Energy Exchange Rate Coefficients in Modeling Carbon Dioxide Kinetics: Calculation Optimization

Vestnik St. Petersburg University: Mathematics. 2019. Vol. 52. No. 4. P. 428–435.

Gorikhovskii V.I., Нагнибеда Е. А.

 In this paper considers algorithms for calculating vibrational energy exchange rate coefficients for collisions of carbon dioxide molecules are considered. For numerical modeling of CO2 vibrational kinetics in the state-to-state approach, it is necessary to solve a system of several thousands of differential equations for level populations of three vibrational CO2 modes at an each step of calculations. The right hand parts of these kinetic equations contain energy exchange rate coefficients for collisions of molecules from different levels of three vibrational CO2 modes. There are hundreds of thousands of these coefficients due to the large number of energy exchanges. From the numerical point of view, this modeling qualifies as Big Data and requires the development of rapid numerical methods or pre-calculations. Such an amount of data also requires a quick access data structure. Until now for the state-to-state description of CO2 vibrational relaxation has used only simplified kinetic schemes with a limited numbers of vibrational levels and energy transitions have been used. In the present paper the problem is solved in the complete formulation. An effective scheme for calculating the coefficients is proposed on the basis of parallel computations and convolute code optimization, together with an optimal data structure for their storage.

Keywords: parallel algorithms, carbon dioxide, state-to-state approach, Vibrational kinetics, optimization of numerical calculations