Location: BondGraph Basic @ 84d221b7f03d / BG Tutorial Fluid Systems / 2-SingleBifurcation.cellml
- Author:
- Soroush Safaei <ssaf006@aucklanduni.ac.nz>
- Date:
- 2019-02-07 18:01:48+13:00
- Desc:
- adding TMDD
- Permanent Source URI:
- https://models.fieldml.org/workspace/43b/rawfile/84d221b7f03de97977775c1cfbdb20d4807f8e8d/BG Tutorial Fluid Systems/2-SingleBifurcation.cellml
<?xml version='1.0'?>
<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="mm" units_ref="mm"/>
<units name="mm3" units_ref="mm3"/>
<units name="mm3_per_s" units_ref="mm3_per_s"/>
<units name="mm6_per_J" units_ref="mm6_per_J"/>
<units name="J_per_s" units_ref="J_per_s"/>
<units name="gJ_per_m3" units_ref="gJ_per_m3"/>
<units name="gJ_s_per_m3" units_ref="gJ_s_per_m3"/>
<units name="eJ_s_per_m6" units_ref="eJ_s_per_m6"/>
<units name="pJ_s2_per_m5" units_ref="pJ_s2_per_m5"/>
<units name="eJ_s2_per_m6" units_ref="eJ_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="mm3"/>
<variable initial_value="0" name="q_out1" units="mm3"/>
<variable initial_value="0" name="q_out2" units="mm3"/>
<variable initial_value="0" name="q_bif" units="mm3"/>
<variable name="q_d" units="mm3"/>
<variable initial_value="0" name="q1" units="mm3"/>
<variable initial_value="0" name="q2" units="mm3"/>
<variable initial_value="0" name="q3" units="mm3"/>
<variable name="v_in" units="mm3_per_s"/>
<variable initial_value="0" name="v1" units="mm3_per_s"/>
<variable initial_value="0" name="v2" units="mm3_per_s"/>
<variable initial_value="0" name="v3" units="mm3_per_s"/>
<variable initial_value="0" name="v4" units="mm3_per_s"/>
<variable initial_value="0" name="v5" units="mm3_per_s"/>
<variable name="u1" units="gJ_per_m3"/>
<variable name="u2" units="gJ_per_m3"/>
<variable name="u3" units="gJ_per_m3"/>
<variable initial_value="0" name="u_out1" units="gJ_per_m3"/>
<variable initial_value="0" name="u_out2" units="gJ_per_m3"/>
<variable name="u_bif" units="gJ_per_m3"/>
<!-- Constitutive parameters-->
<variable initial_value="0.004e-9" name="mu" units="gJ_s_per_m3"/>
<variable initial_value="1050e-15" name="rho" units="pJ_s2_per_m5"/>
<variable initial_value="20" name="l1" units="mm"/>
<variable initial_value="20" name="l2" units="mm"/>
<variable initial_value="20" name="l3" units="mm"/>
<variable initial_value="2.3" name="r1" units="mm"/>
<variable initial_value="2" name="r2" units="mm"/>
<variable initial_value="1.5" name="r3" units="mm"/>
<variable initial_value="0.5" name="h1" units="mm"/>
<variable initial_value="0.5" name="h2" units="mm"/>
<variable initial_value="0.5" name="h3" units="mm"/>
<variable initial_value="400000e-9" name="E1" units="gJ_per_m3"/>
<variable initial_value="400000e-9" name="E2" units="gJ_per_m3"/>
<variable initial_value="400000e-9" name="E3" units="gJ_per_m3"/>
<variable name="C1" units="mm6_per_J"/>
<variable name="C2" units="mm6_per_J"/>
<variable name="C3" units="mm6_per_J"/>
<variable initial_value="1e-5" name="C_bif" units="mm6_per_J"/>
<variable name="R1" units="eJ_s_per_m6"/>
<variable name="R2" units="eJ_s_per_m6"/>
<variable name="R3" units="eJ_s_per_m6"/>
<variable name="R4" units="eJ_s_per_m6"/>
<variable name="R5" units="eJ_s_per_m6"/>
<variable name="I1" units="eJ_s2_per_m6"/>
<variable name="I2" units="eJ_s2_per_m6"/>
<variable name="I3" units="eJ_s2_per_m6"/>
<variable name="I4" units="eJ_s2_per_m6"/>
<variable name="I5" units="eJ_s2_per_m6"/>
<variable initial_value="20.93" name="a1" units="dimensionless"/>
<variable initial_value="0.199" name="b1" units="dimensionless"/>
<variable initial_value="0.08563" 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>
</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>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>
</apply>
<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>