1D Wärmediffusion PDE Implementierung in Modelica (Dymola)

Question

Ich habe versucht, eine 1D Wärmediffusion Beispiel von Peter Fritzon "Objektorientierte Modellierung und Simulation mit Modelica 3.3" basierend auf der Grid-Funktion Finite-Differenz-Ansatz zu 1D Wärmediffusion zu implementieren ich erhalte eine Fehlermeldung:

Translation of Heat_diffusion_Test_1D.HeatDiffusion1D: 

The DAE has 50 scalar unknowns and 50 scalar equations. 

Cannot find differentiation function: 
Heat_diffusion_Test_1D.DifferentialOperators1D.pder(
u, 
1) 
with respect to time 

    Failed to differentiate the equation 
    Heat_diffusion_Test_1D.FieldDomainOperators1D.right(Heat_diffusion_Test_1D.DifferentialOperators1D.pder (
    u, 
    1)) = 0; 

    in order to reduce the DAE index. 

    Failed to reduce the DAE index. 

    Translation aborted. 

    ERROR: 1 error was found 

    WARNING: 1 warning was issued 

ich bin ein ganz neuer Anwender der Programmiersprache, Sie haben keine Ahnung, wie ich das Problem beheben könnte? Offensichtlich liegt das Problem in der Randbedingung der rechten Grenze. Vielen Dank im Voraus!

hier ist der Code:

package Heat_diffusion_Test_1D 
import SI = Modelica.SIunits; 
    model HeatDiffusion1D 
    import SI = Modelica.SIunits; 
    parameter SI.Length L=1; 
    import Heat_diffusion_Test_1D.Fields.*; 
    import Heat_diffusion_Test_1D.Domains.*; 
    import Heat_diffusion_Test_1D.FieldDomainOperators1D.*; 
    import Heat_diffusion_Test_1D.DifferentialOperators1D.*; 
    constant Real PI=Modelica.Constants.pi; 

    Domain1D rod(left=0, right=L, n=50); 
    Field1D u(domain=rod, redeclare type FieldValueType=SI.Temperature, start={20*sin(PI/2*x)+ 300 for x in rod.x}); 

    equation 
    interior(der(u.val))=interior(4*pder(u,x=2)); 
    left(u.val)=20*sin(PI/12*time)+300; 
    right(pder(u,x=1)) = 0; 
    //right(u.val)=320; 

    annotation (Icon(coordinateSystem(preserveAspectRatio=false)), Diagram(
      coordinateSystem(preserveAspectRatio=false))); 
    end HeatDiffusion1D; 

    package Fields 

    record Field1D "Field over a 1D spatial domain" 
     replaceable type FieldValueType = Real; 
     parameter Domains.Domain1D domain; 
     parameter FieldValueType start[domain.n]=zeros(domain.n); 
     FieldValueType val[domain.n](start=start); 

     annotation (Icon(coordinateSystem(preserveAspectRatio=false)), Diagram(
      coordinateSystem(preserveAspectRatio=false))); 
    end Field1D; 
    annotation(); 
    end Fields; 

    package Domains 
    import SI = Modelica.SIunits; 
    record Domain1D "1D spatial domain" 
     parameter SI.Length left=0.0; 
     parameter SI.Length right=1.0; 
     parameter Integer n=100; 
     parameter SI.Length dx = (right-left)/(n-1); 
     parameter SI.Length x[n]=linspace(right,left,n); 

     annotation (Icon(coordinateSystem(preserveAspectRatio=false)), Diagram(
      coordinateSystem(preserveAspectRatio=false))); 
    end Domain1D; 
    annotation(); 
    end Domains; 

    package FieldDomainOperators1D 
    "Selection operators of field on 1D domain" 

    function left "Returns the left value of the field vector v1" 
     input Real[:] v1; 
     output Real v2; 

    algorithm 
     v2 := v1[1]; 
    end left; 

    function right "Returns the left value of the field vector v1" 
     input Real[:] v1; 
     output Real v2; 

    algorithm 
     v2 := v1[end]; 

    end right; 

    function interior 
     "returns the interior values of the field as a vector" 
     input Real v1[:]; 
     output Real v2[size(v1,1)-2]; 

    algorithm 
     v2:= v1[2:end-1]; 

    end interior; 


    end FieldDomainOperators1D; 

    package DifferentialOperators1D 
    "Finite difference differential operators" 

    function pder 
     "returns vector of spatial derivative values of a 1D field" 
     input Heat_diffusion_Test_1D.Fields.Field1D f; 
     input Integer x=1 "Diff order - first or second order derivative"; 
     output Real df[size(f.val,1)]; 

    algorithm 
     df:= if x == 1 then SecondOrder.diff1(f.val, f.domain.dx) 
    else 
     SecondOrder.diff2(f.val, f.domain.dx); 

    end pder; 

    package SecondOrder 
     "Second order polynomial derivative approximations" 

     function diff1 "First derivative" 
     input Real u[:]; 
     input Real dx; 
     output Real du[size(u,1)]; 

     algorithm 
     du := cat(1, {(-3*u[1] + 4*u[2] - u[3])/2/dx}, (u[3:end] - u[1:end-2])/2/dx, {(3*u[end] -4*u[end-1] + u[end-2])/2/dx}); 

     end diff1; 

     function diff2 
     input Real u[:]; 
     input Real dx; 
     output Real du2[size(u,1)]; 
     algorithm 
     du2 :=cat(1, {(2*u[1] - 5*u[2] + 4*u[3]- u[4])/dx/dx}, (u[3:end] - 2*u[2:end-1] + u[1:end-2])/dx/dx, {(2*u[end] -5*u[end-1] + 4*u[end-2] - u[end-3])/dx/dx}); 
     end diff2; 
     annotation(); 
    end SecondOrder; 

    package FirstOrder 
     "First order polynomial derivative approximations" 

     function diff1 "First derivative" 
     input Real u[:]; 
     input Real dx; 
     output Real du[size(u,1)]; 

     algorithm 
       // Left, central and right differences 
     du := cat(1, {(u[2] - u[1])/dx}, (u[3:end]-u[1:end-2])/2/dx, {(u[end] - u[end-1])/dx}); 

     end diff1; 
     annotation(); 
    end FirstOrder; 
    annotation(); 
    end DifferentialOperators1D; 
    annotation (uses(Modelica(version="3.2.1"))); 
end Heat_diffusion_Test_1D; 

Answer 1

Ihre Implementierung übersetzen und in Dymola 2015 FD01 wenn Sie inline alle Funktionen im Paket FieldDomainOperators1D und DifferentialOperators1D mit annotation(Inline=true) simulieren.

[...] Note that inline semantics is needed for the pder() function and the grid function. [...] This makes it possible to put calls to such a function at places where function calls are usually not allowed. [...]