Adiabatic compression of ideal collisionless gas in 3D space

The purpose of this study is to find an analytical solution for the adiabatic compression of collisionless gas with movable and unmovable boundaries in 3D space. The paper presents a detailed inference of a class of exact solutions for determining the variation of molecular distribution density in the space/velocity space with time. In contrast to the 1D case, the velocity space is piecewise discontinuous. To calculate the macroscopic values of the exact solution, we should integrate the particle distribution density over the velocities. We also compared the class of exact solutions with the Monte Carlo simulation results. The paper contains curves that compare the analytical and numerical solutions for different moving wall velocities and numbers of particles, and tables with max estimated errors for the macroscopic quantities. It is shown that as the number of particles increases, the numerical solution approaches the analytical one. The PV chart is used to compare the adiabatic and analytical solution curves at different boundary velocities. The software package performance is assessed. The class of solutions can be used to verify the software.