Efficient interpolation of precomputed kinetic data employing reduced multivariate Hermite Splines. (4th March 2017) - Klingenberger, Markus; Hirsch, Ofer; Votsmeier, Martin
Highlights: Reduced Hermite spline interpolation speeds up surface kinetic models. It is an order of magnitude faster than tensor product spline interpolation. Several orders of magnitude less memory is required than for tensor product splines. It is local, thereby allowing in-situ, adaptive generation of lookup tables. Abstract: Detailed surface kinetics can be efficiently implemented into complex reactor simulations by the use of precomputed solutions of the chemical rate equations. In this work we propose reduced Hermite splines as an interpolation method for the precomputed rate data. The reduced Hermite splines require significantly less storage space and less execution time than the tensor product splines that have been previously used for this task. Using previously published test cases on NH3 oxidation, we demonstrate that despite of the reduced storage requirements and faster interpolation times, reduced Hermite interpolation achieves the same interpolation accuracy as conventional full tensor product splines. In many cases, the derivatives of the interpolated function with respect to the input quantities can be cheaply obtained during the computation of the function values. If these derivatives are provided as additional information, the accuracy of the reduced Hermite method even outperforms conventional tensor product splines, in our demonstration example by a factor of three. The advantage of the reduced Hermite schemes with respect to storage requirements and evaluation time strongly increase with the dimensionality of the interpolation problem. It is therefore expected that the reduced Hermite splines will allow to significantly extend the application range of solution mapping methods to higher dimensional problems (i.e. problems with a larger number of relevant chemical species).