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Figures

   figure404
Figure: (a) Effect of mesh non - uniformity on Laplacian: a mesh with uniform mesh spacing but non - constant number of neighbors of each triangle vertex. (b) Laplacian of tex2html_wrap_inline1207 on mesh (a), using standard stiffness matrix; (c) Laplacian of tex2html_wrap_inline1207 on mesh (a), using modified stiffness matrix, eq.37.

   figure411
Figure 2: Growth rate tex2html_wrap_inline909 as a function of number of mesh points N. The upper curves were obtained for zero viscosity, by advancing the magnetic potential or the current. The current advancement method gives somewhat larger tex2html_wrap_inline909 for low N, but the two methods agree closely for larger N. The lower curve was obtained with viscosity tex2html_wrap_inline919 which agrees with a previously reported, finite difference calculation.

   figure416
Figure 3: (a) A calculation of the coalescence instability. Contours of magnetic flux tex2html_wrap_inline921 at time t = 0. The flux forms a checkerboard diamond shaped pattern. (b) Contours of magnetic flux tex2html_wrap_inline921 at time t = 0.21 The diamonds have distorted to form pentagons. Current sheets have formed along the short sides of the pentagons.

   figure422
Figure 4: (a) A blowup view of contours of current C at time t = 0.21 The view is centered on the separatrix, on short side of a flux pentagon. The horizontal scale is about half of the scale tex2html_wrap_inline933 of the previous figure, while the vertical scale is about tex2html_wrap_inline935 The current sheet has unremarkable structure. (b) A blowup view of the mesh supporting the previous figure. The mesh is highly refined along the current sheet, which is well resolved. The minimum scale length of the mesh is 0.022 the size of the initial mesh separations.

   figure428
Figure 5: (a) Time history of the log of the peak current density. In the latter part of the run, the current density grows exponentially, as indicated by the approximately linear growth of the log of the peak current. (b) Time history of the number of mesh points N. In the latter part of the run, the number of mesh points grows exponentially, keeping pace with the peak current density.

   figure434
Figure 6: (a) A calculation of the bipolar vortex tilt instability. Contours of magnetic flux tex2html_wrap_inline921 at time t = 0. The flux contours consist of two interior flux systems, centered on o - points, and an exterior flux system whose contours intersect the boundary. (b) Contours of magnetic flux tex2html_wrap_inline921 at time t = 7. The inner flux blobs have tilted from their initial positions. The separatrix winds around the edges of the tilted flux blobs.

   figure440
Figure 7: (a) A blowup view of contours of current C at time t = 7. The current is localized along the separatrix. (b) A blowup view of the mesh, corresponding to the contours in (a). The refinement is able to resolve the moving, curved current sheet.

   figure446
Figure 8: (a) Time history of the log of the peak current density. In the latter part of the run, the current density grows exponentially, as indicated by the approximately linear growth of the log of the peak current. (b) Time history of the number of mesh points N. In the latter part of the run, the number of mesh points grows exponentially, keeping pace with the peak current density.

   figure452
Figure 9: (a) Mesh used for magnetic separatrix computation. There are about 800 mesh points. (b) Equilibrium magnetic flux function tex2html_wrap_inline921 calculated with 2D CRMHD, on a mesh like that of (a), but with about four times as many mesh points.


next up previous
Next: About this document Up: An Adaptive Finite Previous: References

Hank Strauss
Wed Jan 7 14:07:46 EST 1998