Accuracy of bicompact schemes in the problem of Taylor–Green vortex decay

For the unsteady incompressible Navier–Stokes equations, a high-order accurate bicompact scheme having the fourth order of approximation in space and the second order of approximation in time has been constructed for the first time. The scheme is obtained by applying the Marchuk–Strang splitting method with respect to physical processes. The convective part of the equations is discretized by additionally using locally one-dimensional splitting. The grid convergence of the proposed scheme with an order higher than the theoretical one is demonstrated on the exact solution of the two-dimensional Taylor–Green vortex problem. The developed bicompact scheme is used to compute the decay of the three-dimensional Taylor–Green vortex (in both laminar and turbulent regimes). It is shown that the scheme well resolves vortex structures and reproduces the turbulent spectrum of kinetic energy with high accuracy.