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

Timestamp:

Apr 26, 2016 7:58:41 PM (9 years ago)

Author:

Giersch

Comment:

--

doc/tec/pres

@@ -35 +35 @@
 \end{align*}
 }}}
-The exact solution of that Equation would give a ''π^∗^'' that yields a ''u,,i,,^t+Δt^'' free of divergence when used in the first equation mentioned above. In practice, a numerically efficient reduction of divergence by several orders of magnitude is found to be sufficient. Note that the differentials in
-the above equation are used for convenience and that the model code uses finite differences instead. When employing a Runge Kutta time stepping scheme, the formulation above is used to solve the Poisson equation for each substep. ''π^∗^'' is then calculated from its weighted average over these substeps.
+The exact solution of that Equation would give a ''π^∗^'' that yields a ''u,,i,,^t+Δt^'' free of divergence when used in the first equation mentioned above. In practice, a numerically efficient reduction of divergence by several orders of magnitude is found to be sufficient. Note that the differentials in the equation above are used for convenience and that the model code uses finite differences instead. When employing a Runge Kutta time stepping scheme, the formulation above is used to solve the Poisson equation for each substep. ''π^∗^'' is then calculated from its weighted average over these substeps.
 
 In case of cyclic lateral boundary conditions, the solution of the Poisson equation is achieved by using a direct fast Fourier transform (FFT). The Poisson equation is Fourier transformed in both horizontal directions, the resulting tri-diagonal matrix is solved along the "z" direction, and then transformed back ([#schumann1988 see, e.g., Schumann and Sweet, 1988]). PALM provides the inefficient but less restrictive Singleton-FFT ([#singleton1969 Singleton, 1969])