By Renata Dmowska, Barry Saltzman
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Additional resources for Advances in Geophysics, Vol. 45
21) and are connected by lines to show the prism surfaces of the simulated ice crystal. Note that Eq. 21) also generates points on the basal surfaces, which are not shown to avoid confusion. the particle are completely fixed. The relative magnitudes of a and c determine whether the particle looks more nearly planar or columnar, according to whether c > a or a > c, respectively. The parameters A and B determine the shape of the cross section, as explained in Wang (1987, 1997). 21). 14 represents a hexagonal ice plate.
4. The Numerical Scheme To solve Eqs. 3) with the appropriate initial and boundary conditions, we adopt a numerical approach utilizing the finite difference method. It is also necessary to set up a mesh grid. Due to the more complicated shapes of these ice crystals, it is decided that the simplest way to set up grids is to use the Cartesian coordinate system. In order to prescribe the inner boundary conditions with adequate precision, the grid spacing near the crystal surface has to be small. On the other hand, the grid spacing far from the crystal can be larger to save computing time.
25) where x and z are the respective horizontal and vertical coordinates of the surface (see Fig. 19), while a, C, and X are parameters to be determined. The parameters a and C have dimensions of length whereas A is a dimensionless number; C is one-half the length from the apex to the bottom along the z-axis, the center point being defined as the origin O, and a is defined in the following paragraph. 26) is the equation of an ellipse whose semi-axes in the x and z directions are a and C, respectively.