Changes between Version 11 and Version 12 of doc/tec/advection

Timestamp:

Jan 10, 2011 1:42:47 PM (14 years ago)

Author:

suehring

Comment:

--

doc/tec/advection

@@ -26 +26 @@
 \[ F_{i-\frac{1}{2}}^{5} &=& F_{i-\frac{1}{2}}^{6} - \frac{|u_{i-\frac{1}{2}}|}{60} \left[10(\psi_{i}-\psi_{i-1}) -5(\psi_{i+1} - \psi_{i-2})-(\psi_{i+2} - \psi_{i-3}) \right] . \]
 }}}
-The 5^th^ order upwind discretization (WS5) consists of the centered non dissipative 6^th^ (WS6) order flux and an artificially added numerical dissipation term. This term is necessary to stabilize the numerical solution, because higher order centered fluxes exhibits worse stability properties. The absolute value of the advective velocity component at the beginning of the dissipation term removes a sign-dependent effect of the velocity and assures a dissipative effect also for u < 0. 
+The 5^th^ order upwind discretization (WS5) consists of a centered non dissipative 6^th^ (WS6) order flux and an artificially added numerical dissipation term. This term is necessary to stabilize the numerical solution, because higher order centered fluxes exhibits worse stability properties. The absolute value of the advective velocity component in the dissipation term removes a sign-dependent effect of the velocity and assures a dissipative effect also for u < 0. 
 
 === Numerical properties ===
@@ -67 +67 @@
 === Statistical evaluation of turbulent fluxes ===
 
-The evaluation of turbulent fluxes should be consistent with the discretization in the prognostic equations because otherwise some unphysical effects occur. For example the computation of the turbulent fluxes as variances and covariances induces some conspicuous kinks in the vertical heat and momentum fluxes near the surface, while the temperature and velocity profiles show no conspicuity. In order to compute the turbulent fluxes as they appear in the prognostic equations, the fluxes are computed in the advection routines, buffered and then reused for the statistics. To receive the turbulent and not the mean signal and to remove the influence of Galilei transformation, the centered flux F,,i+1/2,, has to be multiplied with a factor 
+The statistical evaluation of turbulent fluxes should be consistent with the discretization in the prognostic equations because otherwise some unphysical effects occur. For example the computation of the turbulent fluxes as variances and covariances induces some conspicuous kinks in the vertical heat and momentum fluxes near the surface, while the temperature and velocity profiles show no conspicuity. In order to compute the turbulent fluxes as they appear in the prognostic equations, the fluxes are computed in the advection routines, buffered and then reused for the statistics. To receive the turbulent and not the mean signal and to remove the influence of Galilei transformation, the centered flux F,,i+1/2,, has to be multiplied with a factor 
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 #!Latex