Hi, Wolfgang, Thank you for your reply. I am learning dealii to build up a geothermal model, which includes a Laplace equation and a heat transfer considering both convection and diffusion. The Laplace equation describes a pressure distibution in a site with several wellbores. The heat transfer equation describes the site temperature change with the change in the wellbore temperature. I think the model can be established by combining Step-4 and Step-31. Do you think these two example code is good for our model? Thank you very much.
Best, Xiang On Tuesday, October 22, 2019 at 9:02:48 PM UTC-7, Wolfgang Bangerth wrote: > > On 10/22/19 10:41 AM, Xiang Sun wrote: > > > > In step-31, why did you define the residual by multiplying T^(a-1)? What > does > > "a" mean? Thank you very much. > > I assume you mean here? > > https://dealii.org/developer/doxygen/deal.II/step_31.html#Stabilizationweakformandspacediscretizationforthetemperatureequation > > > To understand the form stated there, you have to go back to the paper by > Guermond and Popov. In essence, this goes back to some deep theory about > hyperbolic equations that says that a weak solution is a physical solution > only if it satisfies an entropy inequality. There are many ways to define > an > entropy pair (a pair of functions), and one of these is to choose E=T^a. > The > differential inequality E then has to satisfy is obtained by multiplying > the > equation for T by T^{a-1}. > > The theory is not particularly simple, and requires substantial background > of > hyperbolic equations. Going to the papers by Guermond and coauthors will > give > you the necessary insight. > > Best > W. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bang...@colostate.edu > <javascript:> > www: http://www.math.colostate.edu/~bangerth/ > > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/3281a95a-9d53-4456-adc8-3d92d512023f%40googlegroups.com.
