The parareal algorithm on the model for combustion of methane
L. van der Linden (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Domenico Lahaye – Mentor (TU Delft - Mathematical Physics)
C. Vuik – Graduation committee member (TU Delft - Numerical Analysis)
J.L.A. Dubbeldam – Graduation committee member (TU Delft - Mathematical Physics)
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Abstract
In this work, the parareal algorithm is analysed and executed on the model for combustion of methane. The parareal algorithm is designed to generate an approximation to an initial value problem faster than a serial numerical time-integration method by using two propagators, the coarse propagator and the fine propagator. With the use of two different propagators, some computations can be carried out in parallel, which leads to a faster method. In this research, the parareal algorithm is executed on the two-step mechanism for combustion of methane. The temperature rise due to the combustion is assumed to be zero. The model is implemented in Python and with the use of the librarymultiprocessing, computations are executed in parallel. Different time-integration methods are implemented that can be used in the coarse and fine propagator. In this research, we will focus on the case that the both propagators use the same time-integration method. One can distinguish the propagators by using a different time-step for a chosen time-integration method. With the use of the absolute error the accuracy can be examined. Because the analytic solution to the problem for combustion of methane is unknown, a time-integration method, from which we know that it gives a small absolute error, is used as representation of the analytic solution. The parareal algorithm executed on the model for combustion of methane gives an accurate result for the right choice of propagators. However, for this choice of propagators, the parareal algorithm does not result in a significant speedup compared to the fine propagator in serial, assuming that we have enough processors available. This is because the running time of the propagators do not differ much. To generate a better speedup, two different time-integration methods can be considered for the propagators. Moreover, the model for combustion of methane can be divided into more than two partial reaction and then themulti-level parallelization [1] can be examined.