How to use properly the function PDEPE to hyperbolic equation
in [Matlab]
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From: Thiago Oliveira on 29 Jul 2010 22:50 hi everybody I'm trying to use the function pdepe for this equation: [1 - x^2]*dT/dZ = [(1/x)*d/dx*(x*dT/dx) + (1/Constant) * d2T/dZ] This equation represent a heat equation (forced convection) I already solve this equation making some simplifications, so it was turned in a parabolic equation. But that form represent a hyperbolic equation and I am not knowing how I put this equation on pdepe form.... Can anyone help me to solve this problem? Best Regards Thiago
From: Torsten Hennig on 29 Jul 2010 22:34 > hi everybody > > I'm trying to use the function pdepe for this > equation: > > [1 - x^2]*dT/dZ = [(1/x)*d/dx*(x*dT/dx) + > (1/Constant) * d2T/dZ] > > This equation represent a heat equation (forced > convection) > > I already solve this equation making some > simplifications, so it was turned in a parabolic > equation. > > But that form represent a hyperbolic equation and I > am not knowing how I put this equation on pdepe > form.... > > Can anyone help me to solve this problem? > > Best Regards > > Thiago If you mean [1 - x^2]*dT/dZ = [(1/x)*d/dx*(x*dT/dx) + (1/Constant) * d^2T/dZ^2] : this is a stationary convection-diffusion equation in 2d. Since pdepe is only suited to solve 1d-problems, you will have to use a different program to solve it. Best wishes Torsten.
From: Thiago Oliveira on 30 Jul 2010 07:17 Thanks for help Torsten, but I already solve this problem without "(1/Constant) * d^2T/dZ^2" term, that represent axial conduction using pdepe. I read in manual that pdepe is suitable to solve problems in 2D and hyperbolic equations, but I'm not so experienced on that function, so I dont know how to use it in that case.... :( Anyway, thanks a lot for your help! I am still waiting for the solution! :) Best Regards Thiago Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote in message <1083225386.26679.1280471674680.JavaMail.root(a)gallium.mathforum.org>... > > hi everybody > > > > I'm trying to use the function pdepe for this > > equation: > > > > [1 - x^2]*dT/dZ = [(1/x)*d/dx*(x*dT/dx) + > > (1/Constant) * d2T/dZ] > > > > This equation represent a heat equation (forced > > convection) > > > > I already solve this equation making some > > simplifications, so it was turned in a parabolic > > equation. > > > > But that form represent a hyperbolic equation and I > > am not knowing how I put this equation on pdepe > > form.... > > > > Can anyone help me to solve this problem? > > > > Best Regards > > > > Thiago > > If you mean > [1 - x^2]*dT/dZ = [(1/x)*d/dx*(x*dT/dx) + > (1/Constant) * d^2T/dZ^2] : > this is a stationary convection-diffusion equation > in 2d. > Since pdepe is only suited to solve 1d-problems, > you will have to use a different program to solve it. > > Best wishes > Torsten.
From: Torsten Hennig on 30 Jul 2010 03:39 > Thanks for help Torsten, > > but I already solve this problem without > "(1/Constant) * d^2T/dZ^2" term, that represent axial > conduction using pdepe. > That's clear. Without axial conduction, you can interpret the axial variable as time variable. But incorporating 'backmixing in time' is impossible. > I read in manual that pdepe is suitable to solve > problems in 2D and hyperbolic equations, but I'm not > so experienced on that function, so I dont know how > to use it in that case.... :( I would be surprised if this is the case. The 'pe' in pdepe stands for parabolic-elliptic - and these are the problem types pdepe is designed for. Maybe you read about the pde toolbox. > > Anyway, thanks a lot for your help! > > I am still waiting for the solution! :) > > Best Regards > > Thiago > > Best wishes Torsten. > > Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote > in message > <1083225386.26679.1280471674680.JavaMail.root(a)gallium. > mathforum.org>... > > > hi everybody > > > > > > I'm trying to use the function pdepe for this > > > equation: > > > > > > [1 - x^2]*dT/dZ = [(1/x)*d/dx*(x*dT/dx) + > > > (1/Constant) * d2T/dZ] > > > > > > This equation represent a heat equation (forced > > > convection) > > > > > > I already solve this equation making some > > > simplifications, so it was turned in a parabolic > > > equation. > > > > > > But that form represent a hyperbolic equation and > I > > > am not knowing how I put this equation on pdepe > > > form.... > > > > > > Can anyone help me to solve this problem? > > > > > > Best Regards > > > > > > Thiago > > > > If you mean > > [1 - x^2]*dT/dZ = [(1/x)*d/dx*(x*dT/dx) + > > (1/Constant) * d^2T/dZ^2] : > > this is a stationary convection-diffusion equation > > in 2d. > > Since pdepe is only suited to solve 1d-problems, > > you will have to use a different program to solve > it. > > > > Best wishes > > Torsten.
From: Thiago Oliveira on 30 Jul 2010 12:24 Torsten, Sorry by my mistakes... You're completely right about your comments... This pdepe function isn't suitable to hiperbolic equations.... And the article that I read maybe was talking about the pde tool...... Do you know something about the pde tool to solve this kind of problem? Best Regards and again, sorry by my mistakes Thiago Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote in message <360018553.27787.1280490065383.JavaMail.root(a)gallium.mathforum.org>... > > Thanks for help Torsten, > > > > but I already solve this problem without > > "(1/Constant) * d^2T/dZ^2" term, that represent axial > > conduction using pdepe. > > > > That's clear. Without axial conduction, you can interpret > the axial variable as time variable. But > incorporating 'backmixing in time' is impossible. > > > I read in manual that pdepe is suitable to solve > > problems in 2D and hyperbolic equations, but I'm not > > so experienced on that function, so I dont know how > > to use it in that case.... :( > > I would be surprised if this is the case. > The 'pe' in pdepe stands for parabolic-elliptic - > and these are the problem types pdepe is designed for. > Maybe you read about the pde toolbox. > > > > > Anyway, thanks a lot for your help! > > > > I am still waiting for the solution! :) > > > > Best Regards > > > > Thiago > > > > > > Best wishes > Torsten. > > > > > Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote > > in message > > <1083225386.26679.1280471674680.JavaMail.root(a)gallium. > > mathforum.org>... > > > > hi everybody > > > > > > > > I'm trying to use the function pdepe for this > > > > equation: > > > > > > > > [1 - x^2]*dT/dZ = [(1/x)*d/dx*(x*dT/dx) + > > > > (1/Constant) * d2T/dZ] > > > > > > > > This equation represent a heat equation (forced > > > > convection) > > > > > > > > I already solve this equation making some > > > > simplifications, so it was turned in a parabolic > > > > equation. > > > > > > > > But that form represent a hyperbolic equation and > > I > > > > am not knowing how I put this equation on pdepe > > > > form.... > > > > > > > > Can anyone help me to solve this problem? > > > > > > > > Best Regards > > > > > > > > Thiago > > > > > > If you mean > > > [1 - x^2]*dT/dZ = [(1/x)*d/dx*(x*dT/dx) + > > > (1/Constant) * d^2T/dZ^2] : > > > this is a stationary convection-diffusion equation > > > in 2d. > > > Since pdepe is only suited to solve 1d-problems, > > > you will have to use a different program to solve > > it. > > > > > > Best wishes > > > Torsten.
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