Changes between Version 21 and Version 22 of doc/tec/discret

Timestamp:

Jan 14, 2020 12:30:18 PM (5 years ago)

Author:

Giersch

Comment:

--

doc/tec/discret

@@ -10 +10 @@
 ''Δy''). The grid can be stretched in the vertical direction well above the ABL to save computational time in the free atmosphere. The Arakawa staggered C-grid ([#harlow Harlow and Welch, 1965]; [#arakawa Arakawa and Lamb, 1977]) is used, where scalar quantities are defined at the center of each grid volume, whereas velocity components are shifted by half a grid width in their respective direction so that they are defined at the edges of the grid volumes (see Fig. 1). 
 
-The bottom boundary of the model domain is indicated by the first ''w''-component (''w(k=0)'') whereas the top boundary is indicated by ''w(k=nz)''. In case of no-slip (Dirichlet) condition at the ground, the first grid point for scalars and ''u'',''v'' is defined at the same height as ''w(k=0)'' (0m) to simulate a constant flux layer using Monin–Obukhov similarity theory. In case of free-slip (Neumann) condition, however, the first grid point for scalars and ''u'',''v'' lies at ''-dz/2'' within the ground and using a constant flux layer is not allowed anymore. At the top boundary, the last scalar grid point (''nz+1'') is ''dz/2'' above ''w(k=nz)'', similar to the bottom in case of free-slip (Neumann) condition. However, if the user wants to have exact symmetric vertical boundaries, he or she must shift the uppermost grid point for scalars and ''u'',''v'' to the height of ''w(k=nz)''. In addition, a symmetric behavior between bottom and top boundary requires additional changes in the reduction of the order of the advection scheme close to the boundaries. These cahnges and the adjustments to a strictly symmetric grid structure are automatically done if [../../app/initialization_parameters#topography topography] = 'closed_channel'. 
+The bottom boundary of the model domain is indicated by the first ''w''-component (''w(k=0)'') whereas the top boundary is indicated by ''w(k=nz)''. In case of no-slip (Dirichlet) condition at the ground, the first grid point for scalars and ''u'',''v'' is defined at the same height as ''w(k=0)'' (0m) to simulate a constant flux layer using Monin–Obukhov similarity theory. In case of free-slip (Neumann) condition, however, the first grid point for scalars and ''u'',''v'' lies at ''-dz/2'' within the ground and using a constant flux layer is not allowed anymore. At the top boundary, the last scalar grid point (''nz+1'') is ''dz/2'' above ''w(k=nz)'', similar to the bottom in case of free-slip (Neumann) condition. However, if the user wants to have exact symmetric vertical boundaries, he or she must shift the uppermost grid point for scalars and ''u'',''v'' to the height of ''w(k=nz)''. In addition, a symmetric behavior between bottom and top boundary requires additional changes in the reduction of the order of the advection scheme close to the boundaries. These cahnges and the adjustments to a strictly symmetric grid structure are automatically done if [../../app/initialization_parameters#topography topography] = 'closed_channel' is used. 
 
 '''Note''': Due to same array sizes of ''u'', ''v'', and ''w'' the uppermost grid point of the model domain is ''w(k=nz+1)''. This point doesn't play a role for solving the model equations.