Kinetic Schemes

Kinetic schemes are numerical methods which rely on an asymptotic relationship between Boltzmann type equations and certain macroscopic balance laws. Since the scalar differential operator of the Boltzmann equation is generally easier to discretize than a system of non-linear transport equations, this relationship is attractive from a numerical point of view. However, the reduced complexity of the differential operator comes with the price of an increase in the number of independent variables and a stiff behavior close to the macroscopic limit. Different approaches to deal with these difficulties lead to different kinetic schemes,

In this project, various aspects of kinetic schemes for hyperbolic conservation laws as well as the incompressible Euler and Navier-Stokes equations are studied.