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PDE solution using NDSolve not smooth

srinivas.gk

Posted 4 years ago

I am trying to solve 2 simultaneous PDE using NDSolve and the solution is not smooth. I think this has to do with setting of the computational grid, but I am not sure how to change it. PDEin:=-2.4669065517374813Derivative[0, 1][Tfin][\[Tau], z] + Derivative[1, 0][Tfin][\[Tau], z] == 0.0001770831817216026(-Tfin[\[Tau], z] + Tfo[\[Tau], z]) PDEo:=0.9327310058932085Derivative[0, 1][Tfo][\[Tau], z] + Derivative[1, 0][Tfo][\[Tau], z] == 0.07577538961255041(10 + 0.026z - Tfo[\[Tau], z]) + 0.00006695469437122687(Tfin[\[Tau], z] - Tfo[\[Tau], z]) IC:={Tfin[0, z] == 10 + 0.026z, Tfo[0, z] == 10 + 0.026z} tA=NDSolve[{PDEin,PDEo,IC,Tfo[\[Tau],0]==10,Tfin[\[Tau],L]==Tfo[\[Tau],L]},{Tfin,Tfo},{\[Tau],0,3600},{z,0,L}] t:=3000 Plot[Evaluate[{Tfin[t,z],Tfo[t,z]}/.tA],{z,0,L}]

I am trying to solve 2 simultaneous PDE using NDSolve and the solution is not smooth. I think this has to do with setting of the computational grid, but I am not sure how to change it.

PDEin:=-2.4669065517374813*Derivative[0, 1][Tfin][\[Tau], z] + Derivative[1, 0][Tfin][\[Tau], z] == 0.0001770831817216026*(-Tfin[\[Tau], z] + Tfo[\[Tau], z])
PDEo:=0.9327310058932085*Derivative[0, 1][Tfo][\[Tau], z] + Derivative[1, 0][Tfo][\[Tau], z] == 0.07577538961255041*(10 + 0.026*z - Tfo[\[Tau], z]) + 0.00006695469437122687*(Tfin[\[Tau], z] - Tfo[\[Tau], z])
IC:={Tfin[0, z] == 10 + 0.026*z, Tfo[0, z] == 10 + 0.026*z}
tA=NDSolve[{PDEin,PDEo,IC,Tfo[\[Tau],0]==10,Tfin[\[Tau],L]==Tfo[\[Tau],L]},{Tfin,Tfo},{\[Tau],0,3600},{z,0,L}]
t:=3000
Plot[Evaluate[{Tfin[t,z],Tfo[t,z]}/.tA],{z,0,L}]

POSTED BY: srinivas.gk

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Updating Name

Posted 4 years ago

Using StiffnessSwitching seems to have smoothened out the solution. Thank you for the suggestions. tA = NDSolve[{Subscript[PDE, in], Subscript[PDE, out], IC, Subscript[T, f, o][\[Tau], 0] == 10, Subscript[T, f, in][\[Tau], L] == Subscript[T, f, o][\[Tau], L]}, {Subscript[T, f, in], Subscript[T, f, o]}, {\[Tau], 0, 3600}, {z, 0, L}, Method -> "StiffnessSwitching"]

Using StiffnessSwitching seems to have smoothened out the solution. Thank you for the suggestions.

tA = NDSolve[{Subscript[PDE, in], Subscript[PDE, out], IC, 
   Subscript[T, f, o][\[Tau], 0] == 10, 
   Subscript[T, f, in][\[Tau], L] == 
    Subscript[T, f, o][\[Tau], L]}, {Subscript[T, f, in], Subscript[T,
    f, o]}, {\[Tau], 0, 3600}, {z, 0, L}, 
  Method -> "StiffnessSwitching"]

POSTED BY: Updating Name

srinivas.gk

Posted 4 years ago

Thanks for the suggestion Neil. I will take a look at the suggested link. The differential equations are for a heat balance between coaxial tubes with heat loss/gain from surroundings. This is why the wavy solution seems strange.