Modelica（Dymola）の1D熱拡散PDEの実装

Question

1D熱拡散のグリッド関数の有限差分アプローチに基づくPeter Fritzonの "Object Oriented Modeling and Simulation with Modelica 3.3"の1D熱拡散の例を実装しようとしましたが、私は問題を解決できる方法上の任意のアイデアを持っているか、私はプログラミング言語のかなり新しいユーザー午前

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 

：私は、エラーを取得していますか？明らかに、問題は右境界の境界条件にあります。 ありがとうございます！ここ

はコードです：

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

パッケージFieldDomainOperators1DとDifferentialOperators1Dであなたinlineすべての機能ならばあなたの実装はannotation(Inline=true)とDymola 2015 FD01に翻訳し、シミュレートします。私は `pder`演算子はModelica標準ライブラリの現在のバージョンで定義されているか分からない、と私はその3.3ライブラリーとは思わない

[...] 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. [...]