[adrpo]

Implements #1686, part of #1432: acausal components, each a separate FMI 3.0 Model Exchange FMU with fmi-ls-dae, connected through their terminals in an SSP and integrated as one DAE with IDA. It builds on #1646. The FMUs come from OpenModelica with --simCodeTarget=C+Rust --daeMode --fmuAcausalComponent (OpenModelica/OpenModelica#17665, not merged yet).

What the FMUs carry

• the fmi-ls-dae manifest;
• FMI 3.0 terminals: one per connector, inflow for flows and signal for potentials, and a TerminalStreamMemberVariable per stream variable that pairs it with the variable standing for its inStream ('inStream(port.h_outflow)');
• extra/org.openmodelica.fmi-ls-dae-acausal/fmi-ls-manifest.xml, which names the residual standing for each flow (ConnectorResidual) and for each stream's inStream (StreamResidual). While its terminal is unconnected, those residuals read flow = 0 and inStream(h) = h.

What this does

• Connectors: the members of an acausal component's terminals (p.v, p.i) become connectors of SSP 2.0 kind unspecified, the kind SSP defines "for acausal connections of Modelica models". In C++ they are oms_causality_bidir.

• Connections: a connection between two such connectors is acausal (oms_connection_acausal).

  • It stays out of the directed graphs.
  • A member may be connected any number of times.
  • The SSD stores it as an ordinary ssd:Connection.
  • In Python, addConnection between two terminals expands them member by member and refuses terminals whose members differ.

• System: in DAE mode, SystemSC::collectAcausalConnections builds the connection sets and replaces the residuals of the connected flows with the equations of the sets:

  • k-1 rows v_1 - v_m = 0 for the potentials of a set of k members;
  • one row sum(i_m) = 0 for its flows.

  The unknowns don't change, and the system stays square. Each row reads the members' values from the FMU. That is needed because a member may be computed by the component, not be an unknown: in the source, n.i is the alias -p.i, and the ground's p.v is a constant. A row's sparsity is the member's own column plus the columns the replaced residuals reach, since those take the flow and the potentials as arguments.

• Streams: a stream variable is connected like the other members, by its member name. Each connected stream's StreamResidual row becomes the mixing rule of its set:

  • s_i - sum_{j≠i} max(-m_j, eps)*h_j / sum_{j≠i} max(-m_j, eps) = 0, where s_i stands for inStream(h_i), m_j is the flow of h_j's terminal into its component, and eps = 1e-7 (OpenModelica's flowThreshold);
  • for two members it is s_i - h_j = 0.

  The terminal of a connected stream must have exactly one flow. The row's sparsity is built as for the other rows, from the inStream variable and the other members' stream and flow variables.

• Aliases and parameters: a terminal member may be an FMI 3.0 <Alias> (b.p in a component with a.p = b.p). The FMI library doesn't list aliases, so the terminals reader resolves them from modelDescription.xml, in C++ and in Python. A terminal member that is a (calculated) parameter, such as a boundary's fixed pressure, is connected acausally too.

• Refused: a set that mixes flows, potentials and stream variables, sets that don't give as many equations as they free residuals, and an acausal connection whose component is not in DAE mode.

model.addComponent(CRef('default', 'V'), 'resources/AcausalSource.fmu')
model.addComponent(CRef('default', 'RC'), 'resources/AcausalRC.fmu')
model.addComponent(CRef('default', 'G'), 'resources/AcausalGround.fmu')
model.addConnection(CRef('default', 'V', 'p'), CRef('default', 'RC', 'p'))
model.addConnection(CRef('default', 'V', 'n'), CRef('default', 'G', 'p'))

Tests

Three electrical FMUs (source, RC branch, ground) and two fluid FMUs (a pressure/enthalpy boundary, and a mixing volume behind a flow resistance), exported with the compiler of OpenModelica/OpenModelica#17665. The models are in the comments of DaeMode3.py and DaeMode5.py. Like DaeMode1/2, the tests only run on Linux: the FMUs carry only x86_64-linux binaries, and those need glibc 2.38.

Test	Circuit	Result	Analytic
DaeMode3.py	source, RC, ground	vc(1) = 0.632121, i = 0.367879	1 − e⁻¹, e⁻¹
DaeMode4.py	two RC branches in parallel (a three-way node), R2 = 2	vc2(1) = 0.393469, source current 0.671145	1 − e^-0.5, e⁻¹ + e^-0.5/2
DaeMode4.py	an RC alone, unconnected	p.i = 0	flow = 0
DaeMode4.py	a flow connected to a potential	refused
DaeMode5.py	boundary (p = 2, h = 2), volume, boundary (p = 1)	h(1) = 1.632121, 1 kg/s	2 − e⁻¹
DaeMode5.py	two branches (h = 2 and 4) mixing in a node of three terminals, then a volume	h3(1) = 1.160709, node p = 1.666667, mix 1.566937	3 − 4e^(−1/3) + 2e^(−2/3), 5/3, (h1 + h2)/2

Locally, ctest gives 132 tests, 0 failed.

Not in this PR

• components that prescribe a flow (a mass flow source, a current source): an FMU solves its own initial system with the placeholder residuals as ordinary equations, where the prescribed flow contradicts flow = 0, so exitInitializationMode fails. DaeMode5 therefore uses pressure boundaries and flow resistances;
• array connectors;
• nested terminals;
• index detection across FMUs: two state potentials joined by a connection give index 2.

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[codecov]

Codecov Report

❌ Patch coverage is 72.86585% with 89 lines in your changes missing coverage. Please review.
✅ Project coverage is 31.36%. Comparing base (3046f82) to head (bf1c8ad).

Files with missing lines	Patch %	Lines
src/OMSimulatorLib/SystemSC.cpp	77.88%	17 Missing and 29 partials ⚠️
src/OMSimulatorLib/ComponentFMU3ME.cpp	54.28%	7 Missing and 9 partials ⚠️
src/OMSimulatorLib/LsDae.cpp	78.94%	7 Missing and 5 partials ⚠️
src/OMSimulatorLib/System.cpp	22.22%	3 Missing and 4 partials ⚠️
src/OMSimulatorLib/Connector.cpp	0.00%	6 Missing ⚠️
src/OMSimulatorLib/Connection.cpp	0.00%	1 Missing ⚠️
src/OMSimulatorLib/LsDae.h	88.88%	0 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1687      +/-   ##
==========================================
+ Coverage   30.22%   31.36%   +1.13%     
==========================================
  Files          74       74              
  Lines       14661    14989     +328     
  Branches     9432     9646     +214     
==========================================
+ Hits         4431     4701     +270     
- Misses       8892     8911      +19     
- Partials     1338     1377      +39     

Flag	Coverage Δ
linux	31.36% <72.86%> (+1.13%)	⬆️

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[adrpo]

This has a connection with how SSP terminals are handled #1548.