1991 Fiscal Year Final Research Report Summary
Numerical Method of 3D time-dependent Incompressible Accurate MHD Code Using the Curvilinear Coordinate Method
| Project/Area Number |
02680014
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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 |
プラズマ理工学
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| Research Institution | Yokkaichi University |
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Principal Investigator |
TAKEMOTO Yukimasa Yokkaichi University, Faculty of Economics, Associate Professor, 経済学部, 助教授 (80155051)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAJIMA Noriyoshi National Institute for Fusion Science, Assistant Professor, 大型ヘリカル研究部, 助手 (30172315)
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| Project Period (FY) |
1990 – 1991
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| Keywords | Incompressible MHD eqs. / Generalized Coordinates / Multi-domain method / Pressure puission solver / Free boundary problems / Numerical Simulation / 圧力場のポアソン・ソルバ- |
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| Research Abstract |
Recently, many time-dependent problems are newly brought forward as large Tokamaks and helical systems are operated.
In order to explain physical mechanisms of MHD phenomena including above ones, we are developing a 3D incompressible MHD code in the generalized coordinate system. The equations of time-dependent incompressible MHD code in the conservative nondimensional form are as follows ;
*B/=-*. [vB-Bv+1/((*B)^T-*B))
<@D7*v(/)*t@>D7=-*・[vv-BB+I(<@D7B<@D12@>D1(/)2@>D7+p)]
*^2p=*・[(*XB)XB-v・*v]
*・v=0
*・B=0
where B is the magnetic field, v is the velocity, p is the pressure, and s is the Lundquist number. The time development of the above equations is solved by the second-order Adams-Bashforth scheme and the fourth-order central differencing method for the space derivatives is used.
In order to check the calculation, we see that in the resulting toroidal equilibrium of a circular cross-section periodic cylinder. the flux surfaces are concentric circles.
Avoiding the accumulating errors near the magnetic axis, we adopted a multi-domain method that has two domains(one is orthogonal grids in Cartesian coordinates near the axis, the other is cylindrical grids in the curvilinear coordinate system).
We also considered a computation technique of the plasma free boundary problems in Generalized Coordinates. To satisfy the momentum flux conservation(continuity equation), the finite volume method and staggered grid system is used. If we use the regular grid system for the same computation. we can not satisfy the momentum flux conservation in free boundary problems.
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Research Products
(15 results)
