| Project/Area Number |
06640548
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
固体地球物理学
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| Research Institution | The University of Tokyo |
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Principal Investigator |
OGAWA Masaki University of Tokyo, College of Arts and Sciences, associate professor, 教養学部, 助教授 (30194450)
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| Project Period (FY) |
1994 – 1995
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| Project Status |
Completed (Fiscal Year 1995)
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| 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)
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| Keywords | Mantle Convection / Numerical Simulation / Three-dimensional / Temperature-dependent viscosity / Numerical technique / Time-dependent / 対流のパターン |
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| Research Abstract |
A numerical code has been developed for three-dimensional simulations of mantle convection as a time-dependent convection of a Newtonian fluid with a strongly temperature-dependent 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 time-dependent, the huge linear equation must be fully and accurately solved at each time-step. Because of the size of the coefficient matrix, however, direct methods of linear equations are not a practical choice in the three-dimensional 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 time-integration of the basic equations in three-dimensional 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 three-dimensional simulation of a thermal convection of a fluid with a strongly temperature-dependent viscosity and succeeded in accurately integrating the basic equations by 80,000 time steps. The number of mesh points was 33x33x33 and the cpu-time was 5.4 second for each time-step in the simulation.
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