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：本文提出了一种适用于非弹性玻尔兹曼方程的埃米尔特谱方法，使当今硬件能够承担二维周期问题的计算负担。该新算法基于埃米尔特展开，其中针对VHS模型的展开系数可简化为若干求和形式，并能精确推导得出。此外，通过结合二次碰撞算子与线性化碰撞算子构建了一种新的碰撞模型，有助于平衡计算成本与精度。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准确性与高效性。