Using Reduced Chemistry Models in Multidimensional Simulations without Introducing Error

Using Reduced Chemistry Models in Multidimensional Simulations without Introducing Error 

We would like to solve the approximate model, Eq. (7) rather than the full model, Eq. (6) above, but we need to have some control over the error introduced by this approximation. 

The difficulty is that Y(t) and Tapprox(0 can follow rather different trajectories while we can bound the error fflappr0x(T) — n( Y) at a single point Y, it is not so easy to bound the error fflapProx(Tapprox(0) — 0J( Y(t)) along the whole 

There is, however, one important class of reacting-flow simulations where bounding the deviation between co( Y) and (uappmx( Y) immediately allows one to control the approximation error steady-state simulations. For steady-states, the left-hand side of Eq. (6) and Eq. (7) vanish, and one wants to ensure that the solution Fapprox to the approximate equation 

If one were able to guarantee that the reduced chemistry model reproduced the full-chemistry source term within a tolerance e for all F s in some range Y 

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