Multiple semi-coarsened multigrid method with application to large eddy simulation

Abstract

SUMMARYThe Multiple Semi-coarsened Grid (MSG) multigrid method of Mulder (J. Comput. Phys. 1989; 83:303 -323) is developed as a solver for fully implicit discretizations of the time-dependent incompressible Navier-Stokes equations. The method is combined with the Symmetric Coupled Gauss-Seidel (SCGS) smoother of Vanka (Comput. Methods Appl. Mech. Eng. 1986; 55:321-338) and its robustness demonstrated by performing a number of large-eddy simulations, including bypass transition on a at plate and the turbulent thermally-driven cavity ow. The method is consistently able to reduce the non-linear residual by 5 orders of magnitude in 40-80 work units for problems with signiÿcant and varying coe cient anisotropy. Some discussion of the parallel implementation of the method is also included.

A modification of the artificial compressibility algorithm with improved convergence characteristics

“…In particular the inclusion of the additional elements on the off-diagonals arising from the convection and diffusion schemes is found to make little difference in the rate of convergence and hence these elements are not used in the present work. For the SCGS algorithm, this unimportance of the off-diagonals has been reported by others [21,22]. When these off-diagonals terms are dropped the left-hand side of Equation (21) differs from Equation (18) only in the centre coefficients Table I.…”

“…Making a sweep in the direction opposite to the main velocity component can be unstable and presents a problem in recirculating flows. The algorithm does have the advantage of easy-to-choose under-relaxation parameters for the changes in velocity and pressure; the authors have used ∼ 0.9 to solve very different flow problems, while others [21,22] have used values in the range (0.2 ↔ 0.75). A more serious defect is that it is an inherently serial algorithm.…”

“…Once this matrix inversion has been done, the amount of computational work needed to determine p i, j,k is the same as for the case of explicit convection and diffusion. Note that as the general procedure involves solving for the changes in the velocity and pressure, it may be possible to change the matrix in Equation (21) and still obtain a solution. In particular the inclusion of the additional elements on the off-diagonals arising from the convection and diffusion schemes is found to make little difference in the rate of convergence and hence these elements are not used in the present work.…”

Incompressible flows and the Boussinesq approximation: 50 years of CFD

“…Following up on the previous point, indeed, it is worth pointing out that RANS have been occasionally used for RB (Kenjeres and Hanjalic [142,143]), and vice versa, LES has been sporadically applied to problems with horizontal temperature difference (Peng and Davidson [144], Sergent et al [145], Salat et al [146], Ham et al [147], Sergent et al [148], Zhang et al [149]). In practice, the intrinsic ability of LES to deal with highly unsteady dynamics (for which no steady flow "in mean" may exist) goes some way to explain why it has enjoyed a widespread use for the simulation of turbulent RB convection (Eidson [150], Wong and Lilly [151], Kimmel and Domaradzki [152], Sergent et al [153], Kenjeres and Hanjalic [143], Dabbagh et al [154], Togni et al [155]).…”