ContribDieselFoamChemistryPropertiesChemistrySolver

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Options:

• ODE
• EulerImplicit
• sequential

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• ODE

Use a stiff Ordinary Differential Equations solver to solve the chemistry.

• EulerImplicit

Equations will be linearized and the equation system solved implictly, or semi-implict really since the equations are non-linear. If the reaction rate is

$\dot \omega = k_f c_1 c_2 - k_b c_3 c_4$, we re-write it as

$\dot \omega = P_f c_f - P_b c_b, P_f = k_f \max(c_1,c_2), c_f = \min(c_1,c_2), P_b = k_b \max(c_3, c_4), c_b = \min(c_3, c_4)$

Solving the system $\frac{dc}{dt} = S_c \dot \omega$, $S_c$ is the stoichiometric coefficient matrix.

We construct the maxtrix-vector system $A^n c^{n+1} = c^n$

from $\frac{c^{n+1}-c^n}{\delta t} = S_c \dot \omega^{n+1}$

The reaction rate is evaluate semi-implicit as

$\dot \omega^{n+1} = P_f^n c_f^{n+1} - P_b^n c_b^{n+1}$

• sequential

Do not use this. This was implemented to compare with how KIVA calculate the chemistry.