Boundary Conditions in AortaCFD

This page covers the practical configuration of inlet, outlet, and wall boundary conditions in AortaCFD. For the underlying theory, see Boundary Conditions: Concepts. For research directions not yet implemented, see Advanced Boundary Condition Methods.

1. Inlet Boundary Conditions

Configuration

AortaCFD reads CSV data files and applies velocity profiles across the inlet cross-section with automatic inlet geometry detection and orientation:

{
  "inlet": {
    "type": "TIMEVARYING",
    "csv_file": "BPM75.csv",
    "data_type": "velocity",
    "profile": "womersley",
    "orientation": "auto"
  }
}

Available Inlet Types and Profiles

Inlet Types

Type	Description	Required Config
`CONSTANT`	Steady flow	`cardiac_output`, `flowrate`, or `velocity`
`TIMEVARYING`	Pulsatile from CSV	`csv_file` with time-flow columns
`WOMERSLEY`	Analytical pulsatile	Computed from flow waveform
`MRI`	Patient-specific 4D flow	Pre-processed OpenFOAM boundary data

Velocity profiles: plug, parabolic, womersley, wall_distance

The wall_distance profile computes a velocity distribution based on the distance from the nearest wall, providing a smooth blending between plug and parabolic shapes suitable for non-circular inlet cross-sections.

Input Data Format

Create a CSV file with time series data:

Time,Value
0.00,0.12
0.05,0.25
0.10,0.42
0.15,0.35
0.20,0.22
0.30,0.15
0.40,0.10
0.60,0.08
0.80,0.12

Orientation Detection

{
  "inlet": {
    "orientation": "auto"  // Automatic detection using outlet positions
    // or manually specify: "in" or "out"
  }
}

Womersley Profile Implementation

AortaCFD provides a Womersley profile implementation suitable for most cardiovascular applications:

# From AortaCFD-app/src/aortacfd_lib/inlet_mapping.py
def womersley_profile(self, r, t, omega, alpha):
    """
    Womersley profile for pulsatile cardiovascular simulations
    """
    R = self.radius
    z = 1j**1.5 * alpha * r / R
    z0 = 1j**1.5 * alpha
    bessel_ratio = jv(0, z) / jv(0, z0)
    v_r_t = (1 - bessel_ratio) * np.exp(1j * omega * t)
    return np.real(v_r_t)

AortaCFD Profile Options

The application supports three inlet velocity profiles: - Plug flow: Uniform velocity across cross-section - Parabolic: Poiseuille-like profile for steady flow - Womersley: Pulsatile profile with frequency-dependent shape

Patient-Specific Data Processing

From Doppler Ultrasound

import numpy as np
import pandas as pd

def process_doppler_data(doppler_file, cardiac_period=0.8):
    """
    Convert Doppler ultrasound measurements to OpenFOAM format
    """
    data = pd.read_csv(doppler_file)
    time = np.linspace(0, cardiac_period, len(data))

    # Apply calibration factor (typically 0.5 for mean from max velocity)
    mean_velocity = data['velocity_max'] * 0.5

    with open('inletVelocity.dat', 'w') as f:
        f.write('(\n')
        for t, v in zip(time, mean_velocity):
            f.write(f'    {t:.3f}    (0 0 {v:.3f})\n')
        f.write(')\n')

2. Outlet Boundary Conditions

3-Element Windkessel Configuration

{
  "outlets": {
    "type": "3EWINDKESSEL",
    "windkessel_settings": {
      "systolic_pressure": 120,
      "diastolic_pressure": 80,
      "methodology": "murray_law_automatic",
      "enable_stabilization": true,
      "betaT": 0.3,
      "betaN": 0.0
    }
  }
}

AortaCFD computes all Windkessel parameters (R, C, Z) automatically from the blood pressure settings and outlet geometry using Murray's law. See Windkessel Theory for the mathematical derivation.

Zero-Gradient Outlets

For stability testing and initial validation:

{
  "outlets": {
    "type": "ZEROGRADIENT",
    "outlet_settings": {
      "outlet1": {"type": "fixedValue", "pressure": 0},
      "outlet2": {"type": "zeroGradient"}
    }
  }
}

Multiple Outlet Flow Monitoring

For aortic branches, use Murray's law for flow distribution:

// In system/controlDict
functions
{
    outletFlowDistribution
    {
        type            surfaceFieldValue;
        libs            ("libfieldFunctionObjects.so");

        writeControl    timeStep;
        writeInterval   1;

        regionType      patch;
        name            outlet_1;

        operation       sum;
        fields          (phi);
    }
}

3. Wall Boundary Conditions

AortaCFD uses standard no-slip boundary conditions for vessel walls:

// From U.tpl template
{{ wall_patch }}
{
    type            fixedValue;
    value           uniform (0 0 0);
}

// From p.tpl template
{{ wall_patch }}
{
    type            zeroGradient;
}

Troubleshooting

Common Configuration Issues

Typical Problems

Problem: Simulation fails to start

Check CSV file format (comma-separated, no extra spaces)
Verify STL file units match scale_factor setting
Ensure orientation setting matches geometry

Problem: Unphysical results

Validate pressure ranges (systolic 110-140, diastolic 60-90 mmHg)
Check Murray's law flow distribution makes sense
Verify inlet flow rate is physiologically realistic

Performance Tips

Start with coarse mesh refinement for initial validation
Use plug profile for faster testing, upgrade to womersley for final results
Try ZEROGRADIENT outlets first, then upgrade to 3EWINDKESSEL once stable

Quick Reference

AortaCFD File Structure

AortaCFD automatically generates all necessary OpenFOAM files from the JSON configuration:

Input Files (You Provide):

config.json -- Main case configuration file
inlet.stl, outlet1.stl, etc. -- Geometry files
BPM75.csv -- Inlet waveform data (CSV format)

Auto-Generated Files:

0/U -- Generated from inlet profile and outlet settings
0/p -- Generated from outlet pressure conditions
0/k, 0/omega -- Generated for RANS simulations
constant/boundaryData/*/points -- Inlet geometry mapping
constant/boundaryData/*/[time]/U -- Time-varying inlet data
system/controlDict -- Generated with monitoring functions
system/fvSchemes -- Generated based on simulation profile
system/fvSolution -- Generated with appropriate solvers

Configuration Parameters

Parameter	Default/Typical	Range	Notes
Systolic pressure (mmHg)	120	110-140	Used in Windkessel calculation
Diastolic pressure (mmHg)	80	60-90	Used in Windkessel calculation
Murray's law exponent	2.7	2.5-3.0	Flow distribution calculation
Profile type	"womersley"	plug, parabolic, womersley	Inlet velocity profile
Orientation	"auto"	auto, in, out	Automatic detection recommended
Scale factor	0.001	-	STL units to metres conversion
Cardiac period (s)	0.8	0.6-1.0	75 BPM default

Example Configuration

{
  "inlet": {
    "profile": "womersley",
    "orientation": "auto"
  },
  "outlets": {
    "type": "3EWINDKESSEL",
    "windkessel_settings": {
      "systolic_pressure": 120,
      "diastolic_pressure": 80
    }
  }
}