Exemple : utilisation de pdesolve avec des unités

Fonctions > Résolution et optimisation > Fonctions des blocs de résolution > Exemple : utilisation de pdesolve avec des unités

Utilisez la fonction pdesolve pour résoudre l'équation de la chaleur.

1. Créez les paramètres d'entrée suivants : nTime et nX sont le nombre de points de la grille.τMax est la limite supérieure de la trange, et a est un coefficient.

2. Configurez le bloc de solutions d'équation différentielle partielle. Utilisez l'équation de la chaleur et ajoutez un jeu de conditions initiales. Utilisez les unités (m) dans le bloc de résolution.

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  <solveblock>
    <regions>
      <region id="" actualWidth="182.17999999999998" actualHeight="29.943200000000004" top="38.40000000000002" left="38.4" solve-block-category="constraint">
        <math resultRef="32">
          <apply xmlns="http://schemas.mathsoft.com/math50">
            <equal />
            <apply>
              <minus />
              <apply>
                <id xml:space="preserve">
                  <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">T<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">t</Subscript></Span>
                </id>
                <sequence>
                  <id xml:space="preserve">x</id>
                  <id xml:space="preserve">t</id>
                </sequence>
              </apply>
              <apply>
                <mult />
                <apply>
                  <pow />
                  <id xml:space="preserve">a</id>
                  <real>2</real>
                </apply>
                <apply>
                  <id xml:space="preserve">
                    <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">T<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">xx</Subscript></Span>
                  </id>
                  <sequence>
                    <id xml:space="preserve">x</id>
                    <id xml:space="preserve">t</id>
                  </sequence>
                </apply>
              </apply>
            </apply>
            <real>0</real>
          </apply>
          <resultFormat>
            <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
          </resultFormat>
        </math>
      </region>
      <region id="" actualWidth="197.97000000000003" actualHeight="47.2" top="76.800000000000026" left="57.6" solve-block-category="constraint">
        <math resultRef="33">
          <apply xmlns="http://schemas.mathsoft.com/math50">
            <equal />
            <apply>
              <id xml:space="preserve">
                <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">T<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">x</Subscript></Span>
              </id>
              <sequence>
                <apply>
                  <scale />
                  <real>0</real>
                  <id xml:space="preserve">m</id>
                </apply>
                <id xml:space="preserve">t</id>
              </sequence>
            </apply>
            <apply>
              <scale />
              <apply>
                <neg />
                <parens>
                  <apply>
                    <scale />
                    <real>10</real>
                    <apply>
                      <pow />
                      <id xml:space="preserve">e</id>
                      <apply>
                        <scale />
                        <real>-0.1</real>
                        <id xml:space="preserve">t</id>
                      </apply>
                    </apply>
                  </apply>
                </parens>
              </apply>
              <apply>
                <div />
                <real>1</real>
                <id labels="UNIT" xml:space="preserve">m</id>
              </apply>
            </apply>
          </apply>
          <resultFormat>
            <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
          </resultFormat>
        </math>
      </region>
      <region id="" actualWidth="127.37333333333335" actualHeight="47.2" top="115.20000000000003" left="57.6" solve-block-category="constraint">
        <math resultRef="34">
          <apply xmlns="http://schemas.mathsoft.com/math50">
            <equal />
            <apply>
              <id xml:space="preserve">
                <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">T<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">x</Subscript></Span>
              </id>
              <sequence>
                <apply>
                  <scale />
                  <real>1</real>
                  <id labels="UNIT" xml:space="preserve">m</id>
                </apply>
                <id xml:space="preserve">t</id>
              </sequence>
            </apply>
            <apply>
              <scale />
              <real>0</real>
              <apply>
                <div />
                <real>1</real>
                <id labels="UNIT" xml:space="preserve">m</id>
              </apply>
            </apply>
          </apply>
          <resultFormat>
            <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
          </resultFormat>
        </math>
      </region>
      <region id="" actualWidth="80.710000000000008" actualHeight="25.6" top="153.60000000000008" left="57.6" solve-block-category="constraint">
        <math resultRef="35">
          <apply xmlns="http://schemas.mathsoft.com/math50">
            <equal />
            <apply>
              <id xml:space="preserve">T</id>
              <sequence>
                <id xml:space="preserve">x</id>
                <real>0</real>
              </sequence>
            </apply>
            <real>0</real>
          </apply>
          <resultFormat>
            <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
          </resultFormat>
        </math>
      </region>
      <region id="" actualWidth="267.43666666666672" actualHeight="44.2" top="192.00000000000006" left="38.4" solve-block-category="solver">
        <math resultRef="36">
          <define xmlns="http://schemas.mathsoft.com/math50">
            <id labels="VARIABLE" xml:space="preserve">T</id>
            <apply>
              <id labels="KEYWORD" xml:space="preserve">Pdesolve</id>
              <sequence>
                <id labels="VARIABLE" xml:space="preserve">T</id>
                <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">x</id>
                <matrix rows="2" cols="1">
                  <apply>
                    <scale />
                    <real>0</real>
                    <id labels="UNIT" xml:space="preserve" label-is-contextual="true">m</id>
                  </apply>
                  <apply>
                    <scale />
                    <real>1</real>
                    <id labels="UNIT" xml:space="preserve">m</id>
                  </apply>
                </matrix>
                <id xml:space="preserve">t</id>
                <matrix rows="2" cols="1">
                  <real>0</real>
                  <id labels="VARIABLE" xml:space="preserve">τMax</id>
                </matrix>
              </sequence>
            </apply>
          </define>
          <resultFormat>
            <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
          </resultFormat>
        </math>
      </region>
    </regions>
  </solveblock>
</region>

3. Pour représenter la solution dans un tracé 3D, utilisez la fonction CreateMesh.

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  <math resultRef="37">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve">u</id>
      <apply>
        <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">CreateMesh</id>
        <sequence>
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">T</id>
          <apply>
            <scale />
            <real>0</real>
            <id labels="UNIT" xml:space="preserve" label-is-contextual="true">m</id>
          </apply>
          <apply>
            <scale />
            <real>1</real>
            <id labels="UNIT" xml:space="preserve" label-is-contextual="true">m</id>
          </apply>
          <real>0</real>
          <id labels="VARIABLE" xml:space="preserve">τMax</id>
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">nX</id>
          <id labels="VARIABLE" xml:space="preserve">nTime</id>
        </sequence>
      </apply>
    </define>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

4. Représentez la solution à l'aide d'un tracé 3D.

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  <plot background-type="transparent">
    <plot3D>
      <traces>
        <trace3D num-of-points="41" resultRef="40" SurfaceFill="#FFC3D9A5">
          <traceStyle color="#FF2775A0">surface</traceStyle>
        </trace3D>
      </traces>
      <graph-size width="209.03226521707361" height="195.618020566802" />
      <axes>
        <xAxis start="0" end="1" rank="1">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <numberFormat>
            <general precision="3" />
          </numberFormat>
          <xyDomain scale-type="linear" allow-negative-values="true" auto-scale="true">
            <startValue />
            <endValue />
          </xyDomain>
        </xAxis>
        <yAxis start="0" end="20" rank="1">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <numberFormat>
            <general precision="3" />
          </numberFormat>
          <xyDomain scale-type="linear" allow-negative-values="true" auto-scale="true">
            <startValue />
            <endValue />
          </xyDomain>
        </yAxis>
        <zAxis start="-0.00055" end="0.00165" rank="1">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <numberFormat>
            <general precision="3" />
          </numberFormat>
          <zDomain scale-type="linear" allow-negative-values="true" auto-scale="true">
            <startValue />
            <endValue />
          </zDomain>
        </zAxis>
      </axes>
      <plotEquations>
        <plotEquation>
          <math>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">U</id>
          </math>
          <math>
            <placeholder xmlns="http://schemas.mathsoft.com/math50" />
          </math>
        </plotEquation>
      </plotEquations>
      <CameraTransformMatrix Rows="4" Columns="4">
        <Cells>
          <Cell>0.0011441619532079339</Cell>
          <Cell>0.091956017087953423</Cell>
          <Cell>0.9957624123327542</Cell>
          <Cell>0</Cell>
          <Cell>0.32809858802063024</Cell>
          <Cell>0.94060649816846953</Cell>
          <Cell>-0.087239510212507962</Cell>
          <Cell>0</Cell>
          <Cell>-0.94464279356394487</Cell>
          <Cell>0.32680805761879472</Cell>
          <Cell>-0.029094433198413844</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0.8341587442339774</Cell>
        </Cells>
      </CameraTransformMatrix>
      <CameraType>Orthographique</CameraType>
    </plot3D>
  </plot>
</region>

5. Représentez la solution à l'aide d'un tracé d'isolignes.

Rubriques associées

Equations différentielles partielles dans les blocs de résolution

Solveur d'équations différentielles partielles

Exemple : équation différentielle partielle (PDE) dans les blocs de résolution

Exemple : Ajout d'unités aux blocs de résolution

CreateSpace et CreateMesh

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