Adaptive and Hyperbolic Quadrature-Based Moment Method for the Boltzmann Equation
主 题: Adaptive and Hyperbolic Quadrature-Based Moment Method for the Boltzmann Equation
报告人: Julian Koellermeier(RWTH Aachen University, Germany)
时 间: 2014-08-18 10:00-11:00
地 点: 理科一号楼1418（主持人：李若）
We want to solve flow problems involving rarefied gases and use the Boltzmann equation as the starting point. With the help of a non-linear transformation of the velocity, we allow for an efficient adaptive discretiza-tion of the velocity phase space. Afterwards, we perform a series expansion of the unknown distribution function in different basis functions. Unfortunately, standard projection methods for this approach lead to PDE systems that are in general not hyperbolic. Due to lack of hyperbolicity, numerical computations can break down or yield nonphysical solutions. We therefore apply quadrature-based projection methods. The quadrature-based projection methods modify the structure of the system in the desired way so that the resulting system of equations is globally hyperbolic. In our talk, we will present another explanation of the quadrature-based projection method and compare the derivation to a very similar approach proposed by Cai et al.