Program Overview

A 2D incompressible Navier-Stokes solver using the Immersed Boundary Method (IBM) with direct forcing. Rigid bodies are represented by Lagrangian markers on an Eulerian fluid grid, with no-slip conditions enforced at the boundary using a fractional-step method on a staggered grid. Arbitrary body shapes are supported with configurable translation, rotation, and oscillation. The solver is CPU-parallelised.

ibm.mp4

Quick Start

brew install gcc ffmpeg

git clone https://github.com/obdwinston/Immersed-Boundary.git && cd Immersed-Boundary

chmod +x run.sh && ./run.sh

Solver Verification

animation.mp4

Metric	Current	Reference	Error (%)
$St$	0.195	0.195	0.2
$C_{L,\text{avg}}$	0.000	0.000	0.0
$C_{L,\text{min}}$	-0.653	-0.600	8.8
$C_{L,\text{max}}$	0.653	0.600	8.9
$C_{L,\text{amp}}$	1.306	1.200	8.9
$C_{D,\text{avg}}$	1.649	1.500	9.9
$C_{D,\text{min}}$	1.455	1.300	11.9
$C_{D,\text{max}}$	1.843	1.700	8.4
$C_{D,\text{amp}}$	0.389	0.400	2.9

Parameter	Description	Value
nx, ny	Grid dimensions	1400, 800
xl, xr	Domain x-bounds	-10.0, 25.0
yb, yt	Domain y-bounds	-10.0, 10.0
nS	Lagrangian markers	128
Lc	Characteristic length	1.0
Xc0, Yc0	Initial body position	0.0, 0.0
Th0	Initial body angle	0
Vx_mean, Vy_mean, Om_mean	Mean velocities	0, 0, 0
Ax, Ay, Ath	Oscillation amplitudes	0, 0.2, 0
frx, fry, frth	Oscillation frequencies	0, 0.195, 0
phx, phy, phth	Oscillation phases	0, 0, 0
U_inf	Mean freestream velocity	1.0
Re	Reynolds number	185
wall_type	Boundary condition	slip
dt	Time step	0.002
nt	Total time steps	100000
n_field	Field save interval	100
n_force	Force output interval	50
tol	SOR convergence tolerance	1.0e-5
maxiter	Max SOR iterations	200000
omega	SOR relaxation factor	1.9

Governing Equations

Solution Algorithm

Appendix