Numerical Simulation of Supersonic Flows with Nonequilibrium Chemical Reactions

A new efficient implicit fully coupled numerical method for calculating thermochemical nonequilibrium flows is developed. Such flows are described by partial differential equations for conservation of mass, momentum, total energy, conservation of mass for each component, transfer of turbulent characteristics, etc. The total number of equations can be very large, which greatly complicates the solution of the general finite volume vector equation by using the standard fully implicit approach. The proposed method allows one to reduce operations with block tridiagonal matrices to inversion of 5 × 5 matrices and trivial operations of matrix multiplication. The numerical method is used to calculate the afterburning of the jet and for the supersonic combustion of hydrogen in the channel. The results show that for the considered problems, the new method is about two times more efficient than the standard fully implicit method.