From: bangerth Date: Fri, 27 Oct 2006 21:12:34 +0000 (+0000) Subject: A word about time steps X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=77bc15c8d368ea28db4a58baf1bf6257bf197632;p=dealii-svn.git A word about time steps git-svn-id: https://svn.dealii.org/trunk@14107 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-21/doc/intro.dox b/deal.II/examples/step-21/doc/intro.dox index f8c20763a8..c8fb3af26a 100644 --- a/deal.II/examples/step-21/doc/intro.dox +++ b/deal.II/examples/step-21/doc/intro.dox @@ -350,9 +350,17 @@ therefore have to do after solving for the velocity is to loop over all quadrature points in the domain and determine the maximal magnitude of the velocity. We can then set the time step for the saturation equation to @f[ - \triangle t_{n+1} = \frac h{\max_{\mathbf{x}}|\mathbf{u}^{n+1}(\mathbf{x})|}. + \triangle t_{n+1} = \frac {\min_K h_K}{\max_{\mathbf{x}}|\mathbf{u}^{n+1}(\mathbf{x})|}. @f] +Why is it important to do this? If we don't, then we will end up with lots of +places where our saturation is larger than one or less than zero, as can +easily be verified. (Remember that the saturation corresponds to something +like the water fraction in the fluid mixture, and therefore must physically be +between 0 and 1.) On the other hand, if we choose our time step according to +the criterion listed above, this only happens very very infrequently — +in fact only once for the entire run of the program. + Note that we will have similar restrictions on the time step also in @ref step_23 "step-23" and @ref step_24 "step-24" where we solve the time dependent wave equation, another hyperbolic problem. @@ -428,11 +436,11 @@ functions introduced at the end of the results section of @ref step_20