Solution adaptive triangular meshes with application to the simulation of plasma equilibrium
A new discrete Laplace operator is constructed on a local mesh molecule, second order accurate on symmetric cell regions, based on local Taylor series expansions. This discrete Laplacian is then compared to the one commonly used in the literature. A truncation error analysis of gradient and Laplace operators calculated at triangle centroids reveals that the maximum bounds of their truncation errors are minimized on equilateral triangles, for a fixed triangle perimeter. A new adaptive strategy on arbitrary triangular grids is developed in which a uniform grid is defined with respect to the solution surface, as opposed to the x,y plane. Departures from mesh uniformity arises from a spacially dependent mean-curvature of the solution surface. The power of this new adaptive technique is applied to the problem of finding free-boundary plasma equilibria within the context of MHD. The geometry is toroidal, and axisymmetry in the toroidal direction is assumed. We are led to conclude that the grid should move, not towards regions of high curvature of magnetic flux, but rather towards regions of greater toroidal current density. This has a direct bearing on the accuracy with which the Grad-Shafranov equation is being approximated.
- Research Organization:
- Columbia Univ., New York (USA). School of Engineering and Applied Science
- DOE Contract Number:
- AC02-76ET53016
- OSTI ID:
- 6959362
- Report Number(s):
- DOE/ET/53016-94; COO-2456/84; ON: DE84010389
- Resource Relation:
- Other Information: Portions are illegible in microfiche products. Original copy available until stock is exhausted. Thesis
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
EQUILIBRIUM PLASMA
MAGNETOHYDRODYNAMICS
PLASMA SIMULATION
COMPUTER CALCULATIONS
LAPLACE EQUATION
MATHEMATICAL MODELS
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID MECHANICS
HYDRODYNAMICS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA
SIMULATION
700105* - Fusion Energy- Plasma Research- Plasma Kinetics-Theoretical- (-1987)