Thank you very much Prof. Bangerth. So, by multiplying with an additional weight factor it simply becomes a 1D coupled system with homogeneous Neumann.
Thanks & Regards Pawan On Sat, Apr 21, 2018 at 4:33 PM, Wolfgang Bangerth <[email protected]> wrote: > On 04/21/2018 03:06 AM, Pawan Kumar wrote: > >> >> $$u_t = u_{rr}+ \frac{1}{r} u_r - \frac{1}{r} \frac{\partial}{\partial >> r} (r \lambda(u) \frac{\partial v}{\partial r}) +f(u,v)$$ >> $$v_t = v_{rr} + \frac{1}{r} v_r + g(u,v) $$ >> >> But at $r=0$, it becomes : >> >> $$u_t = 2u_{rr}-2uv_{rr}-u_r h_r +f(u,v)$$ >> $$v_t = 2v_{rr}+g(u,v)$$ >> >> So, my doubts are: >> >> 1. Since, its a time dependent, vector valued \& non-linear set of PDEs, >> which tutorials should I follow to solve these? I found 21, 26, 31 \& 31 >> related but some of them are too complicated, is there any relatively >> simpler way !! \\ >> > > You just have a system of coupled heat equations. 21, 26, 22 seems like a > reasonably choice. > > > 2. How to handle the condition at $r=0$ with the homogeneous Neumann BC? >> > > You don't have to do anything special if you don't just multiply by a test > function (say, w(r)) and then integrate over r=0...R, but if you also > multiply by a weight factor 2*pi*r. So, for example, out of the u_t term, > you'll get > > \int_{r=0}^R w(r) u_t(r) 2*pi r dr > > This way, the singularity disappears in all relevant terms. > > Best > W. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: [email protected] > 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/fo > rum/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 [email protected]. > For more options, visit https://groups.google.com/d/optout. > -- 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 [email protected]. For more options, visit https://groups.google.com/d/optout.
