Partially implicit scheme for chemically reacting flows at all Mach numbers

Chemical reactions make computations of chemically reacting flows stiff. Th e degree of stiffness increases as the Mach number decreases because the fl ow timescale increases while the reaction timescales remain constant. Thus, the computation of reacting flows at low Mach numbers is more difficult th an that in high Mach number. In the present study a new implicit scheme tha t employs partially implicit treatment of chemical source terms at mixed ti me levels has been developed. The chemical Jacobian is reduced to a partial form of the full chemical Jacobian (a lower triangular matrix) and thus sa ves time in matrix inversion. In addition, robust calculation of the reacti ng flows is made possible because a negative real eigenvalue of the partial chemical Jacobian allows larger time-step sizes than the full chemical Jac obian. For applications at all Mach numbers, a preconditioned lower upper s ymmetric Gauss-Seidel scheme employing an approximate flux Jacobian splitti ng is incorporated. For high-Mach-number flows the partially implicit schem e maintains similar convergence rates to the fully implicit one; therefore, it enhances computational efficiency by reducing computing time per iterat ion. For low-Mach-number reacting flows it also enables robust calculation of reactions as well as the fully implicit one; however, its convergence ra te is rather slow. Furthermore, more stable and efficient computations are possible when the fully implicit scheme is coupled with the partially impli cit one.