In its classical formulation, the lattice Boltzmann method (LBM) is applicable in the range of subsonic velocities and small temperature ratios. The novel Particle-on-demand method (PonD) allows to numerically solve the discrete Boltzmann equation for high Mach numbers. In comparison with the standard LBM, the collision step is simple, but the streaming step is implicit, not mass conserving and computationally heavy. A large part of the computational cost comes from matrix inversions during the rescaling of the discrete distribution functions (DF) from one gauge to another. To avoid matrix inversions, we propose another method of discrete DF rescaling, where the discrete DF are restored from the moments, while the conversion to a different reference frame is in the moment space. Results obtained by this improved method were compared to results, received by standard PonD for a number of problems. This improvement is validated to produce similar results to the original PonD, and is computationally cheaper in comparison with PonD.

在经典公式中，格子玻尔兹曼法（LBM）适用于亚音速和小温度比的范围。新颖的按需粒子方法（PonD）可以对高马赫数的离散Boltzmann方程进行数值求解。与标准LBM相比，冲突步骤简单，但流传输步骤是隐式的，不节省大量资源，并且计算量大。计算成本的很大一部分来自离散分布函数（DF）从一个量表到另一个量表的重新缩放过程中的矩阵求逆。为避免矩阵求逆，我们提出了另一种离散DF重新缩放的方法，其中离散DF从矩恢复，而到不同参考帧的转换则在矩空间中。将通过这种改进方法获得的结果与结果进行比较，标准PonD收到了许多问题。该改进经过验证可产生与原始PonD相似的结果，并且与PonD相比在计算上更便宜。