抄録
In order to estimate dynamic wind load on the spatial structures, for which it can be critical load, by reproducing wind around them with high accuracy, three-dimensional large eddy simulation (3D LES) with high resolution model is required. For such a simulation, which leads to a large-scale problem, as it requires a large amount of computational time, development of calculation algorithm to speed up 3D LES is desired to promote practical use. In the case of using splitting method, where pressure and wind velocity are solved separately, computational time is mostly spent in solving pressure poison equation.
In this paper, the multigrid preconditioned conjugate gradient (CG) method (MG method) using plural two-dimensional coarse meshes is proposed in order to reduce computational time for three-dimensional large eddy simulation around a structure with cylindrical roofs.
So far, the authors proposed the MG method using singular two-dimensional coarse mesh for the model, which is constructed in the way that three-dimensional mesh is generated by extruding the two-dimensional mesh in the spanwise direction, namely the direction perpendicular to streamwise direction. In this model, however, three-dimensional flow field cannot be generated. Thus, in this paper, we propose the method using plural two-dimensional coarse meshes applicable to the model where analytical domain is added on either side of the structure in order to generate a three-dimensional flow field around it.
Applicability of the proposed method is confirmed in comparison with diagonal preconditioned CG method (DIAG method) for two turbulence models, which are standard Smagorinsky model (SSM) and dynamic Smagorinsky model (DSM), and for two mesh resolution cases of Ny40 and Ny80 where the numbers of division in the spanwise direction of the analytical domain are 40 and 80, respectively.
Major findings obtained from numerical results are described below:
1) Significant error of wind load between the MG method and DIAG method is not observed in terms of statistical amount, that is, mean and fluctuating pressure coefficient.
2) For each turbulence model and mesh resolution model, the MG method results in speedup ranging from 118.2% to 137.6% compared to the DIAG method.
3) For different turbulent models of SSM and DSM, equivalent speedup effect is confirmed although the number of convergence fluctuates only for DSM until about 2,500 step, when sine function by which inflow turbulence are multiplied to prevent from numerical instability at an initial stage reaches 1.0.
4) In the MG method, as the scale of mesh model increases, the number of iteration dose not increase and computational time on the coarsest mesh relatively decreases. Thus, it is expected that the MG method has more speedup effect for larger scale problems.
