Errors in solving coupled pdes












1












$begingroup$


I am trying to solve following coupled PDEs:
enter image description here
I am not sure about suitable BCs.



 ClearAll[V, Rho, T]
gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38;
System = {D[V[x, t],t] == -1/gamma/exp[-x/H]*{D[Rho[x, t], x] + D[T[x,
t],x]} + Rho[x, t]/exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}],
D[Rho[x, t], t] == - D[{exp[-x/H]*V[x, t]}, x],
D[T[x, t], t] == D[{exp[-x/H]*V[x, t]}, x] - V[x, t]*Rho[x, t]*gpara -
gamma*exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}],
V[x, t] == 0 /. x -> 0,
V[x, t] == 0 /. x -> 1,
Rho[x, t] == 0 /. x -> 0,
Rho[x, t] == 0 /. x -> 1,
T[x, t] == 0 /. x -> 0,
T[x, t] == 0 /. x -> 1,
D[T[x, t], x] == 0 /. x -> 1,
V[x, 0] == Sin[Pi*x/L],
Rho[x, 0] == 0,
T[x, 0] == 0};
{V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0, 1}, {t, 0, 5}]
Plot3D[{V[x, t], Rho[x, t], T[x, t]}, {x, 0, 1}, {t, 0, 5}]


General::ivar: 3 is not a valid variable.
........
Also, how i can import variable gpara in .txt format to this code?










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    1












    $begingroup$


    I am trying to solve following coupled PDEs:
    enter image description here
    I am not sure about suitable BCs.



     ClearAll[V, Rho, T]
    gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38;
    System = {D[V[x, t],t] == -1/gamma/exp[-x/H]*{D[Rho[x, t], x] + D[T[x,
    t],x]} + Rho[x, t]/exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}],
    D[Rho[x, t], t] == - D[{exp[-x/H]*V[x, t]}, x],
    D[T[x, t], t] == D[{exp[-x/H]*V[x, t]}, x] - V[x, t]*Rho[x, t]*gpara -
    gamma*exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}],
    V[x, t] == 0 /. x -> 0,
    V[x, t] == 0 /. x -> 1,
    Rho[x, t] == 0 /. x -> 0,
    Rho[x, t] == 0 /. x -> 1,
    T[x, t] == 0 /. x -> 0,
    T[x, t] == 0 /. x -> 1,
    D[T[x, t], x] == 0 /. x -> 1,
    V[x, 0] == Sin[Pi*x/L],
    Rho[x, 0] == 0,
    T[x, 0] == 0};
    {V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0, 1}, {t, 0, 5}]
    Plot3D[{V[x, t], Rho[x, t], T[x, t]}, {x, 0, 1}, {t, 0, 5}]


    General::ivar: 3 is not a valid variable.
    ........
    Also, how i can import variable gpara in .txt format to this code?










    share|improve this question









    New contributor




    Danial is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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    $endgroup$















      1












      1








      1





      $begingroup$


      I am trying to solve following coupled PDEs:
      enter image description here
      I am not sure about suitable BCs.



       ClearAll[V, Rho, T]
      gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38;
      System = {D[V[x, t],t] == -1/gamma/exp[-x/H]*{D[Rho[x, t], x] + D[T[x,
      t],x]} + Rho[x, t]/exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}],
      D[Rho[x, t], t] == - D[{exp[-x/H]*V[x, t]}, x],
      D[T[x, t], t] == D[{exp[-x/H]*V[x, t]}, x] - V[x, t]*Rho[x, t]*gpara -
      gamma*exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}],
      V[x, t] == 0 /. x -> 0,
      V[x, t] == 0 /. x -> 1,
      Rho[x, t] == 0 /. x -> 0,
      Rho[x, t] == 0 /. x -> 1,
      T[x, t] == 0 /. x -> 0,
      T[x, t] == 0 /. x -> 1,
      D[T[x, t], x] == 0 /. x -> 1,
      V[x, 0] == Sin[Pi*x/L],
      Rho[x, 0] == 0,
      T[x, 0] == 0};
      {V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0, 1}, {t, 0, 5}]
      Plot3D[{V[x, t], Rho[x, t], T[x, t]}, {x, 0, 1}, {t, 0, 5}]


      General::ivar: 3 is not a valid variable.
      ........
      Also, how i can import variable gpara in .txt format to this code?










      share|improve this question









      New contributor




      Danial is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      I am trying to solve following coupled PDEs:
      enter image description here
      I am not sure about suitable BCs.



       ClearAll[V, Rho, T]
      gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38;
      System = {D[V[x, t],t] == -1/gamma/exp[-x/H]*{D[Rho[x, t], x] + D[T[x,
      t],x]} + Rho[x, t]/exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}],
      D[Rho[x, t], t] == - D[{exp[-x/H]*V[x, t]}, x],
      D[T[x, t], t] == D[{exp[-x/H]*V[x, t]}, x] - V[x, t]*Rho[x, t]*gpara -
      gamma*exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}],
      V[x, t] == 0 /. x -> 0,
      V[x, t] == 0 /. x -> 1,
      Rho[x, t] == 0 /. x -> 0,
      Rho[x, t] == 0 /. x -> 1,
      T[x, t] == 0 /. x -> 0,
      T[x, t] == 0 /. x -> 1,
      D[T[x, t], x] == 0 /. x -> 1,
      V[x, 0] == Sin[Pi*x/L],
      Rho[x, 0] == 0,
      T[x, 0] == 0};
      {V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0, 1}, {t, 0, 5}]
      Plot3D[{V[x, t], Rho[x, t], T[x, t]}, {x, 0, 1}, {t, 0, 5}]


      General::ivar: 3 is not a valid variable.
      ........
      Also, how i can import variable gpara in .txt format to this code?







      differential-equations






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      Danial is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      edited 2 hours ago







      Danial













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      asked 2 hours ago









      Danial Danial

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          1 Answer
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          $begingroup$

          Here is a version that fixes the syntax errors but there is a warning message indicating instability you should look into:



          ClearAll[V, Rho, T]
          gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38;
          System = {
          D[V[x, t],
          t] == -1/gamma/Exp[-x/H]*(D[Rho[x, t], x] + D[T[x, t], x]) +
          Rho[x, t]/Exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}],
          D[Rho[x, t], t] == -D[Exp[-x/H]*V[x, t], x],
          D[T[x, t], t] ==
          D[Exp[-x/H]*V[x, t], x] - V[x, t]*Rho[x, t]*gpara -
          gamma*Exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}],
          V[0, t] == 0, V[1, t] == 0, V[x, 0] == Sin[Pi*x/L],
          Rho[0, t] == 0, Rho[1, t] == 0, Rho[x, 0] == 0,
          T[0, t] == 0, T[1, t] == 0, Derivative[1, 0][T][1, t] == 0,
          T[x, 0] == 0};
          {V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0, 1}, {t, 0, 5}]


          enter image description here



          Plot3D[{V[x, t], Rho[x, t], T[x, t]}, {x, 0, 1}, {t, 0, 5}]


          enter image description here






          share|improve this answer









          $endgroup$













          • $begingroup$
            Thank you very much. I am using mathematica 11.3, when i use this code in my .nb, its showing errors: General::ivar: 3 is not a valid variable. I need to install different version of mathematica to avoid errors?
            $endgroup$
            – Danial
            12 mins ago












          • $begingroup$
            @Danial, works for me in V11.3. Try quiting your kernel, perhaps?
            $endgroup$
            – user21
            10 mins ago












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          1 Answer
          1






          active

          oldest

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          1 Answer
          1






          active

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          active

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          active

          oldest

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          4












          $begingroup$

          Here is a version that fixes the syntax errors but there is a warning message indicating instability you should look into:



          ClearAll[V, Rho, T]
          gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38;
          System = {
          D[V[x, t],
          t] == -1/gamma/Exp[-x/H]*(D[Rho[x, t], x] + D[T[x, t], x]) +
          Rho[x, t]/Exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}],
          D[Rho[x, t], t] == -D[Exp[-x/H]*V[x, t], x],
          D[T[x, t], t] ==
          D[Exp[-x/H]*V[x, t], x] - V[x, t]*Rho[x, t]*gpara -
          gamma*Exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}],
          V[0, t] == 0, V[1, t] == 0, V[x, 0] == Sin[Pi*x/L],
          Rho[0, t] == 0, Rho[1, t] == 0, Rho[x, 0] == 0,
          T[0, t] == 0, T[1, t] == 0, Derivative[1, 0][T][1, t] == 0,
          T[x, 0] == 0};
          {V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0, 1}, {t, 0, 5}]


          enter image description here



          Plot3D[{V[x, t], Rho[x, t], T[x, t]}, {x, 0, 1}, {t, 0, 5}]


          enter image description here






          share|improve this answer









          $endgroup$













          • $begingroup$
            Thank you very much. I am using mathematica 11.3, when i use this code in my .nb, its showing errors: General::ivar: 3 is not a valid variable. I need to install different version of mathematica to avoid errors?
            $endgroup$
            – Danial
            12 mins ago












          • $begingroup$
            @Danial, works for me in V11.3. Try quiting your kernel, perhaps?
            $endgroup$
            – user21
            10 mins ago
















          4












          $begingroup$

          Here is a version that fixes the syntax errors but there is a warning message indicating instability you should look into:



          ClearAll[V, Rho, T]
          gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38;
          System = {
          D[V[x, t],
          t] == -1/gamma/Exp[-x/H]*(D[Rho[x, t], x] + D[T[x, t], x]) +
          Rho[x, t]/Exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}],
          D[Rho[x, t], t] == -D[Exp[-x/H]*V[x, t], x],
          D[T[x, t], t] ==
          D[Exp[-x/H]*V[x, t], x] - V[x, t]*Rho[x, t]*gpara -
          gamma*Exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}],
          V[0, t] == 0, V[1, t] == 0, V[x, 0] == Sin[Pi*x/L],
          Rho[0, t] == 0, Rho[1, t] == 0, Rho[x, 0] == 0,
          T[0, t] == 0, T[1, t] == 0, Derivative[1, 0][T][1, t] == 0,
          T[x, 0] == 0};
          {V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0, 1}, {t, 0, 5}]


          enter image description here



          Plot3D[{V[x, t], Rho[x, t], T[x, t]}, {x, 0, 1}, {t, 0, 5}]


          enter image description here






          share|improve this answer









          $endgroup$













          • $begingroup$
            Thank you very much. I am using mathematica 11.3, when i use this code in my .nb, its showing errors: General::ivar: 3 is not a valid variable. I need to install different version of mathematica to avoid errors?
            $endgroup$
            – Danial
            12 mins ago












          • $begingroup$
            @Danial, works for me in V11.3. Try quiting your kernel, perhaps?
            $endgroup$
            – user21
            10 mins ago














          4












          4








          4





          $begingroup$

          Here is a version that fixes the syntax errors but there is a warning message indicating instability you should look into:



          ClearAll[V, Rho, T]
          gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38;
          System = {
          D[V[x, t],
          t] == -1/gamma/Exp[-x/H]*(D[Rho[x, t], x] + D[T[x, t], x]) +
          Rho[x, t]/Exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}],
          D[Rho[x, t], t] == -D[Exp[-x/H]*V[x, t], x],
          D[T[x, t], t] ==
          D[Exp[-x/H]*V[x, t], x] - V[x, t]*Rho[x, t]*gpara -
          gamma*Exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}],
          V[0, t] == 0, V[1, t] == 0, V[x, 0] == Sin[Pi*x/L],
          Rho[0, t] == 0, Rho[1, t] == 0, Rho[x, 0] == 0,
          T[0, t] == 0, T[1, t] == 0, Derivative[1, 0][T][1, t] == 0,
          T[x, 0] == 0};
          {V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0, 1}, {t, 0, 5}]


          enter image description here



          Plot3D[{V[x, t], Rho[x, t], T[x, t]}, {x, 0, 1}, {t, 0, 5}]


          enter image description here






          share|improve this answer









          $endgroup$



          Here is a version that fixes the syntax errors but there is a warning message indicating instability you should look into:



          ClearAll[V, Rho, T]
          gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38;
          System = {
          D[V[x, t],
          t] == -1/gamma/Exp[-x/H]*(D[Rho[x, t], x] + D[T[x, t], x]) +
          Rho[x, t]/Exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}],
          D[Rho[x, t], t] == -D[Exp[-x/H]*V[x, t], x],
          D[T[x, t], t] ==
          D[Exp[-x/H]*V[x, t], x] - V[x, t]*Rho[x, t]*gpara -
          gamma*Exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}],
          V[0, t] == 0, V[1, t] == 0, V[x, 0] == Sin[Pi*x/L],
          Rho[0, t] == 0, Rho[1, t] == 0, Rho[x, 0] == 0,
          T[0, t] == 0, T[1, t] == 0, Derivative[1, 0][T][1, t] == 0,
          T[x, 0] == 0};
          {V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0, 1}, {t, 0, 5}]


          enter image description here



          Plot3D[{V[x, t], Rho[x, t], T[x, t]}, {x, 0, 1}, {t, 0, 5}]


          enter image description here







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered 1 hour ago









          user21user21

          21k55998




          21k55998












          • $begingroup$
            Thank you very much. I am using mathematica 11.3, when i use this code in my .nb, its showing errors: General::ivar: 3 is not a valid variable. I need to install different version of mathematica to avoid errors?
            $endgroup$
            – Danial
            12 mins ago












          • $begingroup$
            @Danial, works for me in V11.3. Try quiting your kernel, perhaps?
            $endgroup$
            – user21
            10 mins ago


















          • $begingroup$
            Thank you very much. I am using mathematica 11.3, when i use this code in my .nb, its showing errors: General::ivar: 3 is not a valid variable. I need to install different version of mathematica to avoid errors?
            $endgroup$
            – Danial
            12 mins ago












          • $begingroup$
            @Danial, works for me in V11.3. Try quiting your kernel, perhaps?
            $endgroup$
            – user21
            10 mins ago
















          $begingroup$
          Thank you very much. I am using mathematica 11.3, when i use this code in my .nb, its showing errors: General::ivar: 3 is not a valid variable. I need to install different version of mathematica to avoid errors?
          $endgroup$
          – Danial
          12 mins ago






          $begingroup$
          Thank you very much. I am using mathematica 11.3, when i use this code in my .nb, its showing errors: General::ivar: 3 is not a valid variable. I need to install different version of mathematica to avoid errors?
          $endgroup$
          – Danial
          12 mins ago














          $begingroup$
          @Danial, works for me in V11.3. Try quiting your kernel, perhaps?
          $endgroup$
          – user21
          10 mins ago




          $begingroup$
          @Danial, works for me in V11.3. Try quiting your kernel, perhaps?
          $endgroup$
          – user21
          10 mins ago










          Danial is a new contributor. Be nice, and check out our Code of Conduct.










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