Changes between Version 26 and Version 27 of doc/tec/discret

Timestamp:

Mar 15, 2023 1:08:58 PM (2 years ago)

Author:

raasch

Comment:

--

doc/tec/discret

@@ -19 +19 @@
 
 It is thus possible to calculate the derivatives of the velocity components at the center of the volumes (same location as the scalars). By the same token, derivatives of scalar quantities can be calculated at the edges of the volumes. In this way it is possible to calculate derivatives over only one grid length and the effective spatial model resolution can be increased by a factor of two in comparison to non-staggered grids.
-By default, the advection terms in the first five equations in Sect. [wiki:doc/tec/gov governing equations] are discretized using an upwind-biased 5th-order differencing scheme in combination with a 3rd-order Runge–Kutta  time-stepping scheme after [#williamson Williamson (1980)]. [#wicker Wicker and Skamarock(2002)] compared different time- and advection differencing schemes and found that this combination give the best results regarding accuracy and algorithmic simplicity. However, the 5th-order differencing scheme is known to be overly dissipative. It is thus also possible to use a 2nd-order scheme after [#piacsek Piacsek and Williams(1970)]. The latter scheme is non-dissipative, but it suffers from immense numerical dispersion. Time discretization can also be achieved using 2nd-order Runge–Kutta or 1st-order Euler schemes. For more information about the advection and time differencing schemes see [wiki:doc/tec/discret#Higherorderadvectionscheme Higher order advection scheme] and [wiki:doc/tec/discret#Timeintegration time integration].  
+By default, the advection terms in the first five equations in Sect. [wiki:doc/tec/gov governing equations] are discretized using an upwind-biased 5th-order differencing scheme in combination with a 3rd-order Runge–Kutta  time-stepping scheme after [#williamson Williamson (1980)]. [#wicker Wicker and Skamarock(2002)] compared different time- and advection differencing schemes and found that this combination give the best results regarding accuracy and algorithmic simplicity. However, the 5th-order differencing scheme is known to be overly dissipative. It is thus also possible to use a 2nd-order scheme after [#piacsek Piacsek and Williams(1970)]. The latter scheme is non-dissipative, but it suffers from immense numerical dispersion. Time discretization can also be achieved using 2nd-order Runge–Kutta or 1st-order Euler schemes. For more information about the advection and time differencing schemes see [wiki:doc/tec/discret#Higherorderadvectionscheme Higher order advection scheme] and [wiki:doc/tec/discret#temporal time integration].  
 
 == Higher order advection scheme ==