Main Article Content
Existence and boundedness of the solutions of the boundary value problem for the four velocity two dimensional Broadwell model for bounded boundary conditions is proved and exact analytic solutions are built. An application to the determination of the accommodation coefficients on the boundaries of a flow in a box is performed.
d'Almeida A. Transition of unsteady flows to steady state in the process of evaporation and condensation. CRMécanique. 2008;336:612-615.
d'Almeida A, Gatignol R. The half space problem in discrete kinetic theory. Mathematical Models and Methods in Applied Sciences. 2003;13:99-119.
Platkowski T, Illner R. Discrete velocity models of the Boltzmann equation: a survey on the mathematical aspects of the theory. SIAM Review. 1988;213-255.
d'Almeida A. Exact solutions for discrete velocity models. Mechanic Research Communications. 2007;34:405-409.
d'Almeida A, Gatignol R. Boundary conditions for discrete models of gases and applications to Couette flows. Computational Fluid Dynamics (Publisher: D. Leutlo, D. and Srivastava, R. C.), Eds. Springer-Verlag. 1995;115-130.
Cornille H, d'Almeida A. Temperature and pressure criteria for half- space discrete velocity models. Eur. J. Mech. Fluids B. 2002;21:355-370.
Natta T, Agosseme KA, d'Almeida A. Existence and uniqueness of solution of the ten discrete velocity model C1. JAMCS. 2018;29:1-12.
Cercignani C, Illner R, Shinbrot M. A boundary value problem for the two dimensional broadwell model. Commun. Math. Phys. 1988;114:687-698.
Cabannes H. The discrete boltzmann equation (Theory and applications). Lecture Notes, Spring Quarter; 1980.
Smart DR. Fixed point theorems. Cambridge University Press, New York; 1974.
Gatignol R. Kinetic theory boundary conditions for discrete velocity gases. Phys. Fluids. 1977;20:2022-2030.
Cercignani C. Mathematical methods in kinetic theory. Plenum Press; 1969.