From the Boltzmann Equation to an Incompressible Navier–Stokes–Fourier System
نویسندگان
چکیده
We establish a Navier–Stokes–Fourier limit for solutions of the Boltzmann equation considered over any periodic spatial domain of dimension two or more. We do this for a broad class of collision kernels that relaxes the Grad small deflection cutoff condition for hard potentials and includes for the first time the case of soft potentials. Appropriately scaled families of DiPerna–Lions renormalized solutions are shown to have fluctuations that are compact. Every limit point is governed by a weak solution of a Navier–Stokes–Fourier system for all time.
منابع مشابه
Hydrodynamic Limit with Geometric Correction of Stationary Boltzmann Equation
We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. The classical theory claims that the solution can be approximated by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer derived from Milne problem. In this paper, we construct counterexamples to disprove such formulation in...
متن کاملTurbulent Flow over Cars
In this paper the flow behaviour over a number of car bodies is studied. For this purpose the unsteady 2-D incompressible Navier-Stokes equations have been applied. After averaging and nondimensionalizing the equations, the system of equations has been transformed from the Cartesian (x-y) coordinates to a body fitted generalized (-) coordinate. As the flow is incompressible, the density in the ...
متن کاملLattice Boltzmann Model for the Incompressible NavierStokes Equation
In the last decade or so, the lattice Boltzmann (LB) method has emerged as a new and effective numerical technique of computational fluid dynamics (CFD).(1-5) Modeling of the incompressible Navier-Stokes equation is among many of its wide applications. Indeed, the lattice Boltzmann equation (LBE) was first proposed to simulate the incompressible NavierStokes equations.(1) The incompressible Nav...
متن کاملBoundary Layers and Hydrodynamic Limits of Boltzmann Equation (i): Incompressible Navier-stokes-fourier Limit
We establish an incompressible Navier-Stokes-Fourier limit for solutions to the Boltzmann equation (with a general collision kernel) considered over a bounded domain. Appropriately scaled families of DiPerna-Lions renormalized solutions with Maxwell reflection boundary conditions are shown to have fluctuations that converge as the Knudsen number ε goes to zero. Every limit point is a weak solut...
متن کاملThe Incompressible Navier – Stokes for the Nonlinear Discrete Velocity Models
We establish the incompressible Navier–Stokes limit for the discrete velocity model of the Boltzmann equation in any dimension of the physical space, for densities which remain in a suitable small neighborhood of the global Maxwellian. Appropriately scaled families solutions of discrete Boltzmann equation are shown to have fluctuations that locally in time converge strongly to a limit governed ...
متن کامل