An analytical solution to Boltzmann equation of dilute granular flow with homotopy analysis method

The homotopy analysis method （HAM）, as a new mathematical tool, has been employed to solve many nonlinear problems. As a fundamental equation in non-equilibrium statistical mechanics, the Boltzmann integro-differential equation （BE） describing the movement of particles is of strong nonlinearity. In this work, HAM is preliminarily applied to dilute granular flow which is relatively simple. By choosing the Maxwell velocity distribution function as the initial solution, the concrete expression of the first-order approximate solution to BE with collision term being the BGK model is given. Furthermore it is consistent with the solution using Chapman-Enskog method but does not rely on little parameters.