IBMC - Immersed Boundary Method for Cilia and Particles Using Lattice Spring Method

A Fortran-based computational fluid dynamics (CFD) framework implementing the Immersed Boundary Method (IBM) to simulate the interaction between fluids and immersed structures such as cilia and elliptical particles.

Oscillation of a Morphing Particle Above Cilia Bed

Overview

IBMC simulates fluid-structure interactions using a fixed Eulerian grid for the fluid and a Lagrangian representation for immersed boundaries. The code is specifically designed to model:

1. Ciliary structures - Flexible hair-like projections that can generate fluid motion
2. Elliptical particles - Closed-loop structures with customizable aspect ratios
3. Fluid-structure interactions - Two-way coupling between fluid flow and immersed structures

The solver implements a 2D incompressible Navier-Stokes solution coupled with immersed boundary forces using a projection method on a staggered grid.

Features

• 2D incompressible flow solver
• Staggered grid arrangement
• RK2 time integration scheme
• Pressure-Poisson equation solver with AMGX acceleration
• Immersed boundary method with:
  • Spring-connected ciliary structures
  • Deformable elliptical particles
  • Force coupling between structure
• Dynamic Resting Length: Features a novel implementation that allows for time-varying resting length of springs, enabling active cilia/particle motion
• Cell-based neighbor list for efficient particle-particle interactions
• NVTX instrumentation for NVIDIA profiling

Code Structure

The codebase is organized into the following modules:

Module	Description
mod_mesh	Defines computational mesh and grid management
mod_time	Time advancement and Navier-Stokes solution methods
mod_pressure	Pressure Poisson solver and sparse matrix generation
mod_amgx	NVIDIA AmgX-based pressure solver acceleration
mod_boundary	Boundary condition implementations
mod_particle	Particle data structure for immersed boundary points
mod_ib	Immersed boundary representation
mod_cilia	Ciliary structure implementation
mod_cilia_array	Management of multiple cilia
mod_closed_cilia	Closed-loop (elliptical) particle implementation
mod_ibm	Core immersed boundary method functions
mod_io	Input/output routines
mod_inter_particle_force	Particle interaction forces
mod_cell	Cell data structure for neighbor lists
mod_dims	Dimension tracking utility
ftn_c	Fortran to C interface for AmgX
nvtx	NVIDIA Tools Extension for performance profiling

Prerequisites

• Fortran compiler (gfortran recommended)
• NVIDIA HPC SDK (for AmgX acceleration, optional)
• NVIDIA CUDA Toolkit (for AmgX acceleration, optional)

Installation

1. Clone the repository:

git clone https://github.com/your-username/ibmc.git
cd ibmc

2. Build the executable:

make

Usage

1. Configure your simulation by editing input_params.dat:

# Example configuration
&stype
simtype      = 2/       # Simulation type (1=all, 2=cilia, 3=particle)    

&time
dt      = 0.0001,       # Time step    
it_save = 100,          # Save interval
tsim    = 28.0/         # Simulation duration

# ... other parameters

2. Run the simulation:

./ibmc

3. View the results: Output files are generated in the current directory with the following naming conventions:

• u_[timestep].txt - x-velocity
• v_[timestep].txt - y-velocity
• ib_loc_c[timestep].txt - Cilia positions
• ib_loc_p[timestep].txt - Particle positions The provided matlab script cilia_vis.m can be used for this purpose

Simulation Types

The code supports three simulation modes (controlled by simtype in input_params.dat):

1. All (simtype=1): Simulates both cilia and particles together
2. Cilia (simtype=2): Simulates only cilia structures
3. Particle (simtype=3): Simulates only elliptical particles

Parameter Configuration

Key parameters in input_params.dat:

Domain and Grid

• Lx, Ly: Domain size in x and y directions
• Nx, Ny: Number of grid points

Flow Properties

• nu: Kinematic viscosity
• rho: Fluid density
• utop: Top wall velocity (for lid-driven cavity) or inlet velocity
• tp: Time period for oscillatory flows

Cilia Properties

• nc: Number of cilia
• lc: Length of each cilium
• xoc, yoc: Position of first cilium
• dc: Distance between adjacent cilia
• wbl: Width between cilia layers
• ko, kd: Spring stiffness constants

Particle Properties

• nparticles: Number of particles
• radius: Particle radius
• ar: Aspect ratio
• npparticles: Number of nodes per particle layer
• xop, yop: Initial position
• kop, kod: Spring stiffness constants

Technical Details

Fluid Solver

• 2D incompressible Navier-Stokes equations
• Second-order finite difference discretization
• Projection method for pressure-velocity coupling
• RK2 time integration

Immersed Boundary Method

• Discrete delta function for force spreading and velocity interpolation
• Spring-based force calculations between connected nodes
• Two-way coupling between fluid and structures
• Support for different boundary types (open cilia, closed particles)

Performance Optimizations

• Cell-based neighbor list for efficient force calculations
• AmgX acceleration for pressure Poisson equation (optional)
• NVTX annotations for performance analysis

Acknowledgments

• The immersed boundary method implementation is inspired by the work of Charles Peskin
• AmgX integration based on NVIDIA's AmgX library

Contact

For questions or contributions, please contact [[email protected]]