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

Timestamp:

Oct 10, 2012 9:20:50 AM (13 years ago)

Author:

suehring

Comment:

--

doc/tec/advection

@@ -24 +24 @@
 {{{
 #!Latex
-\[ F_{i-\frac{1}{2}}^{5} &=& F_{i-\frac{1}{2}}^{6} - \frac{|u_{i-\frac{1}{2}}|}{60} \left[10(\psi_{i}-\psi_{i-1}) -5(\psi_{i+1} - \psi_{i-2})-(\psi_{i+2} - \psi_{i-3}) \right] . \]
+\[ F_{i-\frac{1}{2}}^{5} &=& F_{i-\frac{1}{2}}^{6} - \frac{|u_{i-\frac{1}{2}}|}{60} \left[10(\psi_{i}-\psi_{i-1}) -5(\psi_{i+1} - \psi_{i-2})+(\psi_{i+2} - \psi_{i-3}) \right] . \]
 }}}
 The 5^th^ order upwind discretization (WS5) consists of 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.