Numerical computation of the hypersonic leading edge problem using the Burnett equations

The hypersonic rarefied flow near the sharp leading edge of a flat plate is computed for the first time using a finite-difference solution of the complete, unsteady Burnett equations. The computation is advanced in time from the initial conditions until the steady-state solution is reached. The computational region extends from the leading edge to the strong-interaction regime. Schamberg’s second-order wall slip and temperature jump boundary conditions are employed at the wall. The numerical results are compared with experimental data, a Monte Carlo simulation, and a finite-difference solution of the complete Navier–Stokes equations. Based on these comparisons, it is evident that the Burnett equations in conjunction with Schamberg’s second-order boundary conditions give a much less accurate description of the rarefied flow field near the leading edge than do the Navier–Stokes equations.