(442h) Comparison of Lattice Boltzmann and the Finite Volume Method within Respiratory Ducts

Authors: 
Berger, M., MUI – Medical University of Innsbruck
Kraxner, M., MCI - The Entrepreneurial School
Pillei, M., MCI - The Entrepreneurial School
Mehrle, A., MCI - University of Applied Sciences

Breathing appertains to the most important functions of the human body. Minutes without oxygen lead to unconsciousness, in worst case to death. Diagnostic identification whether a nose surgery is necessary and successful or not is so far done either by rhinomanometry or endoscopy. Unfortunately, both methods are very uncomfortable for the patients and the outcome of a succeeding surgery cannot be ensured.

So there is the need to develop a prediction tool for nose surgeries. A flow simulation technique called Lattice Boltzmann (LB) is used to simulate the flow within respiratory ducts, because it is easy applicable for complex geometries [1]. Though, the best results are useless when they are not validated by measurements or other simulations. Therefore, the conventional Finite Volume Method (FVM) within respiratory ducts are compared. The big advantage of LB is that there is no need of a meshing process [2]. For all FVM simulations the software package OpenFoam with the transient solver pisoFoam is used. The implementation works with a flexible adjustable time step size in order to achieve a constant Courant number. Simulations with a smaller Courant number than 5 results in a stable simulation. Though, for complex geometries the mesh must be prepared with very good quality not having time step sizes in the range of nanoseconds and a huge computational time.

However, LB uses a different approach. The fluid flow is not calculated by the discretization of the Navier-Stokes equations but by statistical methods. The smaller the lattice velocity, the more stable and accurate are the results. Though, there are limitations of the method and the lattice grid points must be increased. As a consequence, a compromise between speed and accuracy is presented. This method is so far only applicable for respiratory duct velocities up to 2 cm/s. In order to assure short computational time a grid refinement algorithm is implemented. All simulation results are evaluated on a line through the duct. Despite the complexity of the geometry the LB differs from the FVM solution within a range of 10%.           

[1]            Mohamad, A., Lattice Boltzmann Method, Fundamentals and Engineering Applications with computer codes, 2011

[2]            Latt, J., Malaspinas, O., Parmigiani, A., Kontaxakis, D., Lagrava D., Krause, M., Chopard, B., Palabos User Guide, Release 1.0 r1., 2011

[3]            Zhou, J., Lattice Boltzmann Methods for Shallow Water Flows,XI, p19, 2004.