Development of an object-oriented three-dimensional burnett equations solver for computing hypersonic flows in continuum-transition regime

For computation of hypersonic flowfields about space vehicles in low earth orbits, where the local Knudsen numbers (Kn) lie in the continuum-transition regime, a set of extended three-dimensional hydrodynamic equations are required which are more accurate than the Navier- Stokes equations and computationally more efficient than the Direct Simulation Monte Carlo (DSMC) computations. One such set is the Burnett equations which are obtained from the Chapman-Enskog expansion of the Boltzmann equation (with Knudsen number (Kn) as a small parameter) to O(Kn²). In this paper, the threedimensional augmented Burnett equations are derived from the Chapman-Enskog expansion of the Boltzmann equation to O(Kn²) and adding the augmented terms (linear third-order super Burnett terms with coefficients determined from linearized stability analysis to ensure stability of the augmented Burnett equations to small wavelength disturbances). The equations are solved using an explicit time-stepping scheme with Steger-Warming flux-vector splitting algorithm for the convective flux terms and second-order central differencing for the stress and heat flux terms. Maxwell-Smoluchowski slip boundary conditions are employed at the wall. 3-D augmented Burnett equations solver is developed both in FORTRAN77 and object-oriented JAVA. Both the FORTRAN and JAVA codes are applied to compute the three-dimensional hypersonic blunt-body flows for various range of Knudsen numbers and Mach numbers producing identical results. The focus of this paper is on development of a JAVA code for a very complex set of equations and its application to 3-D complex configurations.