Changes between Version 5 and Version 6 of doc/tec/discret

Timestamp:

Apr 14, 2016 1:11:14 PM (9 years ago)

Author:

Giersch

Comment:

--

doc/tec/discret

@@ -1 @@
-[[NoteBox(warn,This site is currently under construction!)]]
-
 = Discretization =
 
@@ -12 +10 @@
 
 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 \citet{piacsek1970}. 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.
-
-\bibitem[{Wicker and Skamarock(2002)}]{wicker2002} Wicker,~L.~J. and
-  Skamarock,~W.~C.: {Time-splitting methods for elastic models using
-    forward time schemes}, Mon. Weather Rev., 130, 2088--2097,
-  2002.
+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.
 
 == References ==
@@ -28 +21 @@
 
 * [=#wicker]'''Wicker LJ, Skamarock WC.''' 1980. Time-splitting methods for elastic models using forward time schemes. Mon. Weather Rev. 130: 2088–2097.
+
+* [=#piacsek]'''Piacsek SA, Williams GP.''' 1970. Conservation properties of convection difference schemes. J. Comput. Phys. 198: 580–616.