Calculation algorithm for the collisional moments of the Boltzmann equation for Maxwell molecules Original Research Article

We present in this paper an analytical calculation algorithm of the collisions integrals for the Maxwellʹs particles. This algorithm is tested by a program written in Maple V and carried out on a personal computer. The formulas obtained of these integrals whose order is lower or equal to 5 are identical to those of Truesdell (1980), those whose order is equal to 6, 7 and 8 are presented at the end of this paper. Even if the resulting formulas for high orders become large, they remain always short and handy compared to those which correspond to the original formula given by the theorem of Truesdell–Muncaster (1980). However, the limits of this algorithm depend only on the capacities of the treating machine.