Improved mode multigrid method for accelerating turbulence flows

Because much computing time is required for the refined turbulence simulations, it is imperative to develop efficient acceleration methods. An improved mode multigrid method is proposed to accelerate the convergence of turbulent flow in this paper. It is found that the zero-frequency shift modes, which are characterized as the boundary layer and the wake of turbulent flows, represent the main modes of turbulent flows, and retaining the shift modes can make the turbulence flow converge faster. Numerical experiments indicate that the improved mode multigrid method can eliminate the problem of irregular residual jump shown in the original mode multigrid method and can be successfully applied to accelerate the turbulent flows to steady state. The improved method is more robust and more efficient compared with the original mode multigrid method. The number of iteration steps can be significantly reduced by 2–3 times than the nonacceleration method while maintaining the computational accuracy. The improved mode multigrid method is further extended to accelerate the convergence of various turbulent flows for complex configurations, which demonstrates that the method can be widely used in engineering problems.