| Author | Message | ||
     muneer Ismael (muneer) Member Username: muneer Post Number: 7 Registered: 12-2007 |
My Dear Tutor I am simulating a pipe flow case including asymmetric velocity profile. But it seems that Flexpde deals with the axisymmetric case in 2D cylinderical coerdinates, where r values are between 0-R. Please Sir, How can I simmlutae the addymetric velocity profile in 2D cylinderical Coerdinates? Many thanks | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1166 Registered: 06-2003 |
There are two straightforward ways of reducing a 3D cylindrical domain to 2D: 1) take a cut plane containing the axis and assume no azimuthal variation (FlexPDE's 2D Cylindrical system) 2) take a cut plane perpendicular to the axis and assume no axial variation. In this case, you simply use 2D cartesian coordinates and specify a circular domain. If you want to use polar coordinates to pose your equations, you can use transformation definitions. See "Samples | Misc | Polar.pde". If you want to simulate azimuthal variation in a 2D cylindrical model, you can expand the azimuthal variation in a power series or Chebyshev polynomials, or whatever, and create one VARIABLE for each coefficient. Then write EQUATIONS to solve for the coefficients. | ||
| muneer Ismael (muneer) Member Username: muneer Post Number: 8 Registered: 12-2007 |
My Dear Sir, Is the second order ordinary diferntial equations could be solved with Flexpde? Many thanks | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1246 Registered: 06-2003 |
FlexPDE requires each equation to be first order or less in time. If you want to use time as the independent variable in an ODE, as we have done in our ODE examples, then each equation must be first order or less. To simulate a second order equation in time, you need to declare a second variable and equation. See our examples: V5: Samples|Misc|Tbessel.pde V6: Samples|Usage|Second_order_time.pde |