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.

翻译：我们为无弹性波尔茨曼方程式建议了Hermite光谱法,该法使得目前硬件能够负担得起二维周期问题计算。新的算法基于Hermite的扩展,VHS模型的扩展系数被减为几个总和,可以精确地计算出来。此外,新碰撞模型是与四面碰撞操作员和线性碰撞操作员相结合的,这帮助我们平衡计算成本和准确性。各种数字实验,包括空间二维模拟实验,显示了这个数字方法的准确性和效率。