Coupling of Kinetic Equations and Their Hydrodynamic Limits.

摘要

During the last two years, the author continued his efforts to reach the above objectives. In particular he focused on the following: Further numerical and theoretical studies of the coupling of Boltzmann equation and its hydrodynamic limits. Numerical and theoretical analysis of the coupling of kinetic equations and their hydrodynamic limits for particular kinetic models. (This gives more insight into the coupling method for the full Boltzmann model). Numerical and mathematical studies of the coupling of BCE and ES-BCE with their hydrodynamic limits. (The study of BCE and ES-BCE led the author to replace in the coupling of Boltzmann equations and their hydrodynamic limits, the Boltzmann equations by ES-BCE model. The author plan now is to show that this resulting coupling is optimal and can be used for the numerical simulation of flows around full airplanes at high altitudes). This study is subdivided into two parts In the monoatomic case. The author is developing and validating his coupling using Direct Simulation Monte Carlo method for the kinetic model. He is also planning on developing a deterministic approach for the kinetic model. This will cut the computer cost considerably and allows for the computations around full airplanes. In the polyatomic case, the author is developing and validating his coupling using Direct Simulation Monte Carlo method for the kinetic model when an internal energy variable is used.