Comparison Between The Navier-Stokes And The Boltzmann Equations For The Simulation Of An Axially Symmetric Compressible Flow With Shock Wave Using The Monte-Carlo Method
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S. S. Nourazar, S. M. Hosseini, A. Ramazani, & H. R. Dehghanpour
An axially symmetric compressible flow past a flat-nosed cylinder at high velocity and low pressure with shock wave is simulated using the Navier-Stokes equation and the Boltzmann equation. The results of the two simulations (Navier-Stokes and Boltzmann) are compared in terms of different Knudsen numbers. In the region close to the shock wave the discrepancies between the results of simulation of the Navier-Stokes equations and the Boltzmann equation for the temperature, the axial velocity and the radial velocity along the boundary is not pronounced. However the discrepancies in the region close to the shock wave for the density is pronounced. Keywords: Boltzmann equation, DSMC. 1 Introduction In the simulation of gas dynamics problems where the velocity distribution is a strict Maxwellian the Euler equation is to be solved. However in the simulation of gas dynamics problems where the velocity distribution is a moderately distorted Maxwellian the Navier-Stokes equation is to be solved. In the gas flow problems where the length scale of the system is comparable to the mean free path for molecules in the gas flow the concept of the continuum
Boltzmann equation, DSMC.