Boundary Wave and Interior Wave Propagations

Ph.DDOCTOR OF PHILOSOPH

Invariance correction to Grad's equations: where to go beyond approximations?

We review some recent developments of Grad's approach to solving the Boltzmann equation and creating a reduced description. The method of the invariant manifold is put forward as a unified principle to establish corrections to Grad's equations. A consistent derivation of regularized Grad's equations in the framework of the method of the invariant manifold is given. A new class of kinetic models to lift the finite-moment description to a kinetic theory in the whole space is established. Relations of Grad's approach to modern mesoscopic integrators such as the entropic lattice Boltzmann method are also discusse

The Green?s Function for the Initial-Boundary Value Problem of One-Dimensional Navier-Stokes Equation

Ph.DDOCTOR OF PHILOSOPH