TVD FINITEDIFFERENCE METHODS FOR COMPUTING HIGHSPEED THERMAL AND CHEMICAL NONEQUILIBRIUM FLOWS WITH STRONG SHOCKS

Partiallydecoupled upwindbased totalvariationdiminishing TVD finitedifference schemes for the solution of the conservation laws governing twodimensional nonequilibrium vibrationally relaxing and chemically reacting flows of thermallyperfect gaseous mixtures are presented. In these methods, a novel partiallydecoupled fluxdifference splitting approach is adopted. The fluid conservation laws and species concentration and vibrational energy equations are decoupled by means of a frozen flow approximation. The resulting partiallydecoupled gasdynamic and thermodynamic subsystems are then solved alternately in a lagged manner within a time marching procedure, thereby providing explicit coupling between the two equation sets. Both timesplit semiimplicit and factored implicit fluxlimited TVD upwind schemes are described. The semiimplicit formulation is more appropriate for unsteady applications whereas the factored implicit form is useful for obtaining steadystate solutions. Extensions of Roe's approximate Riemann solvers, giving the eigenvalues and eigenvectors of the fully coupled systems, are used to evaluate the numerical flux functions. Additional modifications to the Riemann solutions are also described which ensure that the approximate solutions are not aphysical. The proposed partiallydecoupled methods are shown to have several computational advantages over chemistrysplit and fully coupled techniques. Furthermore, numerical results for single, complex, and double Mach reflection flows, as well as cornerexpansion and bluntbody flows, using a fivespecies fourtemperature model for air demonstrate the capabilities of the methods.