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The Broadwell model is a simplified kinetic description for gas dynamics where the main assumption is that the particle distribution function can be represented by a discrete number of velocities. Starting from the Broadwell model and the appropriate boundary conditions we derive two 1D models for gas transport in a thin channel.
In the limit of no interparticle collisions the 1D model is the well known telegraph equation. In the case of collisional flow the 1D model is a system of three first-order hyperbolic PDEs. Both 1D models are validated through numerical simulations that compare the 1D models to the 2D Broadwell system.
Furthermore, in the limit of no inter-particle collisions we are able to rigorously show that under a di. Under a hyperbolic scaling we are able to show that solutions to the collisionless Broadwell model converge weakly to the solutions of the telegraph equation.
Finally, we derive a long-time asymptotic formula for the solution of the collisionless Broadwell system, which reveals oscillations that explain why the convergence in the di. Due to the nonlinearity of the inter-particle collisions, we are not able to prove rigorous convergence results for the collisional Broadwell system.
Source Commun. Zentralblatt MATH identifier Christlieb, Andrew J.
The Broadwell model in a thin channel. Milky Way — This article is about the galaxy.
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Gas Dynamics of Thin Bodies: F I Frankl, E. A. Karpovich: elalfatetap.tk: Books
Aerodynamics — is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is closely related to fluid dynamics and gas dynamics, with much theory shared between them.
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