An approach for accelerating incompressible turbulent flow simulations based on simultaneous modelling of multiple ensembles

The novel approach with modelling of multiple flow states is discussed in the paper. The suggested numerical procedure allows to parallelize the integration in time by the cost of additional computations. Multiple realizations of the same turbulent flow are performed simultaneously. This allows to use more efficient implementations of numerical methods for solving systems of linear algebraic equations with multiple right-hand sides, operating with blocks of vectors. The simple theoretical estimate for the expected simulation speedup, accounting the penalty of additional computations and the linear solver performance improvement, is presented. The two problems of modelling turbulent flows in a plain channel and in a channel with a matrix of wall-mounted cubes are used to demonstrate the correctness of the proposed estimates and efficiency of the suggested approach as a whole. The simulation speedup by a factor of 2 is shown.