Tl . - - - - - AIAA - 99 - 0966 Detonation Solutions from Reactive Navier - Stokes Equations

Two-dimensional reactive Navier-Stokes equations are solved using a simple implicit Beam-Warming finite difference scheme. Comparisons of the detonation wave solutions of reactive Euler equations and reactive Navier-Stokes equations show that physical diffusion is important at high resolution when the numerical diffusion becomes negligible. Hence, for accurate detonation wave solutions it is necessary to solve full reactive Navier-Stokes equations which include physical diffusion. High grid resolution and use of physical diffusion enables the use of simple central difference approximations for spatial derivatives. Also, implicit time stepping allows larger time steps relative to explicit schemes at the expense of inversion of a series of block tri-diagonal matrices with small block sizes. Sample problems indicate that by using this method the computations are up to five times faster than the Roe's method, which is commonly used in detonation computations.