Related papers: Fixed points and flow analysis on off-equilibrium …
We develop a discrete Boltzmann-type model that uses dynamics in phase space to describe the behavior of traffic flows. Firstly, we model the traffic flow at mesoscopic scale using dynamics in phase space, which is considered as an…
In this paper, we study the polyatomic Boltzmann equation based on continuous internal energy, focusing on physically relevant collision kernels of the hard potentials type with integrable angular part. We establish three main results:…
We investigate a one dimensional flow described with the non-compressible coupled Euler and non-compressible Navier-Stokes equations in Cartesian coordinate systems. We couple the two fluids through the continuity equation where different…
The discretized equilibrium distributions of the lattice Boltzmann method are presented by using the coefficients of the Lagrange interpolating polynomials that pass through the points related to discrete velocities and using moments of the…
The motion of rarefied gases for uniform shear flow at the kinetic level is governed by the spatially homogeneous Boltzmann equation with a deformation force. In the paper we study the corresponding Cauchy problem with initial data of…
Starting with the relativistic Boltzmann equation where the collision term was generalized to include gradients of the phase-space distribution function, we recently presented a new derivation of the equations for the relativistic…
The lattice Boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered. Although the equation is a derivative of lattice gas automata, it…
We re-derive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast to the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of…
This study proposes a novel topology optimization method for unsteady fluid flows induced by actively moving rigid bodies. The key idea of the proposed method is to decouple the design and analysis domains by using separate grids. The…
An iterative scheme can be used to find a steady-state solution to the Boltzmann equation, however, it is very slow to converge in the near-continuum flow regime. In this paper, a synthetic iterative scheme is developed to speed up the…
We consider flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are treated with Neumann type flow conditions, and a…
By solving a simple kinetic equation, in the relaxation time approximation, and for a particular set of moments of the distribution function, we establish a set of equations which, on the one hand, capture exactly the dynamics of the…
A new transient effective theory of the relativistic Boltzmann equation is derived for locally momentum-anisotropic systems. In the expansion of the distribution function around a local "quasi-equilibrium" state a non-hydrodynamic dynamical…
Using Wilsonian methods, we study the renormalization group flow of the Nonlinear Sigma Model in any dimension $d$, restricting our attention to terms with two derivatives. At one loop we always find a Ricci flow. When symmetries completely…
A quadrature-based finite-difference lattice Boltzmann model is developed that is suitable for simulating relativistic flows of massless particles. We briefly review the relativistc Boltzmann equation and present our model. The quadrature…
A low-order finite element method is constructed and analysed for an incompressible non-Newtonian flow problem with power-law rheology. The method is based on a continuous piecewise linear approximation of the velocity field and piecewise…
The dissipative dynamics of an expanding massless gas with constant cross section in a spatially flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe is studied. The mathematical problem of solving the full nonlinear relativistic…
Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the {\it velocity-field} plays the central role. The properties of the…
We determine the flow structure in an axisymmetric diffuser or expansion region connecting two cylindrical pipes when the inlet flow is a solid body rotation with a uniform axial flow of speeds Omega and U, respectively. A quasi-cylindrical…
The kinetic energy distribution function satisfying the Boltzmann equation is studied analytically and numerically for a system of inelastic hard spheres in the case of binary collisions. Analytically, this function is shown to have a…