**Numerical Simulation of Hypersonic Rarefied Flows Using the Second-Order Constitutive Model of the Boltzmann Equation** Numerical Simulation of Hypersonic Rarefied Flows Using the Second-Order Constitutive Model of the Boltzmann Equation

DOI: 10.5772/intechopen.70657

Rho Shin Myong

Additional information is available at the end of the chapter Rho Shin Myong

http://dx.doi.org/10.5772/intechopen.70657 Additional information is available at the end of the chapter

### Abstract

Various mathematical theories and simulation methods were developed in the past for describing gas flows in nonequilibrium, in particular, hypersonic rarefied regime. They range from the mesoscale models like the Boltzmann equation, the DSMC, and the highorder hydrodynamic equations. The moment equations can be derived by introducing the statistical averages in velocity space and then combining them with the Boltzmann kinetic equation. In this chapter, on the basis of Eu's generalized hydrodynamics and the balanced closure recently developed by Myong, the second-order constitutive model of the Boltzmann equation applicable for numerical simulation of hypersonic rarefied flows is presented. Multi-dimensional computational models of the second-order constitutive equations are also developed based on the concept of decomposition and method of iterations. Finally, some practical applications of the second-order constitutive model to hypersonic rarefied flows like re-entry vehicles with complicated geometry are described.

Keywords: hypersonic rarefied flows, moment equations, balanced closure, numerical simulation, discontinuous Galerkin
