"Research for the Future Program"

1.Research Institution | Nagoya University | |

2.Research Area | Physical and Engineering Sciences | |

3.Research Field | Computational Science and Engineering | |

4.Term of Project | FY 1997 〜 FY 2001 | |

5.Project Number | 97P01101 | |

6.Title of Project | Computational Science and Engineering for Global Scale Flow Systems |

Name | Institution,Department | Title of Position |

Yukio, Kaneda | Nagoya University, Graduate School of Engineering | Professor |

**8.Core Members**

Names | Institution,Department | Title of Position |

Nobuyuki, Satofuka | Kyoto Institute of Technology, Mechanical & System Engineering | Professor |

Masaaki, Sugihara | Nagoya University, Graduate School of Engineering | Professor |

Hidetoshi, Nishida | Kyoto Institute of Technology, Mechanical & System Engineering | Associate Professor |

**9.Summary of Research Results**

We have developed new computational-scientific methods for global scale flow systems (GSFS). In
particular, we have developed (1) turbulence models free from ad-hoc parameter tuning techniques, (2)
numerical algorithms for flows on spherical geometry, and (3) methods for large-scale numerical
simulations compatible with the paradigm of Massive Parallel Processing.(1) We have performed Direct Numerical Simulations (DNS) of turbulence based on the spectral method, which are currently the largest DNS of incompressible turbulence in the World. By using the DNS data, we have developed spectral closure theories of turbulence and Large Eddy Simulation (LES) models for GSFS. These include probabilistic LES models which provide quantitative estimates of the reliability of predictions obtained by LES. (2) We have developed several algorithms that achieve decisive speed up in large--scale simulations of flows in spherical geometry: (a) fast spherical harmonics transform algorithm, (b) double Fourier series expansion method, and (c) combined compact finite difference scheme. A Fortran 90 package of (a) is now available on our website. The algorithms (b) and (c) were tested and their efficiency was confirmed by applying them to all seven test problems in the now standard benchmark test set proposed by Williamson et al. (3) By applying the higher--order method of lines, we performed DNS with 1024 ^{3} grid points, and
confirmed that the efficiency of parallelization is 90%. In particular, such efficiency was achieved in
computations of global--scale flows in spherical geometry with 10 km horizontal mesh size, both in
cubed sphere coordinates and by a grid-less method.The LES models developed in (1) were then integrated into the codes implementing schemes (2-b), (2-c) and (3-b) and their efficiency was confirmed. A systematic study of the performance of the finite difference scheme was made by comparing DNS results obtained in (1) and (3). |

**10.Key Words**

(1)Large Eddy Simulation (LES) of turbulence、(2)Fast spherical harmonics transform、(3)Large-scale numerical simulation

(4)Spectral closure theories of turbulence、(5)Probabilistic LES、(6)Flows on spherical geometry

(7)Parallel Computational Fluid Dynamics、(8)Higher-order method of lines、(9)Cubed sphere coordinates