Add time-dependent function input for boundary conditions

[Copilot]

Summary

Adds support for specifying boundary conditions using arbitrary time-dependent mathematical expressions (functions of t), as an alternative to the existing tabular time-value arrays. This allows users to write closed-form formulas like 2*pi*cos(2*pi*t) directly in the JSON input file instead of supplying discrete t and Q/P arrays.

Feature: fn field for flow and pressure boundary conditions

FlowReferenceBC and PressureReferenceBC now accept an optional fn field containing a mathematical expression string. When fn is provided, the solver evaluates the expression at each time step to obtain the boundary condition value, bypassing the t/Q or t/P arrays (which become optional when fn is present).

Example input:

{
  "bc_type": "FLOW",
  "bc_values": {
    "fn": "2.0 * (4*ATAN(1.)) * COS(2.0 * (4*ATAN(1.)) * t)"
  }
}

Expression evaluation is powered by the exprtk library (vendored at src/ThirdParty/exprtk.hpp, version 20250101). The library supports standard math operators, functions (sin, cos, exp, log, …), and built-in constants. Any compilation errors in the expression string are reported at model load time with detailed diagnostics before throwing.

Implementation details

• Parameter (src/model/Parameter.h/.cpp): Added a new constructor and update() overload that accept an expression string. Expression state is held in a PIMPL struct (ExprtkImpl) so that exprtk types stay out of the header, keeping compile times manageable. Parameter::get(double time) evaluates the compiled expression when is_function == true. Explicit destructor, move constructor, and move assignment are defined in the .cpp to support the unique_ptr<ExprtkImpl> member.
• InputParameter (src/model/Parameter.h): Added an is_function flag so that the parameter-dispatch logic in SimulationParameters.cpp knows to read a string rather than a numeric array.
• Model (src/model/Model.h/.cpp): Added add_parameter(const std::string expression_string) overload. Also added a fallback that sets cardiac_cycle_period = 1.0 when no cardiac cycle period can be inferred (needed for models that use only function-based BCs with no periodic arrays).
• SimulationParameters.cpp: Extended generate_block() to handle is_function parameters by reading a string field and calling the new Model::add_parameter overload. The t and value arrays are now treated as optional when a function is also declared.
• FlowReferenceBC / PressureReferenceBC: The t and Q/P parameters are now marked optional (is_optional = true); a new optional fn parameter with is_function = true is added to each block's parameter list.
• exprtk.hpp: Vendored at src/ThirdParty/exprtk.hpp. Included only in Parameter.cpp (never in headers) and wrapped in #pragma diagnostic push/pop to suppress -Wshadow warnings from the third-party code. MSVC requires /bigobj for Parameter.cpp due to exprtk's template expansion, added via set_source_files_properties in src/model/CMakeLists.txt.

Tests

• tests/cases/timeDep_Flow.json and timeDep_Pressure.json: Two new minimal test models (RC vessel, one inlet and one outlet) that drive the boundary condition with fn = "2*pi*cos(2*pi*t)".
• tests/test_io.py::test_time_dependent_block: Verifies that the computed flow and pressure at the inlet match the analytical expression to within 0.3% relative tolerance after the initial transient settles.

[ncdorn]

@mrp089 figured I would have copilot take a shot at cleaning this up as it has been sitting as a draft PR for a while. let me know what you think.

[codecov]

Codecov Report

❌ Patch coverage is 72.36842% with 21 lines in your changes missing coverage. Please review.
✅ Project coverage is 78.67%. Comparing base (c7b0ca0) to head (6a5b59c).

Files with missing lines	Patch %	Lines
src/model/Parameter.cpp	63.88%	13 Missing ⚠️
src/solve/SimulationParameters.cpp	66.66%	8 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #223      +/-   ##
==========================================
+ Coverage   78.63%   78.67%   +0.03%     
==========================================
  Files          70       70              
  Lines        2790     2851      +61     
  Branches      318      330      +12     
==========================================
+ Hits         2194     2243      +49     
- Misses        596      608      +12     

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[ncdorn]

this is useful as it allows future handling of string parameters which previously did not exist

[ncdorn]

this looks good to me. I think the changes are significant but it allows for future implementation of string parameters in blocks.

[ncdorn]

@copilot this breaks the buid, please revert this change

[ncdorn]

@copilot instead of creating a dict in this code file, just load the appropriate json from the tests/cases directory and make the desired edit to the config key or value. this keeps the code much cleaner and more concise