- 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/0D/BG_Modules (copy).cellml
<?xml version='1.0'?>
<model name="Vessel_BG_Units" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<!--//////////////////////////////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////// non-BC Vessel ////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////-->
<component name="pv_type">
<variable name="t" public_interface="in" units="second"/>
<!-- 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 name="E" public_interface="in" units="J_per_m3"/>
<variable name="l" public_interface="in" units="metre"/>
<variable name="h" public_interface="in" units="metre"/>
<variable name="r" public_interface="in" units="metre"/>
<variable name="I" public_interface="out" units="J_s2_per_m6"/>
<variable name="C" public_interface="out" units="m6_per_J"/>
<variable name="R" public_interface="out" units="J_s_per_m6"/>
<variable name="R_v" public_interface="out" units="J_s_per_m6"/>
<!-- var C_2: m6_per_J {pub: out};
var R_2: J_s_per_m6 {pub: out};
var C_3: m6_per_J {pub: out};
var R_3: J_s_per_m6 {pub: out};-->
<!-- State Variables-->
<variable name="u_in" public_interface="in" units="J_per_m3"/>
<variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
<variable name="u" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
<!-- var u_C_2: J_per_m3 {init: 0.0, pub: out};
var u_C_3: J_per_m3 {init: 0.0, pub: out};-->
<variable name="v_out" public_interface="in" units="m3_per_s"/>
<!-- Constitutive Relations-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>l</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>E</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_v</ci>
<apply>
<divide/>
<cn cellml:units="second">0.01</cn>
<ci>C</ci>
</apply>
</apply>
<!-- C_2 = sel
case r >= 10.0e-03{metre}:
33{dimensionless}*C;
case r < 10.0e-03{metre}:
2.1{dimensionless}*C;
endsel;-->
<!-- C_3 = sel
case r >= 10.0e-03{metre}:
5{dimensionless}*C;
case r < 10.0e-03{metre}:
1.6{dimensionless}*C;
endsel;-->
<!-- R_2 = 0.17{second}/C_2;-->
<!-- R_3 = sel
case r >= 10.0e-03{metre}:
0.022{second}/C;
case r < 10.0e-03{metre}:
0.014{second}/C;
endsel;-->
<!-- Conservation Laws-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u_in</ci>
<ci>u</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>v</ci>
</apply>
</apply>
<ci>I</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out</ci>
</apply>
<ci>C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u</ci>
<apply>
<plus/>
<ci>u_C</ci>
<apply>
<times/>
<ci>R_v</ci>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- ode(u_C_2, t) = (v-v_out-u_C_2/R_2)/C_2;
ode(u_C_3, t) = (v-v_out-u_C_3/R_3)/C_3;
u = u_C+u_C_2+u_C_3;-->
</component>
<!-------------------------------------------------------------------------------//
-----------------------------------------------------------------------------//-->
<component name="vp_type">
<variable name="t" public_interface="in" units="second"/>
<!-- Constitutive Parameters-->
<variable initial_value="0.004" name="mu" units="J_s_per_m3"/>
<variable initial_value="1050" name="rho" units="J_s_per_m3"/>
<variable name="E" public_interface="in" units="J_per_m3"/>
<variable name="l" public_interface="in" units="metre"/>
<variable name="h" public_interface="in" units="metre"/>
<variable name="r" public_interface="in" units="metre"/>
<variable name="I" public_interface="out" units="J_s2_per_m6"/>
<variable name="C" public_interface="out" units="m6_per_J"/>
<variable name="R" public_interface="out" units="J_s_per_m6"/>
<variable name="R_v" public_interface="out" units="J_s_per_m6"/>
<!-- var C_2: m6_per_J {pub: out};
var R_2: J_s_per_m6 {pub: out};
var C_3: m6_per_J {pub: out};
var R_3: J_s_per_m6 {pub: out};-->
<!-- State Variables-->
<variable name="v_in" public_interface="in" units="m3_per_s"/>
<variable initial_value="0.0" name="u" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
<!-- var u_C_2: J_per_m3 {init: 0.0, pub: out};
var u_C_3: J_per_m3 {init: 0.0, pub: out};-->
<variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
<variable name="u_out" public_interface="in" units="J_per_m3"/>
<!-- Constitutive Relations-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>l</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>E</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_v</ci>
<apply>
<divide/>
<cn cellml:units="second">0.01</cn>
<ci>C</ci>
</apply>
</apply>
<!-- C_2 = sel
case r >= 10.0e-03{metre}:
33{dimensionless}*C;
case r < 10.0e-03{metre}:
2.1{dimensionless}*C;
endsel;-->
<!-- C_3 = sel
case r >= 10.0e-03{metre}:
5{dimensionless}*C;
case r < 10.0e-03{metre}:
1.6{dimensionless}*C;
endsel;-->
<!-- R_2 = 0.17{second}/C_2;-->
<!-- R_3 = sel
case r >= 10.0e-03{metre}:
0.022{second}/C;
case r < 10.0e-03{metre}:
0.014{second}/C;
endsel;-->
<!-- Conservation Laws-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u</ci>
<ci>u_out</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>v</ci>
</apply>
</apply>
<ci>I</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>v_in</ci>
<ci>v</ci>
</apply>
<ci>C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u</ci>
<apply>
<plus/>
<ci>u_C</ci>
<apply>
<times/>
<ci>R_v</ci>
<apply>
<minus/>
<ci>v_in</ci>
<ci>v</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- ode(u_C_2, t) = (v_in-v-u_C_2/R_2)/C_2;
ode(u_C_3, t) = (v_in-v-u_C_3/R_3)/C_3;
u = u_C+u_C_2+u_C_3;-->
</component>
<!-------------------------------------------------------------------------------//
-----------------------------------------------------------------------------//-->
<component name="pp_type">
<variable name="t" public_interface="in" units="second"/>
<!-- Constitutive Parameters-->
<variable initial_value="0.004" name="mu" units="J_s_per_m3"/>
<variable initial_value="1050" name="rho" units="J_s_per_m3"/>
<variable name="E" public_interface="in" units="J_per_m3"/>
<variable name="l" public_interface="in" units="metre"/>
<variable name="h" public_interface="in" units="metre"/>
<variable name="r" public_interface="in" units="metre"/>
<variable name="I" public_interface="out" units="J_s2_per_m6"/>
<variable name="C" public_interface="out" units="m6_per_J"/>
<variable name="R" public_interface="out" units="J_s_per_m6"/>
<variable name="R_v" public_interface="out" units="J_s_per_m6"/>
<!-- var C_2: m6_per_J {pub: out};
var R_2: J_s_per_m6 {pub: out};
var C_3: m6_per_J {pub: out};
var R_3: J_s_per_m6 {pub: out};-->
<!-- State Variables-->
<variable name="u_in" public_interface="in" units="J_per_m3"/>
<variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
<variable name="u" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
<!-- var u_C_2: J_per_m3 {init: 0.0, pub: out};
var u_C_3: J_per_m3 {init: 0.0, pub: out};-->
<variable initial_value="0.0" name="v_d" public_interface="out" units="m3_per_s"/>
<variable name="u_out" public_interface="in" units="J_per_m3"/>
<!-- Constitutive Relations-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>l</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>E</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_v</ci>
<apply>
<divide/>
<cn cellml:units="second">0.01</cn>
<ci>C</ci>
</apply>
</apply>
<!-- C_2 = sel
case r >= 10.0e-03{metre}:
33{dimensionless}*C;
case r < 10.0e-03{metre}:
2.1{dimensionless}*C;
endsel;-->
<!-- C_3 = sel
case r >= 10.0e-03{metre}:
5{dimensionless}*C;
case r < 10.0e-03{metre}:
1.6{dimensionless}*C;
endsel;-->
<!-- R_2 = 0.17{second}/C_2;-->
<!-- R_3 = sel
case r >= 10.0e-03{metre}:
0.022{second}/C;
case r < 10.0e-03{metre}:
0.014{second}/C;
endsel;-->
<!-- Conservation Laws-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u_in</ci>
<ci>u</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>R</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>v</ci>
</apply>
</apply>
<apply>
<divide/>
<ci>I</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_d</ci>
</apply>
<ci>C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u</ci>
<apply>
<plus/>
<ci>u_C</ci>
<apply>
<times/>
<ci>R_v</ci>
<apply>
<minus/>
<ci>v</ci>
<ci>v_d</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v_d</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u</ci>
<ci>u_out</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>R</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>v_d</ci>
</apply>
</apply>
<apply>
<divide/>
<ci>I</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</math>
<!-- ode(u_C_2, t) = (v-v_d-u_C_2/R_2)/C_2;
ode(u_C_3, t) = (v-v_d-u_C_3/R_3)/C_3;
u = u_C+u_C_2+u_C_3;-->
</component>
<!--//////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////// input-BC Vessel ///////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////-->
<component name="vv_type">
<variable name="t" public_interface="in" units="second"/>
<!-- Constitutive Parameters-->
<variable initial_value="0.004" name="mu" units="J_s_per_m3"/>
<variable initial_value="1050" name="rho" units="J_s_per_m3"/>
<variable name="E" public_interface="in" units="J_per_m3"/>
<variable name="l" public_interface="in" units="metre"/>
<variable name="h" public_interface="in" units="metre"/>
<variable name="r" public_interface="in" units="metre"/>
<variable name="I" public_interface="out" units="J_s2_per_m6"/>
<variable name="C" public_interface="out" units="m6_per_J"/>
<variable name="R" public_interface="out" units="J_s_per_m6"/>
<variable name="R_v" public_interface="out" units="J_s_per_m6"/>
<!-- var C_2: m6_per_J {pub: out};
var R_2: J_s_per_m6 {pub: out};
var C_3: m6_per_J {pub: out};
var R_3: J_s_per_m6 {pub: out};-->
<!-- State Variables-->
<variable name="v_in" public_interface="in" units="m3_per_s"/>
<variable name="u" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
<!-- var u_C_2: J_per_m3 {init: 0.0, pub: out};
var u_C_3: J_per_m3 {init: 0.0, pub: out};-->
<variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
<variable name="u_d" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_C_d" public_interface="out" units="J_per_m3"/>
<variable name="v_out" public_interface="in" units="m3_per_s"/>
<!-- Constitutive Relations-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>l</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>E</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_v</ci>
<apply>
<divide/>
<cn cellml:units="second">0.01</cn>
<ci>C</ci>
</apply>
</apply>
<!-- C_2 = sel
case r >= 10.0e-03{metre}:
33{dimensionless}*C;
case r < 10.0e-03{metre}:
2.1{dimensionless}*C;
endsel;-->
<!-- C_3 = sel
case r >= 10.0e-03{metre}:
5{dimensionless}*C;
case r < 10.0e-03{metre}:
1.6{dimensionless}*C;
endsel;-->
<!-- R_2 = 0.17{second}/C_2;-->
<!-- R_3 = sel
case r >= 10.0e-03{metre}:
0.022{second}/C;
case r < 10.0e-03{metre}:
0.014{second}/C;
endsel;-->
<!-- Conservation Laws-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u</ci>
<ci>u_d</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>v</ci>
</apply>
</apply>
<ci>I</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>v_in</ci>
<ci>v</ci>
</apply>
<apply>
<divide/>
<ci>C</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C_d</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out</ci>
</apply>
<apply>
<divide/>
<ci>C</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u</ci>
<apply>
<plus/>
<ci>u_C</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>R_v</ci>
<apply>
<minus/>
<ci>v_in</ci>
<ci>v</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_d</ci>
<apply>
<plus/>
<ci>u_C_d</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>R_v</ci>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- ode(u_C_2, t) = (v-v_out-u_C_2/R_2)/C_2;
ode(u_C_3, t) = (v-v_out-u_C_3/R_3)/C_3;
u_d = u_C_d+u_C_2+u_C_3;-->
</component>
<!--//////////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////// output-BC Vessel ///////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////-->
<component name="pp_BC_type">
<variable name="t" public_interface="in" units="second"/>
<!-- Constitutive Parameters-->
<variable initial_value="0.004" name="mu" units="J_s_per_m3"/>
<variable initial_value="1050" name="rho" units="J_s_per_m3"/>
<variable name="E" public_interface="in" units="J_per_m3"/>
<variable name="l" public_interface="in" units="metre"/>
<variable name="h" public_interface="in" units="metre"/>
<variable name="r" public_interface="in" units="metre"/>
<variable name="I" public_interface="out" units="J_s2_per_m6"/>
<variable name="C" public_interface="out" units="m6_per_J"/>
<variable name="R" public_interface="out" units="J_s_per_m6"/>
<variable name="R_v" public_interface="out" units="J_s_per_m6"/>
<variable name="R_T" public_interface="in" units="J_s_per_m6"/>
<variable name="R_T_2" public_interface="out" units="J_s_per_m6"/>
<variable name="C_T" public_interface="in" units="m6_per_J"/>
<!-- State Variables-->
<variable name="u_in" public_interface="in" units="J_per_m3"/>
<variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
<variable name="u" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_C_T" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="v_T" public_interface="out" units="m3_per_s"/>
<variable name="u_out" public_interface="in" units="J_per_m3"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>l</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>E</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_v</ci>
<apply>
<divide/>
<cn cellml:units="second">0.01</cn>
<ci>C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R_T_2</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>R_T</ci>
</apply>
</apply>
<!-- Conservation Laws-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u_in</ci>
<ci>u</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>v</ci>
</apply>
</apply>
<ci>I</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_T</ci>
</apply>
<ci>C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u</ci>
<apply>
<plus/>
<ci>u_C</ci>
<apply>
<times/>
<ci>R_v</ci>
<apply>
<minus/>
<ci>v</ci>
<ci>v_T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v_T</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u</ci>
<ci>u_out</ci>
</apply>
<ci>u_C_T</ci>
</apply>
<apply>
<times/>
<ci>R_T</ci>
<ci>v_T</ci>
</apply>
</apply>
<apply>
<divide/>
<ci>I</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C_T</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>v_T</ci>
<apply>
<divide/>
<ci>u_C_T</ci>
<ci>R_T_2</ci>
</apply>
</apply>
<ci>C_T</ci>
</apply>
</apply>
</math>
</component>
<!--/////////////////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////// Junctions //////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////////////////////////////////////-->
<component name="pv_jII_type">
<variable name="t" public_interface="in" units="second"/>
<!-- 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 name="E" public_interface="in" units="J_per_m3"/>
<variable name="l" public_interface="in" units="metre"/>
<variable name="h" public_interface="in" units="metre"/>
<variable name="r" public_interface="in" units="metre"/>
<variable name="I" public_interface="out" units="J_s2_per_m6"/>
<variable name="C" public_interface="out" units="m6_per_J"/>
<variable name="R" public_interface="out" units="J_s_per_m6"/>
<variable name="R_v" public_interface="out" units="J_s_per_m6"/>
<!-- var C_2: m6_per_J {pub: out};
var R_2: J_s_per_m6 {pub: out};
var C_3: m6_per_J {pub: out};
var R_3: J_s_per_m6 {pub: out};-->
<!-- State Variables-->
<variable name="u_in" public_interface="in" units="J_per_m3"/>
<variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
<variable name="u" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
<!-- var u_C_2: J_per_m3 {init: 0.0, pub: out};
var u_C_3: J_per_m3 {init: 0.0, pub: out};-->
<variable name="v_out_1" public_interface="in" units="m3_per_s"/>
<variable name="v_out_2" public_interface="in" units="m3_per_s"/>
<!-- Constitutive Relations-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>l</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>E</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_v</ci>
<apply>
<divide/>
<cn cellml:units="second">0.01</cn>
<ci>C</ci>
</apply>
</apply>
<!-- C_2 = sel
case r >= 10.0e-03{metre}:
33{dimensionless}*C;
case r < 10.0e-03{metre}:
2.1{dimensionless}*C;
endsel;-->
<!-- C_3 = sel
case r >= 10.0e-03{metre}:
5{dimensionless}*C;
case r < 10.0e-03{metre}:
1.6{dimensionless}*C;
endsel;-->
<!-- R_2 = 0.17{second}/C_2;-->
<!-- R_3 = sel
case r >= 10.0e-03{metre}:
0.022{second}/C;
case r < 10.0e-03{metre}:
0.014{second}/C;
endsel;-->
<!-- Conservation Laws-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u_in</ci>
<ci>u</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>v</ci>
</apply>
</apply>
<ci>I</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out_1</ci>
</apply>
<ci>v_out_2</ci>
</apply>
<ci>C</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u</ci>
<apply>
<plus/>
<ci>u_C</ci>
<apply>
<times/>
<ci>R_v</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out_1</ci>
</apply>
<ci>v_out_2</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- ode(u_C_2, t) = (v-v_out_1-v_out_2-u_C_2/R_2)/C_2;
ode(u_C_3, t) = (v-v_out_1-v_out_2-u_C_3/R_3)/C_3;
u = u_C+u_C_2+u_C_3;-->
</component>
<!-------------------------------------------------------------------------------//
-----------------------------------------------------------------------------//-->
<component name="vv_jII_type">
<variable name="t" public_interface="in" units="second"/>
<!-- Constitutive Parameters-->
<variable initial_value="0.004" name="mu" units="J_s_per_m3"/>
<variable initial_value="1050" name="rho" units="J_s_per_m3"/>
<variable name="E" public_interface="in" units="J_per_m3"/>
<variable name="l" public_interface="in" units="metre"/>
<variable name="h" public_interface="in" units="metre"/>
<variable name="r" public_interface="in" units="metre"/>
<variable name="I" public_interface="out" units="J_s2_per_m6"/>
<variable name="C" public_interface="out" units="m6_per_J"/>
<variable name="R" public_interface="out" units="J_s_per_m6"/>
<variable name="R_v" public_interface="out" units="J_s_per_m6"/>
<!-- var C_2: m6_per_J {pub: out};
var R_2: J_s_per_m6 {pub: out};
var C_3: m6_per_J {pub: out};
var R_3: J_s_per_m6 {pub: out};-->
<!-- State Variables-->
<variable name="v_in_1" public_interface="in" units="m3_per_s"/>
<variable name="v_in_2" public_interface="in" units="m3_per_s"/>
<variable name="u" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_C" public_interface="out" units="J_per_m3"/>
<!-- var u_C_2: J_per_m3 {init: 0.0, pub: out};
var u_C_3: J_per_m3 {init: 0.0, pub: out};-->
<variable initial_value="0.0" name="v" public_interface="out" units="m3_per_s"/>
<variable name="u_d" public_interface="out" units="J_per_m3"/>
<variable initial_value="0.0" name="u_C_d" public_interface="out" units="J_per_m3"/>
<variable name="v_out_1" public_interface="in" units="m3_per_s"/>
<variable name="v_out_2" public_interface="in" units="m3_per_s"/>
<!-- Constitutive Relations-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rho</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>C</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>l</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>E</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">8</cn>
<ci>mu</ci>
<ci>l</ci>
</apply>
<apply>
<times/>
<pi/>
<apply>
<power/>
<ci>r</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>R_v</ci>
<apply>
<divide/>
<cn cellml:units="second">0.01</cn>
<ci>C</ci>
</apply>
</apply>
<!-- C_2 = sel
case r >= 10.0e-03{metre}:
33{dimensionless}*C;
case r < 10.0e-03{metre}:
2.1{dimensionless}*C;
endsel;-->
<!-- C_3 = sel
case r >= 10.0e-03{metre}:
5{dimensionless}*C;
case r < 10.0e-03{metre}:
1.6{dimensionless}*C;
endsel;-->
<!-- R_2 = 0.17{second}/C_2;-->
<!-- R_3 = sel
case r >= 10.0e-03{metre}:
0.022{second}/C;
case r < 10.0e-03{metre}:
0.014{second}/C;
endsel;-->
<!-- Conservation Laws-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>v</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>u</ci>
<ci>u_d</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>v</ci>
</apply>
</apply>
<ci>I</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_in_1</ci>
<ci>v_in_2</ci>
</apply>
<ci>v</ci>
</apply>
<apply>
<divide/>
<ci>C</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>u_C_d</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out_1</ci>
</apply>
<ci>v_out_2</ci>
</apply>
<apply>
<divide/>
<ci>C</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u</ci>
<apply>
<plus/>
<ci>u_C</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>R_v</ci>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_in_1</ci>
<ci>v_in_2</ci>
</apply>
<ci>v</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_d</ci>
<apply>
<plus/>
<ci>u_C_d</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>R_v</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>v</ci>
<ci>v_out_1</ci>
</apply>
<ci>v_out_2</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- ode(u_C_2, t) = (v-v_out_1-v_out_2-u_C_2/R_2)/C_2;
ode(u_C_3, t) = (v-v_out_1-v_out_2-u_C_3/R_3)/C_3;
u_d = u_C_d+u_C_2+u_C_3;-->
</component>
</model>
