Related papers: New exact solutions for microscale gas flows
While flow optimization has been extensively studied in the continuum regime, its extension to rarefied gas flows remains less explored. Here, based on the Boltzmann model equation, an adjoint topology optimization method is employed to…
Variations of loading level and changes in system topological property may cause the operating point of an electric power systems to move gradually towards the verge of its transmission capability, which can lead to catastrophic outcomes…
(Abridged) A new type of self-similar hot viscous radiative accretion flow onto a rapidly spinning neutron star has recently been discovered. This ``hot brake'' flow forms in the two-temperature zone (close to a central object), but at a…
The system of Navier--Stokes--Fourier equations is one of the most celebrated systems of equations in modern science. It describes dynamics of fluids in the limit when gradients of density, velocity and temperature are sufficiently small,…
In this work we provide analytic and numerical solutions for the Bjorken flow, a standard benchmark in relativistic hydrodynamics providing a simple model for the bulk evolution of matter created in collisions between heavy nuclei. We…
Heat-flux boundary conditions are challenging to implement efficiently in rarefied gas flow simulations because the wall-reflected gas temperature and density must be determined dynamically during the computation. This paper aims to tackle…
This work obtains a fixed-point equation for the solution of linear parabolic partial differential problems based on solutions to heat problems. This is a pointwise equality, so we have required non-standard techniques that involve the…
We present exact, analytic and simple solutions of relativistic perfect fluid hydrodynamics. The solutions allow us to calculate the rapidity distribution of the particles produced at the freeze-out, and fit them to the measured rapidity…
Turbulent fluid flows exhibit a complex small-scale structure with frequently occurring extreme velocity gradients. Particles probing such swirling and straining regions respond with an intricate shape-dependent orientational dynamics,…
Looking for the underlying hydrodynamic mechanisms determining the elliptic flow we show that for an expanding relativistic perfect fluid the transverse flow may derive from a solvable hydrodynamic potential, if the entropy is transversally…
Recently the 14 moments model of Extended Thermodynamics for dense gases and macromolecular fluids has been considered and an exact solution, of the restrictions imposed by the entropy principle and that of Galilean relativity, has been…
For the problems indicated in the title, a further development of a new approach (different from those applied before) is given. A basic problem under consideration arises in viscous incompressible fluid dynamics and describes self-similar…
We present an effective adaptive procedure for the numerical approximation of the steady-state Gross-Pitaevskii equation. Our approach is solely based on energy minimization, and consists of a combination of gradient flow iterations and…
We study in this work a steady shearing laminar flow with null heat flux (usually called "uniform shear flow") in a gas-solid suspension at low density. The solid particles are modeled as a gas of smooth hard spheres with inelastic…
We study a two phase flow with interactions of liquid and rarefied gas inside the gas phase. The gas phase is modeled by the BGK model of the Boltzmann equation. The liquid phase is modeled by the incompressible Navier-Stokes equations. In…
The three-dimensional jump conditions for the pressure and velocity fields, up to the second normal derivative,across an incompressible/inextensible interface in the Stokes regime are derived herein. The fluid viscosity is only piecewise…
A new exact solution of the Navier-Stokes equation is derived for the compressible flows which are far from equilibrium in the limit of extremely low shear viscosity and relatively large volume viscosity. The closed description of the…
In rarefied gas flows, the spatial grid size could vary by several orders of magnitude in a single flow configuration (e.g., inside the Knudsen layer it is at the order of mean free path of gas molecules, while in the bulk region it is at a…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
We establish the long-time existence of large-data weak solutions to a system of nonlinear partial differential equations. The system of interest governs the motion of non-Newtonian fluids described by a simplified viscoelastic rate-type…