| Author | Message | ||
     Andrea Cova (andrea25) New member Username: andrea25 Post Number: 1 Registered: 05-2006 |
Hello,this is my first attempt to use FlexPDE,it seems to be a very useful tool but I have found some difficulties in solving a time-dependant problem concerning a transport-diffusion PDE: c=c(x,y,z,t) represents the concentration of a polluting substance and this variable is governed by the following PDE alfa*(d^2c/dy^2)+beta*(d^2c/dz^2)-u*dc/dx-dc/dt=0 where alfa and beta are the diffusion parameters and u the speed of transport of the wind (we have transport along the x axis,and diffusion along the y and z axis). The initial condition is c(x,y,z,0)=0 (no emission at t=0) and boundary conditions are represented by: 1) the source condition of the pollutant is c(0,y,z,t)=Q(t)*delta(y)*delta(z-h)/u where Q(t) is simply a step function(Q(t)=Qzero,constant,for 0<=t<=a (a=duration of emission) and Q(t)=0 otherwise),h=effective stack heigth of the chimney from which the polluting comes from(it is constant),and "delta" denotes the dirac delta function 2)c(x,+ or - infinite,z,t)=0 3)beta*dc/dz=0 at z=0,H(H is the constant mixing heigth) In this problem the constants alfa,beta,u,Qzero,a,h,H,A,T are given and the domain I would like to study is three-dimensional and represented simply by the x-y-z space with a parallelepipedal structure emerging from the plane z=0,having square base (1,-2)--(5,-2)--(5,2)--(1,2) and fixed heigth z=A.The time interval we are considering is also supposed fixed between 0 and T. I would like to obtain a plot of the different values of the concentration over the domain at the final instant T and possibly an animation with the different graphic configurations of the problem obtained in certain instants during the evolution of the process. Thank you very much for your support, Andrea | ||
| Andrea Cova (andrea25) New member Username: andrea25 Post Number: 2 Registered: 05-2006 |
Please,could you give me some help?I don't know how to resolve this problem... | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 615 Registered: 06-2003 |
It is not clear to me whether your difficulty is that you don't know how to request the plots you want, or that you don't know how to set up the problem itself. The problem is similar to the example "Samples | Time_Dependent | Heatflow | 3D_Bricks.pde", so use that as a starting point. Producing a plot of a 3D field is problematic. FlexPDE can plot contours or surfaces on cut planes through the figure (see Help | Problem Descriptor Reference | The Sections of a Descriptor | Monitors and Plots). Or you can export the data in one of the export formats and use TecPlot, VisIt or Mayavi to plot visualizations of interior values. (See EXPORT in the Help Index. Use VTKLIN format for VisIt.) | ||
| Andrea Cova (andrea25) Junior Member Username: andrea25 Post Number: 3 Registered: 05-2006 |
Thanks for your suggestion, but I still have some problems about how to setup the problem itself,in particular for what concerns the definition of the domain (the boundaries section and the conditions of the problem over the boundaries).Could you give me some help with this problem? Thank you very much! | ||
| Andrea Cova (andrea25) Member Username: andrea25 Post Number: 4 Registered: 05-2006 |
Hello,I have realised the following code to resolve a problem of transport-diffusion. I am working on a Student Flexpde5 and,when I try to run the script,it says "Only specially coded sample problems can be run without license".How can I resolve this fact?Could you give me some suggestions? ------------------------------------------------- title 'Modellizzazione del disastro ecologico di Bhopal' coordinates cartesian3 variables c(threshold=0.1) definitions u=4 { velocità di trasporto del vento pari a 4m s^-1} Ky=[0.0121*X^2*(1+0.0004*X)^(-1)*u]/(2*X) { coefficiente di diffusione lungo l'asse y} Kz=[0.0064*X^2*(1+0.00015*X)^(-1)*u]/(2*X) /* coefficiente di diffusione lungo l'asse z */ a=90 /* durata dell'emissione pari a 90 min*/ Q0=40 /* intensità della sorgente emissiva pari a 40 tons in 90 min */ hmin=39.6 /* effettiva altezza del punto di emissione delle sostanze inquinanti pari a 39,6 m*/ Hmax=200 /* altezza massima raggiunta dagli agenti inquinanti pari a 200 m*/ ampx=100 /* NON RISPONDENTEampiezza del dominio spaziale lungo l'asse x pari ad 1 Km*/ semiampy=100 /* semiampiezza del dominio spaziale lungo l'asse y pari a 100 m*/ initial values c = 0 equations Ky*DYY(c)+Kz*DZZ(c)-u*DX(c)-Dt(c)=0 extrusion surface 'livello terrestre' Z=0 layer 'spessore del rilievo orografico' surface 'livello superiore del rilievo' Z=20 layer 'spessore dell"aria sovrastante' surface 'estremo superiore del dominio in esame' Z=Hmax boundaries region 1 /*regione che identifica l'intero dominio spaziale considerato */ start(0,-semiampy) value(c)=0 line to (ampx,-semiampy) natural(c)=0 line to (ampx,semiampy) value(c)=0 line to (0,semiampy) natural(c)=0 line to close limited region 2 /* regione occupata dal rilievo orografico */ start(20,-10) line to (40,-10) to (40,10) to (20,10) to close time 0 to a plots for t = endtime contour(c) on z=0 as "XY concentration" range=(0,a) contour(c) on x=0 as "YZ concentration" range=(0,a) contour(c) on y=0 as "XZ concentration" range=(0,a) end | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 627 Registered: 06-2003 |
The diagnostic you have reported is what FlexPDE will say if it cannot find a license file. You must go to our website (www.pdesolutions.com/student5.html) and fill out the request form to receive a student license. Once you receive this license, you must copy it without modification to the installation directory of FlexPDE. If your email system garbles the key file, you will probably get some other kind of diagnostic, such as "invalid license key". | ||
| Andrea Cova (andrea25) Member Username: andrea25 Post Number: 6 Registered: 05-2006 |
Hello Robert,I have a student licence on my computer and it seems to work,but when I try to run that code it gives the error message i wrote in the previous post. Maybe there is something in the code that I can't do with a student licence? | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 629 Registered: 06-2003 |
The error message you reported means that FlexPDE cannot find the license file. |