Partially Implicit Scheme for Chemically Reacting Flows at All Mach Numbers

Abstract

Chemical reactions make computations of chemically reacting e ows stiff. The degree of stiffness increases as the Mach number decreases because the e ow timescale increases while the reaction timescales remain constant. Thus, the computation of reacting e ows at low Mach numbers is more dife cult than that in high Mach number. In the present study a new implicit scheme that employs partially implicit treatment of chemical source terms at mixed time levels has been developed. The chemical Jacobian is reduced to a partial form of the full chemical Jacobian(a lower triangular matrix )and thus saves timein matrix inversion. In addition, robust calculation of the reacting e ows is made possible because a negative real eigenvalue of the partial chemical Jacobian allows larger time-step sizes than the full chemical Jacobian. For applications at all Mach numbers, a preconditioned lower upper symmetric Gauss ‐Seidel scheme employing an approximate e ux Jacobian splitting is incorporated. For high-Mach-number e ows the partially implicit scheme maintains similar convergence rates to the fully implicit one; therefore, it enhances computational efe ciency by reducing computing time per iteration. For low-Machnumber reacting e ows it also enables robust calculation of reactions as well as the fully implicit one; however, its convergence rate is rather slow. Furthermore, more stable and efe cient computations are possible when the fully implicit scheme is coupled with the partially implicit one.