计算与应用数学拔尖博士生系列论坛——Approximation of the Boltzmann Collision Operator Based on Hermite Spectral Method
主 题: 计算与应用数学拔尖博士生系列论坛——Approximation of the Boltzmann Collision Operator Based on Hermite Spectral Method
报告人: Yanli Wang (Peking University)
时 间: 2018-04-12 12:00-13:30
地 点: Room 1418, Sciences Building No. 1
12:00-12:30 lunch；12:30-13:30 Talk
Abstract: Boltzmann equation is adopted to describe the statistical behavior of gas molecules. The numerical simulation for this six-dimensional equation is one significant topic after the invention of computers. The difficulty comes partly from its high dimensionality, and partly from its complicated integral operator modeling the binary collision of gas molecules.
This work aims at an affordable way to model and simulate the binary collision between gas molecules. Our new attempt is an intermediate approach between a direct discretization of the quadratic Boltzmann collision operator and simple modelling methods like BGK-type operators. In detail, we first focus on the relatively important physical quantities, which are essentially the first few coefficients in the Hermite expansion, and use an intricate and accurate way to describe their evolution. The strategy comes from the discretization of the quadratic collision operator. For the less important moments, we borrow the idea of the BGK-type operators and let these moments converge to the equilibrium at a constant rate. Although the first part is computationally expensive, we can restrict the number of degrees of freedom such that the computational cost is acceptable. The accuracy of such a model depends apparently on the size of the accurately modelled part. Our numerical examples show that this method can efficiently capture the evolution of lower order moments in the spatially homogeneous Boltzmann equation.