  The present paper deals with the problem of improving the efficiency of large
scale turbulent flow simulations. The high-fidelity methods for modelling
turbulent flows become available for a wider range of applications thanks to
the constant growth of the supercomputers performance, however, they are still
unattainable for lots of real-life problems. The key shortcoming of these
methods is related to the need of simulating a long time integration interval
to collect reliable statistics, while the time integration process is
inherently sequential. 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.
