Efficiently and Accurately Solving Large Kinetic Simulations

Efficiently and Accurately Solving Large Kinetic Simulations 

The methods described in Section II carry out the first step in Fig. 1, constructing a detailed chemical kinetic model from our current understanding of chemistry. However, this step is only useful if we can numerically solve the chemical kinetic simulation to obtain quantitative predictions. In many cases, solving the model is even more challenging than constructing it. 

Most real reacting systems are accurately described by a large system of partial differential equations in (x, y, z, t) most commonly the spatial coordinates are discretized so that one is actually solving equations like this at each mesh point  

There are many ways one can try to reduce the computational burden. Ideally, one would find numerical methods which are guaranteed to retain accuracy while speeding the calculations, and it would be best if the procedure were completely automatic i.e. it did not rely on the user to provide any special information to the numerical routine. Unfortunately, often one is driven to make physical approximations in order to make it feasible to reach a solution. Common approximations of this type are the quasi-steady-state approximation (QSSA), the use of reduced chemical kinetic models, and interpolation between tabulated solutions of the differential equations (Chen, 1988 Peters and Rogg, 1993 Pope, 1997 Tonse et al., 1999). All of these methods were used effectively in the 20th century for particular cases, but all of these approximated-chemistry methods share a serious problem it is hard to know how much error is 

Below we present 21st century numerical solution methods suitable for large chemical kinetic simulations. We present both a method that does not introduce any approximations, and an automated model-reduction method that allows rigorous error control in steady-state simulations. 

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III. Efficiently and Accurately Solving Large Kinetic Simulations... 

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