield a completely integrable Hamiltonian system. In this article, we rederive the analogue of Loitsiansky's invariant in hydrodynamic turbulence from…
In this paper, the generalized analytical solution for one dimensional adiabatic flow behind the strong imploding shock waves propagating in a non-ideal gas is obtained by using the geometrical shock dynamics theory. The equation of state…
This paper presents generalized forms of jump relations for one dimensional shock waves propagating in a dusty gas. The dusty gas is assumed to be a mixture of a perfect gas and spherically small solid particles, in which solid particle are…
The Riemann problem is one of the basic building blocks for numerical methods in computational fluid mechanics. Nonetheless, there are still open questions and gaps in theory and modelling for situations with complex thermodynamic behavior.…
A port-Hamiltonian model for compressible Newtonian fluid dynamics is presented in entirely coordinate-independent geometric fashion. This is achieved by use of tensor-valued differential forms that allow to describe describe the…
The exact structure of a shock is computed in a multiple-speed discrete-velocity gas, the nine-velocity gas, wherein the multiplicity of speeds ensures nontrivial thermodynamics. Obtained as a solution of the model Boltzmann equations, the…
Perfect fluid equations are formulated which are invariant under the $\ell$-conformal Newton-Hooke group for an arbitrary integer or half-integer value of the parameter $\ell$. For $\ell=\frac32$ the corresponding conserved charges are…
In this work, we analytically derive the exact closed dynamical equations for a liquid with short-ranged interactions in large spatial dimensions using the same statistical mechanics tools employed to analyze Brownian motion. Our derivation…
Starting from the microscopic description of a normal fluid in terms of any kind of local interacting many-particle theory we present a well defined step by step procedure to derive the hydrodynamic equations for the macroscopic phenomena.…
We derive general depth-integrated model equations for overland flows featuring the evolution of suspended sediment that may be eroded from or deposited onto the underlying topography ('morphodynamics'). The resulting equations include…
A phase-field model that takes into account the bending energy of fluid vesicles is presented. The Canham-Helfrich model is derived in the sharp-interface limit. A dynamic equation for the phase-field has been solved numerically to find…
A heat equation with uncertain domains is thoroughly investigated. Statistical moments of the solution is approximated by the counterparts of the shape derivative. A rigorous proof for the existence of the shape derivative is presented.…
The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier-Stokes equations coupled with a moving solid. This method presents the advantage to predict an…
We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional,…
We study the two-dimensional structural stability of shock waves in a compressible isentropic inviscid elastic fluid in the sense of the local-in-time existence and uniqueness of discontinuous shock front solutions of the equations of…