A Novel Approach of Unit Conversion in the Lattice Boltzmann Method
The lattice Boltzmann method (LBM) is an alternative method to the conventional computational fluid dynamic (CFD) methods. It gained popularity due to its simplicity in coding and dealing with a complex fluid flow such as the multiphase flow. The method is based on the kinetic theory, which is mesos...
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| Format: | Article |
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MDPI AG
2021-07-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/14/6386 |
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| author | Saleh S. Baakeem Saleh A. Bawazeer Abdulmajeed. A. Mohamad |
| author_facet | Saleh S. Baakeem Saleh A. Bawazeer Abdulmajeed. A. Mohamad |
| author_sort | Saleh S. Baakeem |
| collection | DOAJ |
| description | The lattice Boltzmann method (LBM) is an alternative method to the conventional computational fluid dynamic (CFD) methods. It gained popularity due to its simplicity in coding and dealing with a complex fluid flow such as the multiphase flow. The method is based on the kinetic theory, which is mesoscopic scale. Hence, applying the LBM method for macroscopic problems requires a proper conversion from the physical scale (conventional units) to the mesoscopic scale (lattice units) and vice versa. The Buckingham π theorem and the principle of corresponding states are the popular methods used for data reductions and unit conversion processes in the LBM. Nevertheless, those methods have some issues, such as difficulty in converting specific quantities, such as thermo-physical properties. The current work uses a novel dimensional analysis method systematically for mapping properties’ units between scales. Moreover, the approach has the flexibility in selecting parameters to ensure the stability of the method of solution. Several benchmark examples are used to evaluate the feasibility and accuracy of the proposed approach. In conclusion, the proposed approach showed the flexibility of the mapping between meso-scale to macro-scales and vice versa on solid bases rather than ad-hoc methods. |
| first_indexed | 2024-03-10T09:47:16Z |
| format | Article |
| id | doaj.art-bb4bb4049f794316b990a844e28fc113 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T09:47:16Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-bb4bb4049f794316b990a844e28fc1132023-11-22T03:08:51ZengMDPI AGApplied Sciences2076-34172021-07-011114638610.3390/app11146386A Novel Approach of Unit Conversion in the Lattice Boltzmann MethodSaleh S. Baakeem0Saleh A. Bawazeer1Abdulmajeed. A. Mohamad2Department of Mechanical and Manufacturing Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB T2N 1N4, CanadaMechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, P.O. 5555, Makkah 24382, Saudi ArabiaDepartment of Mechanical and Manufacturing Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB T2N 1N4, CanadaThe lattice Boltzmann method (LBM) is an alternative method to the conventional computational fluid dynamic (CFD) methods. It gained popularity due to its simplicity in coding and dealing with a complex fluid flow such as the multiphase flow. The method is based on the kinetic theory, which is mesoscopic scale. Hence, applying the LBM method for macroscopic problems requires a proper conversion from the physical scale (conventional units) to the mesoscopic scale (lattice units) and vice versa. The Buckingham π theorem and the principle of corresponding states are the popular methods used for data reductions and unit conversion processes in the LBM. Nevertheless, those methods have some issues, such as difficulty in converting specific quantities, such as thermo-physical properties. The current work uses a novel dimensional analysis method systematically for mapping properties’ units between scales. Moreover, the approach has the flexibility in selecting parameters to ensure the stability of the method of solution. Several benchmark examples are used to evaluate the feasibility and accuracy of the proposed approach. In conclusion, the proposed approach showed the flexibility of the mapping between meso-scale to macro-scales and vice versa on solid bases rather than ad-hoc methods.https://www.mdpi.com/2076-3417/11/14/6386lattice Boltzmann methodunit conversionadvection-diffusionphase changedifferentially heated cavitysurface tension |
| spellingShingle | Saleh S. Baakeem Saleh A. Bawazeer Abdulmajeed. A. Mohamad A Novel Approach of Unit Conversion in the Lattice Boltzmann Method Applied Sciences lattice Boltzmann method unit conversion advection-diffusion phase change differentially heated cavity surface tension |
| title | A Novel Approach of Unit Conversion in the Lattice Boltzmann Method |
| title_full | A Novel Approach of Unit Conversion in the Lattice Boltzmann Method |
| title_fullStr | A Novel Approach of Unit Conversion in the Lattice Boltzmann Method |
| title_full_unstemmed | A Novel Approach of Unit Conversion in the Lattice Boltzmann Method |
| title_short | A Novel Approach of Unit Conversion in the Lattice Boltzmann Method |
| title_sort | novel approach of unit conversion in the lattice boltzmann method |
| topic | lattice Boltzmann method unit conversion advection-diffusion phase change differentially heated cavity surface tension |
| url | https://www.mdpi.com/2076-3417/11/14/6386 |
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