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Coreixas C, Wissocq G, Chopard B, Latt J. Impact of collision models on the physical properties and the stability of lattice Boltzmann methods. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190397. [PMID: 32564722 DOI: 10.1098/rsta.2019.0397] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/29/2020] [Indexed: 06/11/2023]
Abstract
The lattice Boltzmann method (LBM) is known to suffer from stability issues when the collision model relies on the BGK approximation, especially in the zero viscosity limit and for non-vanishing Mach numbers. To tackle this problem, two kinds of solutions were proposed in the literature. They consist in changing either the numerical discretization (finite-volume, finite-difference, spectral-element, etc.) of the discrete velocity Boltzmann equation (DVBE), or the collision model. In this work, the latter solution is investigated in detail. More precisely, we propose a comprehensive comparison of (static relaxation time based) collision models, in terms of stability, and with preliminary results on their accuracy, for the simulation of isothermal high-Reynolds number flows in the (weakly) compressible regime. It starts by investigating the possible impact of collision models on the macroscopic behaviour of stream-and-collide based D2Q9-LBMs, which clarifies the exact physical properties of collision models on LBMs. It is followed by extensive linear and numerical stability analyses, supplemented with an accuracy study based on the transport of vortical structures over long distances. In order to draw conclusions as generally as possible, the most common moment spaces (raw, central, Hermite, central Hermite and cumulant), as well as regularized approaches, are considered for the comparative studies. LBMs based on dynamic collision mechanisms (entropic collision, subgrid-scale models, explicit filtering, etc.) are also briefly discussed. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.
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Affiliation(s)
- C Coreixas
- Department of Computer Science, University of Geneva, 1204 Geneva, Switzerland
| | - G Wissocq
- CERFACS, 42 Avenue G. Coriolis, 31057, Toulouse Cedex, France
| | - B Chopard
- Department of Computer Science, University of Geneva, 1204 Geneva, Switzerland
| | - J Latt
- Department of Computer Science, University of Geneva, 1204 Geneva, Switzerland
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Fučík R, Galabov R, Pauš P, Eichler P, Klinkovský J, Straka R, Tintěra J, Chabiniok R. Investigation of phase-contrast magnetic resonance imaging underestimation of turbulent flow through the aortic valve phantom: experimental and computational study using lattice Boltzmann method. MAGNETIC RESONANCE MATERIALS IN PHYSICS BIOLOGY AND MEDICINE 2020; 33:649-662. [PMID: 32108906 DOI: 10.1007/s10334-020-00837-5] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2019] [Revised: 01/20/2020] [Accepted: 02/08/2020] [Indexed: 11/28/2022]
Abstract
OBJECTIVE The accuracy of phase-contrast magnetic resonance imaging (PC-MRI) measurement is investigated using a computational fluid dynamics (CFD) model with the objective to determine the magnitude of the flow underestimation due to turbulence behind a narrowed valve in a phantom experiment. MATERIALS AND METHODS An acrylic stationary flow phantom is used with three insertable plates mimicking aortic valvular stenoses of varying degrees. Positive and negative horizontal fluxes are measured at equidistant slices using standard PC-MRI sequences by 1.5T and 3T systems. The CFD model is based on the 3D lattice Boltzmann method (LBM). The experimental and simulated data are compared using the Bland-Altman-derived limits of agreement. Based on the LBM results, the turbulence is quantified and confronted with the level of flow underestimation. RESULTS LBM gives comparable results to PC-MRI for valves up to moderate stenosis on both field strengths. The flow magnitude through a severely stenotic valve was underestimated due to signal void in the regions of turbulent flow behind the valve, consistently with the level of quantified turbulence intensity. DISCUSSION Flow measured by PC-MRI is affected by noise and turbulence. LBM can simulate turbulent flow efficiently and accurately, it has therefore the potential to improve clinical interpretation of PC-MRI.
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Affiliation(s)
- Radek Fučík
- Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Praha 2, Prague, Czech Republic.
| | - Radek Galabov
- Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Praha 2, Prague, Czech Republic.,Institute for Clinical and Experimental Medicine, Prague, Czech Republic
| | - Petr Pauš
- Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Praha 2, Prague, Czech Republic
| | - Pavel Eichler
- Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Praha 2, Prague, Czech Republic
| | - Jakub Klinkovský
- Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Praha 2, Prague, Czech Republic
| | - Robert Straka
- Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Praha 2, Prague, Czech Republic.,Department of Heat Engineering and Environment Protection, AGH University of Science and Technology, Kraków, Poland
| | - Jaroslav Tintěra
- Institute for Clinical and Experimental Medicine, Prague, Czech Republic
| | - Radomír Chabiniok
- Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Praha 2, Prague, Czech Republic.,Inria, Palaiseau, France.,LMS, Ecole Polytechnique, CNRS, Institut Polytechnique de Paris, Paris, France.,School of Biomedical Engineering & Imaging Sciences (BMEIS), St Thomas' Hospital, King's College London, London, UK.,Division of Pediatric Cardiology, Department of Pediatrics, UT Southwestern Medical Center, Dallas, TX, 75235-7701, USA
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