arXiv subjects

Akira Kageyama

Publications and source records attributed to Akira Kageyama.

24 records · Page 2Linked to original sources

arXiv2004

Multigrid iterative algorithm using pseudo-compressibility for three-dimensional mantle convection with strongly variable viscosity

A numerical algorithm for solving mantle convection problems with strongly variable viscosity is presented. Equations for conservation of mass and momentum for highly viscous and incompressible fluids are solved iteratively by a multigrid method in combination with pseudo-compressibility and local time stepping techniques. This algorithm is suitable for large-scale three-dimensional numerical simulations, because (i) memory storage for any additional matrix is not required and (ii) vectorization and parallelization are straightforward. The present algorithm has been incorporated into a mantle convection simulation program based on the finite-volume discretization in a three-dimensional rectangular domain. Benchmark comparisons with previous two- and three-dimensional calculations including the temperature- and/or depth-dependent viscosity revealed that accurate results are successfully reproduced even for the cases with viscosity variations of several orders of magnitude. The robustness of the numerical method against viscosity variation can be significantly improved by increasing the pre- and post-smoothing calculations during the multigrid operations, and the convergence can be achieved for the global viscosity variations up to 1e10.

physics.geo-ph↗

arXiv2004

A 15.2 TFlops Simulation of Geodynamo on the Earth Simulator

For realistic geodynamo simulations, one must solve the magnetohydrodynamic equations to follow time development of thermal convection motion of electrically conducting fluid in a rotating spherical shell. We have developed a new geodynamo simulation code by combining the finite difference method with the recently proposed spherical overset grid called Yin-Yang grid. We achieved performance of 15.2 Tflops (46% of theoretical peak performance) on 4096 processors of the Earth Simulator.

physics.geo-ph↗

arXiv2004

Application of the Yin-Yang grid to a thermal convection of a Boussinesq fluid with infinite Prandtl number in a three-dimensional spherical shell

A new numerical finite difference code has been developed to solve a thermal convection of a Boussinesq fluid with infinite Prandtl number in a three-dimensional spherical shell. A kind of the overset (Chimera) grid named ``Yin-Yang grid'' is used for the spatial discretization. The grid naturally avoids the pole problems which are inevitable in the latitude-longitude grids. The code is applied to numerical simulations of mantle convection with uniform and variable viscosity. The validity of the Yin-Yang grid for the mantle convection simulation is confirmed.

physics.geo-ph↗

arXiv2004

Numerical and Experimental Investigation of Circulation in Short Cylinders

In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we explore Couette flows having height comparable to the gap between cylinders, centrifugally stable rotation, and high Reynolds number. Experiments in water are compared with numerical simulations. Simulations show that endcaps corotating with the outer cylinder drive a strong poloidal circulation that redistributes angular momentum. Predicted azimuthal flow profiles agree well with experimental measurements. Spin-down times scale with Reynolds number as expected for laminar Ekman circulation; extrapolation from two-dimensional simulations at $Re\le 3200$ agrees remarkably well with experiment at $Re\sim 10^6$. This suggests that turbulence does not dominate the effective viscosity. Further detailed numerical studies reveal a strong radially inward flow near both endcaps. After turning vertically along the inner cylinder, these flows converge at the midplane and depart the boundary in a radial jet. To minimize this circulation in the MRI experiment, endcaps consisting of multiple, differentially rotating rings are proposed. Simulations predict that an adequate approximation to the ideal Couette profile can be obtained with a few rings.

physics.flu-dyn↗

arXiv2004

The "Yin-Yang Grid": An Overset Grid in Spherical Geometry

A new kind of overset grid, named Yin-Yang grid, for spherical geometry is proposed. The Yin-Yang grid is composed of two identical component grids that are combined in a complemental way to cover a spherical surface with partial overlap on their boundaries. Each component grid is a low latitude part of the latitude-longitude grid. Therefore the grid spacing is quasi-uniform and the metric tensors are simple and analytically known. One can directly apply mathematical and numerical resources that have been written in the spherical polar coordinates or latitude-longitude grid. The complemental combination of the two identical component grids enables us to make efficient and concise programs. Simulation codes for geodynamo and mantle convection simulations using finite difference scheme based on the Yin-Yang grid are developed and tested. The Yin-Yang grid is suitable for massively parallel computers.

physics.geo-ph↗

arXiv2001

Magnetorotational Instability in a Rotating Liquid Metal Annulus

Although the magnetorotational instability (MRI) has been widely accepted as a powerful accretion mechanism in magnetized accretion disks, it has not been realized in the laboratory. The possibility of studying MRI in a rotating liquid-metal annulus (Couette flow) is explored by local and global stability analysis and magnetohydrodynamic (MHD) simulations. Stability diagrams are drawn in dimensionless parameters, and also in terms of the angular velocities at the inner and outer cylinders. It is shown that MRI can be triggered in a moderately rapidly rotating table-top apparatus, using easy-to-handle metals such as gallium. Practical issues of this proposed experiment are discussed.

astro-ph↗