Arclength continuation

However, because of the strong nonllnearltles In the reactor fiow problem, continuation procedures must be used to obtain a good Initial guess for the Newton Iteration. A simple first order continuation scheme falls at fiow transition points (bifurcations) where the Jacobian, G, becomes singular. To circumvent this problem an arclength continuation scheme discussed by Keller (26.27) and Chan (2S.) Is used which leads to the Infiated system ... 

Procedures enabling the calculation of bifurcation and limit points for systems of nonlinear equations have been discussed, for example, by Keller (13) Heinemann et al. (14-15) and Chan (16). In particular, in the work of Heineman et al., a version of Keller s pseudo-arclength continuation method was used to calculate the multiple steady-states of a model one-step, nonadiabatic, premixed laminar flame (Heinemann et al., (14)) a premixed, nonadiabatic, hydrogen-air system (Heinemann et al., (15)). 

In this section we apply the adaptive boundary value solution procedure and the pseudo-arclength continuation method to a set of strained premixed hydrogen-air flames. Our goal is to predict accurately and efficiently the extinction behavior of these flames as a function of the strain rate and the equivalence ratio. Detailed transport and complex chemical kinetics are included in all of the calculations. The reaction mechanism for the hydrogen-air system is listed in Table... 

Starting from stoichiometric conditions (< = 1) and then proceeding in the lean direction (< < 1), we anticipate that the peak fiame temperature will be reduced gradually. In addition, as the maximum temperature is lowered and the corresponding adiabatic fiame speed of an unstrained a = 0) fiame is reduced, we anticipate that the fiame will move closer to the plane of symmetry. Ultimately, as the fuel to air ratio is lowered below a critical value, radical production in the fiame will be severely restricted and the fiame will extinguish (lean extinction). The arclength continuation procedure will then generate unphysical solutions for additional continuation steps until a maximum value of the... 

We demonstrate the use of arclength.continuation.m for the study ofmultiple steady states in a nonisothermal CSTR. Consider a perfectly-mixed stirred-tank reactor with A reacting to form B... 

---