Location: BondGraph Basic @ 994dbbb88a76 / BG Tutorial Fluid Systems / 2-SingleBifurcation.cellml
- Author:
- Soroush <ssaf006@aucklanduni.ac.nz>
- Date:
- 2021-04-08 15:18:19+12:00
- Desc:
- modified svg
- Permanent Source URI:
- https://models.fieldml.org/workspace/43b/rawfile/994dbbb88a761fe3a62bfaf8352da94103650bb2/BG Tutorial Fluid Systems/2-SingleBifurcation.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="SingleBifurcation" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:xlink="http://www.w3.org/1999/xlink">
<import xlink:href="Units.cellml">
<units name="m3" units_ref="m3"/>
<units name="m3_per_s" units_ref="m3_per_s"/>
<units name="m6_per_J" units_ref="m6_per_J"/>
<units name="J_per_s" units_ref="J_per_s"/>
<units name="J_per_m3" units_ref="J_per_m3"/>
<units name="J_s_per_m3" units_ref="J_s_per_m3"/>
<units name="J_s_per_m6" units_ref="J_s_per_m6"/>
<units name="J_s2_per_m5" units_ref="J_s2_per_m5"/>
<units name="J_s2_per_m6" units_ref="J_s2_per_m6"/>
</import>
<component name="main">
<variable name="t" units="second"/>
<variable initial_value="1.0" name="period" units="second"/>
<!-- State variables-->
<variable initial_value="0" name="q_in" units="m3"/>
<variable initial_value="0" name="q_out1" units="m3"/>
<variable initial_value="0" name="q_out2" units="m3"/>
<variable initial_value="0" name="q_bif" units="m3"/>
<variable name="q_d" units="m3"/>
<variable initial_value="0" name="q1" units="m3"/>
<variable initial_value="0" name="q2" units="m3"/>
<variable initial_value="0" name="q3" units="m3"/>
<variable name="v_in" units="m3_per_s"/>
<variable initial_value="0" name="v1" units="m3_per_s"/>
<variable initial_value="0" name="v2" units="m3_per_s"/>
<variable initial_value="0" name="v3" units="m3_per_s"/>
<variable initial_value="0" name="v4" units="m3_per_s"/>
<variable initial_value="0" name="v5" units="m3_per_s"/>
<variable name="u1" units="J_per_m3"/>
<variable name="u2" units="J_per_m3"/>
<variable name="u3" units="J_per_m3"/>
<variable initial_value="0" name="u_out1" units="J_per_m3"/>
<variable initial_value="0" name="u_out2" units="J_per_m3"/>
<variable name="u_bif" units="J_per_m3"/>
<!-- Constitutive parameters-->
<variable initial_value="0.004" name="mu" units="J_s_per_m3"/>
<variable initial_value="1050" name="rho" units="J_s2_per_m5"/>
<variable initial_value="20.0e-3" name="l1" units="metre"/>
<variable initial_value="20.0e-3" name="l2" units="metre"/>
<variable initial_value="20.0e-3" name="l3" units="metre"/>
<variable initial_value="2.3e-3" name="r1" units="metre"/>
<variable initial_value="2.0e-3" name="r2" units="metre"/>
<variable initial_value="1.5e-3" name="r3" units="metre"/>
<variable initial_value="0.5e-3" name="h1" units="metre"/>
<variable initial_value="0.5e-3" name="h2" units="metre"/>
<variable initial_value="0.5e-3" name="h3" units="metre"/>
<variable initial_value="0.4e+6" name="E1" units="J_per_m3"/>
<variable initial_value="0.4e+6" name="E2" units="J_per_m3"/>
<variable initial_value="0.4e+6" name="E3" units="J_per_m3"/>
<variable name="C1" units="m6_per_J"/>
<variable name="C2" units="m6_per_J"/>
<variable name="C3" units="m6_per_J"/>
<variable initial_value="1e-5" name="C_bif" units="m6_per_J"/>
<variable name="R1" units="J_s_per_m6"/>
<variable name="R2" units="J_s_per_m6"/>
<variable name="R3" units="J_s_per_m6"/>
<variable name="R4" units="J_s_per_m6"/>
<variable name="R5" units="J_s_per_m6"/>
<variable name="I1" units="J_s2_per_m6"/>
<variable name="I2" units="J_s2_per_m6"/>
<variable name="I3" units="J_s2_per_m6"/>
<variable name="I4" units="J_s2_per_m6"/>
<variable name="I5" units="J_s2_per_m6"/>
<variable initial_value="20.0" name="a1" units="dimensionless"/>
<variable initial_value="0.2" name="b1" units="dimensionless"/>
<variable initial_value="0.08" name="c1" units="dimensionless"/>
<!-- Inlet flow-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_in</ci>
<apply>
<times/>
<ci>a1</ci>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>t</ci>
<apply>
<times/>
<ci>period</ci>
<apply>
<floor/>
<apply>
<divide/>
<ci>t</ci>
<ci>period</ci>
</apply>
</apply>
</apply>
</apply>
<ci>b1</ci>
</apply>
<ci>c1</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<!-- Constitutive relations-->
<apply>
<eq/>
<ci>C1</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<pi/>
<apply>
<power/>
<ci>r1</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>l1</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>E1</ci>
<ci>h1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C2</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<pi/>
<apply>
<power/>
<ci>r2</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>l2</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>E2</ci>
<ci>h2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C3</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<pi/>
<apply>
<power/>
<ci>r3</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>l3</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>E3</ci>
<ci>h3</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R1</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l1</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r1</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R2</ci>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l2</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r2</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R3</ci>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l2</ci>
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<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r2</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R4</ci>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l3</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r3</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R5</ci>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l3</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r3</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l1</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r1</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I2</ci>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l2</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r2</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I3</ci>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l2</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r2</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I4</ci>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l3</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r3</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I5</ci>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l3</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r3</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_bif</ci>
<apply>
<divide/>
<ci>q_bif</ci>
<ci>C_bif</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u1</ci>
<apply>
<divide/>
<ci>q1</ci>
<ci>C1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u2</ci>
<apply>
<divide/>
<ci>q2</ci>
<ci>C2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u3</ci>
<apply>
<divide/>
<ci>q3</ci>
<ci>C3</ci>
</apply>
</apply>
<!-- Conservation laws-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q1</ci>
</apply>
<apply>
<minus/>
<ci>v_in</ci>
<ci>v1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q2</ci>
</apply>
<apply>
<minus/>
<ci>v2</ci>
<ci>v3</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q3</ci>
</apply>
<apply>
<minus/>
<ci>v4</ci>
<ci>v5</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_bif</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>v1</ci>
<ci>v2</ci>
</apply>
<ci>v4</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v1</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u1</ci>
<ci>u_bif</ci>
</apply>
<apply>
<times/>
<ci>R1</ci>
<ci>v1</ci>
</apply>
</apply>
<ci>I1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u_bif</ci>
<ci>u2</ci>
</apply>
<apply>
<times/>
<ci>R2</ci>
<ci>v2</ci>
</apply>
</apply>
<ci>I2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v3</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u2</ci>
<ci>u_out1</ci>
</apply>
<apply>
<times/>
<ci>R3</ci>
<ci>v3</ci>
</apply>
</apply>
<ci>I3</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v4</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u_bif</ci>
<ci>u3</ci>
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<apply>
<times/>
<ci>R4</ci>
<ci>v4</ci>
</apply>
</apply>
<ci>I4</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v5</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u3</ci>
<ci>u_out2</ci>
</apply>
<apply>
<times/>
<ci>R5</ci>
<ci>v5</ci>
</apply>
</apply>
<ci>I5</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_d</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>q_in</ci>
<ci>q_out1</ci>
</apply>
<ci>q_out2</ci>
</apply>
</apply>
</math>
</component>
</model>