# GfsMetricLaplace

(Difference between revisions)
 Revision as of 21:42, 13 June 2012Popinet (Talk | contribs)← Previous diff Current revisionPopinet (Talk | contribs) (Added info on BCs) Line 7: Line 7: The syntax in parameter files is The syntax in parameter files is - MetricLaplace M { spherical = 0 conformal = 0 } + MetricLaplace NAME { spherical = 0 conformal = 0 } The parameter block is optional. If spherical is set to one, the mapping is from the plane in computational coordinates to the sphere in physical coordinates. If conformal is set to one, a conformal Laplace-Beltrami operator is used (the existence of such a mapping depends on the boundary conditions). The parameter block is optional. If spherical is set to one, the mapping is from the plane in computational coordinates to the sphere in physical coordinates. If conformal is set to one, a conformal Laplace-Beltrami operator is used (the existence of such a mapping depends on the boundary conditions). + + In addition to the metric scaling factors, additional variables will be defined for each of the physical coordinates i.e. (NAMEx,NAMEy,NAMEz). Grid generation is controlled by imposing Dirichlet or Neumann boundary conditions on these variables. + + Note that this does not work with adaptivity yet. + + === References === + + + @article{eca1996, + title = {2D orthogonal grid generation with boundary point distribution control}, + author = {Eca, L.}, + journal = {Journal of Computational Physics}, + volume = {125}, + number = {2}, + pages = {440-453}, + year = {1996}, + publisher = {Elsevier} + } +

## Current revision

GfsMetricLaplace computes a numerical orthogonal mapping of the computational space `(rx,ry)` into the physical space `x=(x,y,z)` by solving

2x = -2Hn

where 2 is the Laplace-Beltrami operator, n is the normal to the surface and H is the mean curvature.

The syntax in parameter files is

```MetricLaplace NAME { spherical = 0 conformal = 0 }
```

The parameter block is optional. If `spherical` is set to one, the mapping is from the plane in computational coordinates to the sphere in physical coordinates. If `conformal` is set to one, a conformal Laplace-Beltrami operator is used (the existence of such a mapping depends on the boundary conditions).

In addition to the metric scaling factors, additional variables will be defined for each of the physical coordinates i.e. `(NAMEx,NAMEy,NAMEz)`. Grid generation is controlled by imposing Dirichlet or Neumann boundary conditions on these variables.

Note that this does not work with adaptivity yet.

### References

Eca, L. - 2D orthogonal grid generation with boundary point distribution control

Journal of Computational Physics 125(2):440-453, 1996
Bibtex