BlochFlow

A MATLAB solver for Bloch analysis of flow perturbations in a channel over a lattice of phononic subsurface units

This repository contains a spectral-FEM solver that performes Bloch analysis of flow perturbations in a channel with a lattice of phononic subsurface units. The code computes the Bloch dispersion relations (frequency vs. wavenumber) and mode shapes characterizing the stability characteristics of a channel flow interacting with a periodic arrangement of phononic subsurface (PSub) units. It considers a single unit cell and solves the generalized Orr-Sommerfeld equation coupled with an elastodynamics model for the surface admittance representing the PSub motion.

Features

• Hybrid discretization: Uses Fourier modes in the streamwise and spanwise directions and Finite Elements (FE) in the wall-normal direction.
• Fluid-Structure Interaction: Fully coupled formulation linking the Orr-Sommerfeld fluid equation with a 1D PSub solid model via impedance boundary conditions.
• Metamaterial support: Capable of modeling standard Phononic Crystals (PnC) and Locally Resonant Metamaterials (MM) with internal resonators.
• Flexible geometry: Supports various lattice shapes (square, hexagon).

Installation

1. Clone the repository:

git clone [https://github.com/david-roca/BlochFlow.git](https://github.com/david-roca/BlochFlow.git)

2. Open MATLAB and navigate to the folder.
3. Add the source code to your path:

addpath(genpath('src'));
savepath;

Usage

A complete example is provided in main_example.m.

Citation

If you use this solver in your work, please cite the following paper:

M.I. Hussein, D. Roca, A.R. Harris, A. Kianfar. Scatterless interferences: delay of laminar-to-turbulent flow transition by a lattice of subsurface phonons. Proceedings of the Royal Society A. 482, 20250071 (2026); https://doi.org/10.1098/rspa.2025.0771

@article{Hussein2026,
  author = {Hussein, Mahmoud I. and Roca, David and Harris, Adam R. and Kianfar, Armin},
  title = {Scatterless interference: Delay of laminar-to-turbulent flow transition by a lattice of subsurface phonons},
  journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  volume = {482},
  number = {2337},
  pages = {20250771},
  year = {2026},
  issn = {1364-5021},
  doi = {10.1098/rspa.2025.0771}
}