| Author | Message | |||
     Illya Plotnikov (illya) New member Username: illya Post Number: 1 Registered: 05-2009 |
Hello, I'm trying to reproduce a numerical solution for a second order ODE. The system is à rotating disk containing one-component fluid. Only gravitationnal forces are taken in account, and velocity is taken ase mean. The vertical density distribution (direction z) is studied. So the equation is : dz((1/rho)*dz(rho))=-K*rho. K is a constant. It's analytical solution is known, and I'm trying to reproduce it. But the problem is that the only BC avialable are rho'(0)=0 and Integral(rho)=M. Where M is coloumn density. After a lot of tests with all kind of BC, the analytical solution is impossible to reproduct. Here is my script:
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| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1253 Registered: 06-2003 |
1. You apply an integral constraint on the solution which is very different from the integral of the exact solution. This makes it impossible to find a solution that matches both the constraint and the analytic form. If you correct this, the system behaves somewhat better. 2. You have applied both a value and a natural BC at x=0. The second condition overrides the first, so no value condition is applied. 3. Even with these items corrected, it appears to me that the system as posed does not have a unique solution. Your system is nonlinear, and it is not uncommon for nonlinear systems to admit multiple solutions. FlexPDE is able to find many strange functional shapes that satisfy the constraint and also satisfy the PDE in each mesh cell within the stated tolerance. You will have to find a way of stating the problem so that the solution is unique. |
1D1comp