num_kin_mod2 - Outline for Second Lecture on Numerical...

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Outline for Second Lecture on Numerical Kinetic Models How does CHEMIN work? Very short intro to Numerical solution of ODE’s Overview: What are we trying to accomplish in Kinetics?! Difference between measuring kinetics in the real system, and measuring rate constants in designed experiments. Implications of reactive intermediates. How does CHEMKIN work? Reads chem.inp, surf.inp. Computes thermo (and any other needed properties) for all the species, and computes the reverse rate constants from the thermo. Most of the computations are simple, mostly what this program is doing is parsing the input deck and putting everything in the right format for the next steps. In the old versions, this is called Ckinterp, since it “interprets” the input deck. Reads aurora.inp Sets up a program that returns F(Y), the right hand side of the ODE (or DAE) system, using all the rate constants and molecular properties computed in the first step. Then it calls VODE or DASSL or similar to solve the equations. Postprocessor: Takes the table of yn(ti) computed by VODE and pulls out the columns you want, and plots them. How are ODE’s solved numerically? (the short short version) If we define Y={y i , T} and there is no transport, then Eq.(1) is of the form: dY/dt = F(Y) and we usually know the initial conditions: Y(t o )=Y o The general procedure is to step forward in time with some formula Y(t+ t) = Y(t) + G(Y) t E q . ( 3 ) where G is our best estimate of the average of F(Y(t’)) over the trajectory from Y(t’=t) to Y(t’=t+ t), using lots of little timesteps t until we reach t final . In the simplest approximation called Forward (or Explicit) Euler G=F(Y(t)). This turns out to be pretty inaccurate (just like the rectangle rule is not a very accurate way to compute numerical
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num_kin_mod2 - Outline for Second Lecture on Numerical...

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