Sharp-interface IBM
Represent complex immersed surfaces within a non-uniform Cartesian flow grid, without forcing the mesh to conform to the body.
RESEARCH-DRIVEN COMPUTATIONAL ENGINEERING / IBM + RBF
Complex flows.
Clearly resolved.
Meet VorteXdyn — a published, high-performance immersed boundary solver for accurate simulation of incompressible fluid flows around complex stationary and moving structures.
SHARP-INTERFACE / MESH-FREE RBF / MPI PARALLELISM
FLOW FIELD / CONCEPTUAL VIEWIBM·RBF / 3D
GHOST-CELL RECONSTRUCTIONNON-CONFORMAL GRID
02 + 03 DIMENSIONAL FLOWSRBF THIN-PLATE SPLINESMPI PARALLEL SOLVERFSI MOVING BOUNDARIES
01 / CORE CAPABILITIES
A different way to model complex geometry.
The published methodology combines a sharp-interface immersed boundary formulation with mesh-free interpolation to resolve fluid–structure interactions on Cartesian grids.
RBF interpolation
Reconstruct pressure and velocity near immersed surfaces with multidimensional thin-plate-spline radial basis functions.
Moving boundaries
Model stationary, oscillating and deforming bodies using ghost cells and an iterative flow-smoothing strategy.
Parallel HPC
Scale 2D and 3D computations using MPI and Cartesian domain decomposition across multiple processors.
FIG / 02 — MULTIDIMENSIONAL GHOST-CELL MODELSCHEMATIC
Fluid nodesGhost cellsImage point
Conceptual diagram based on the terminology in Farooq et al. (2025), Section 3. It is not a numerical simulation output.
02 / INSIDE THE SOLVER
The mathematics behind the flow.
VorteXdyn couples a non-staggered Navier–Stokes discretization with geometric boundary treatment, mesh-free reconstruction and parallel computation.
01
Discretize the flow domain
Use a non-uniform Cartesian grid and a triangulated surface representation for the immersed body.
02
Locate the interface
Classify fluid, solid and ghost cells; identify the boundary-intercept and mirrored image points.
03
Interpolate with radial basis functions
Apply thin-plate-spline RBF interpolation to reconstruct the fluid field near the interface.
04
Advance and synchronize
Enforce boundary conditions, smooth changes around moving bodies and exchange data across MPI subdomains.
φGC = 2φBI − φIPDIRICHLET GHOST-CELL RECONSTRUCTION / PAPER EQ. 13
03 / VALIDATION CASES
From canonical flows to bio-inspired motion.
The paper validates the solver with representative stationary, moving and fluid–structure-interaction cases in two and three dimensions.
CASE 01 / PAPER §5.2, §5.5.2
Cylinders and vortex shedding
Stationary circular and square cylinders, including three-dimensional wake structures and comparisons with published drag and Strouhal data.
CASE 02 / PAPER §5.3–5.4
Oscillating and flexible airfoils
Plunging and pitching airfoil simulations, plus coupled fluid–structure response and flow-induced motions.
CASE 03 / PAPER §5.3.3
Tandem swimming bodies
Two interacting undulating foils, used to evaluate moving multi-body boundaries and the resulting wake dynamics.
CASE 04 / PAPER §5.5.1
Three-dimensional biological flows
Complex moving eel and Jack Fish geometries, demonstrating coherent 3D vortical structures in the simulated wakes.
Visuals are original schematic illustrations, not figures or measured results reproduced from the paper.
2nd
Order spatial accuracyGrid convergence analysis reports second-order spatial accuracy for the presented method (Figure 7).
~80%
Parallel efficiencyReported for one 2D test with 12 processors; performance varies with case and processor count (Section 5.1).
2D / 3D
Validated configurationsStationary, moving, flexible and multi-body examples discussed throughout the results section.
04 / PEER-REVIEWED PUBLICATION
An accurate immersed boundary method using radial-basis functions for incompressible flows
This research introduces VorteXdyn, a parallel sharp-interface immersed boundary solver using RBF-based ghost-cell interpolation and an iterative strategy to mitigate spurious pressure oscillations.
05 / RESEARCH & COLLABORATION
Let's advance computational engineering.
Explore the published numerical methodology and its validation studies. Contact details for the VortexDyn website owner can be added here once confirmed.
READ THE SCIENCE
Access the complete study
Paper, formulation, parallelization methodology, numerical results and supplementary materials are available through the publisher.
Open publication ↗Company email, location and enquiry forms are intentionally not invented; personalize this section before a commercial launch.