A numerical model of threedimensional mantle convection ; the effects of strong temperaturedependence of viscosity
Project/Area Number  06640548 
Research Category 
GrantinAid for General Scientific Research (C)

Allocation Type  Singleyear Grants 
Research Field 
固体地球物理学

Research Institution  The University of Tokyo 
Principal Investigator 
OGAWA Masaki University of Tokyo, College of Arts and Sciences, associate professor, 教養学部, 助教授 (30194450)

Project Period (FY) 
1994 – 1995

Project Status 
Completed(Fiscal Year 1995)

Budget Amount *help 
¥2,100,000 (Direct Cost : ¥2,100,000)
Fiscal Year 1995 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1994 : ¥1,400,000 (Direct Cost : ¥1,400,000)

Keywords  Mantle Convection / Numerical Simulation / Threedimensional / Temperaturedependent viscosity / Numerical technique / Timedependent / 対流のパターン 
Research Abstract 
A numerical code has been developed for threedimensional simulations of mantle convection as a timedependent convection of a Newtonian fluid with a strongly temperaturedependent viscosity. In the simulations of mantle convection, the discretized momentum and continuity equations form a set of huge linear equations for fluid velocity and pressure. Since the coefficient matrix depends on time when the viscosity depends on temperature and the convection is timedependent, the huge linear equation must be fully and accurately solved at each timestep. Because of the size of the coefficient matrix, however, direct methods of linear equations are not a practical choice in the threedimensional simulation and iterative method must be employed. The problem in an iterative method has been its slow convergence. The slow convergence has practically inhibited accurate timeintegration of the basic equations in threedimensional simulations. Here, I developed an efficient and accurate iterative solver of the momentum and continuity equation designed for a vector parallel computer. I combined an iterative solver of momentum and continuity equations called SIMPLER algorithm with a direct solver of Poisson's equation called SEVP method and succeeded in solving the basic equations with a convergence rate 30 times higher than the convergence rate in the traditional methods. I applied the numerical code to a threedimensional simulation of a thermal convection of a fluid with a strongly temperaturedependent viscosity and succeeded in accurately integrating the basic equations by 80,000 time steps. The number of mesh points was 33x33x33 and the cputime was 5.4 second for each timestep in the simulation.

Report
(3results)
Research Products
(4results)