Development of the ellipsoidal statistical bhatnagar-Gross-krook method for hypersonic flows

To avoid the high computational costs related to the DSMC method for low Knudsen number flows, a new particle method, based on the solution to the ES-BGK model of the Boltzmann equation, is investigated. In this method, a fraction of the particles in a cell is selected for velocity reassign-ment from the local Maxwellian distribution based the collision frequency and an even smaller fraction is selected for rotational energy reassignment based the rotational relaxation rate. Zero-dimensional simulation results show that the method can model well the rotational relaxation. When simulating the argon flow over a cone with a weak shock, it is found that a minimum of forty selected particles for transitional velocity reassignment are required to achieve energy con-servation and then good agreement with flow properties simulated with DSMC. However, same number of simulated particles per cell for the case with nitrogen flow is not sufficient to model the rotational relaxation rate and results show relatively good agreement for transitional temperature but poor agreement for rotational temperature.