非弹性玻尔兹曼方程的Hermite谱方法
Hermite spectral method for the inelastic Boltzmann equation
AI总结：
本文提出一种基于Hermite展开的谱方法求解非弹性玻尔兹曼方程，通过精确推导VHS模型展开系数并结合二次与线性化碰撞算子，在保证精度的同时降低计算成本，使二维周期问题计算变得可行。
摘要：
我们针对非弹性玻尔兹曼方程提出了一种Hermite谱方法，使得二维周期问题的计算在当前硬件条件下变得可行。新算法基于Hermite展开，其中VHS模型的展开系数被化简为若干求和式，并且可以精确推导。此外，通过将二次碰撞算子与线性化碰撞算子相结合，构建了一种新的碰撞模型，这有助于在计算成本与精度之间取得平衡。包括空间二维模拟在内的多种数值实验验证了该数值格式的精度与效率。
英文摘要：
We propose a Hermite spectral method for the inelastic Boltzmann equation, which makes two-dimensional periodic problem computation affordable by the hardware nowadays. The new algorithm is based on a Hermite expansion, where the expansion coefficients for the VHS model are reduced into several summations and can be derived exactly. Moreover, a new collision model is built with a combination of the quadratic collision operator and a linearized collision operator, which helps us to balance the computational cost and the accuracy. Various numerical experiments, including spatially two-dimensional simulations, demonstrate the accuracy and efficiency of this numerical scheme.
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