Development of a Lattice-Boltzmann model in curvilinear coordinates for the acoustic simulation of the Cochlea

Lattice-Boltzmann models have been very powerful tools to simulate fluid dynamics, difusion processes, mechanical waves and electrodynamics. Nevertheless, their applicability has been restricted due to the fact that most of them are build on Cartesian coordinates, which hinders them to take advantage of system’s symmetries to reduce the dimensions of the computational domain or to naturally addressing complex systems with curved boundaries, from which the Cochlea, the main auditory organ in mammals, is a paradigmatic example. This work designs and implements a novel lattice-Boltzmann model for the three-dimensional simulation of acoustic waves in general curvilinear coordinates. The method keeps in the computer the standard structure of a Cartesian system with the same velocity vectors in all cells, but it rescales the macroscopic fields and adds forcing terms to reproduce in the continuous limit the wave equation on general coordinates. The resulting second order method perfectly finds the vibrational normal modes of a Cylinder, a Trumpet and a Torus, keeps the isotropic wave propagation in real space and can be applied to any coordinate system. With this method in hand the simulation of the Cochlea was addressed. The Cochlea was parametrized as a tampered coiled tube with a cardioid as cross section and, it was scaled to have the real dimensions of a human Cochlea. As result, we found that the geometry of the Cochlea itself is enough to reproduce the effect of spatial frequency segregation: At high frequencies the net pressure on the Basilar membrane oscillates with larger amplitude close to the windows, and lower frequencies shift the location of maximal amplitude to the apex. The lower the frequency is the closer to the apex that maximum is located. Those results illustrate the high performance, flexibility and reliability of the proposed method, which constitutes a valuable contribution to the development of more powerful lattice-Boltzmann schemes.

• Autores: Velasco Sabogal, Ali Mauricio
• Fecha de publicación: 2017
• Institución: Universidad Nacional de Colombia
• Repositorio: Universidad Nacional de Colombia
• Idioma: spa
• OAI Identifier: oai:repositorio.unal.edu.co:unal/64089
• Acceso en línea: https://repositorio.unal.edu.co/handle/unal/64089; http://bdigital.unal.edu.co/64848/
• Palabra clave: 5 Ciencias naturales y matemáticas / Science; 53 Física / Physics; 57 Ciencias de la vida; Biología / Life sciences; biology; Cochlea; Basilar Membrane; Acoustics; Waves; Simulation; Lattice-Boltzmann; General Coordinates; Cóclea; Membrana Basilar; Acústica; Ondas; Simulación; Coordenadas generales
• Rights: openAccess
• License: Atribución-NoComercial 4.0 Internacional