The implicit fully coupled numerical method for flows in thermochemical nonequilibrium

Abstract

A new effective implicit fully coupled numerical method to compute a high-speed flowfield that is in thermochemical nonequilibrium has been developed. Such a flowfield is described by coupled partial differential equations for the conservation of mass, momentum, total energy, vibrational energies, rotational energy, mass conservation for each species, etc. The total number of equations can be very large, which greatly complicates the solution of general finite volume vector equation when using the standard fully implicit approach. The proposed method allows us to reduce operations with block tridiagonal matrices to inversion of 4x4 matrices and trivial matrix multiplication operations. Moreover, the approximation factorization error is minimized. The numerical procedures were applied to solve chemical and thermal nonequilibrium flow past a sphere body at Mach 27 and chemically nonequilibrium heterogeneous flow in the channel of a combined ramjet with a solid fuel gas generator. The results indicate that new method is 4-5 times more efficient than the standard fully implicit method.