Parallel Implementation of a Computational Algorithm Based on the Explicit Iterative Scheme for Modeling Subsonic Reacting Gas Flows

The article presents a parallel implementation of a computational algorithm based on an explicitly iterative LI-M scheme constructed to calculate the dynamics of subsonic flows with radical chain chemical reactions, taking into account multicomponent diffusion and heat transfer, and also energy absorption during chemical transformations on the example of methane pyrolysis. The problem involves multi-scale processes, which leads to computational difficulties when using explicit difference schemes. The computational algorithm is partially simplified by using the principle of splitting by physical processes: kinetic equations are calculated in a separate block by the fifth-order three-stage Runge-Kutta method (Radau method); transfer processes are calculated using the Rusanov flow and the WENO scheme. However, even this approach does not provide an acceptable reduction in the estimated time for solving practical problems since the total calculated time step is determined by diffusion processes in the studied subsonic flows. The problem’s solution is possible by using a scheme of local iterations to calculate dissipative terms. It is based on an explicit iterative process, the parameters of which are the roots of Chebyshev polynomials. The efficient use of parallel computing is possible since the scheme is explicit. The developed algorithm was programmatically implemented in C++ using MPI technology. The algorithm showed good performance and stability while using a sufficiently large time step. The parallel algorithm was analyzed in terms of efficiency for various spatial grids. The result of its work are profiles of substances’ concentrations and temperatures along the reactor’s length.