A Non-Equilibrium Interpolation Scheme for IB-LBM Optimized by Approximate Force
A non-equilibrium scheme and an optimized approximate force are proposed for the immersed boundary–lattice Boltzmann method (IB-LBM) to solve the fluid–structure interaction (FSI) equations. This new IB-LBM uses the discrete velocity distribution function and non-equilibrium distribution function to...
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MDPI AG
2023-03-01
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| Online Access: | https://www.mdpi.com/2075-1680/12/3/298 |
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| author | Bowen Liu Weiping Shi |
| author_facet | Bowen Liu Weiping Shi |
| author_sort | Bowen Liu |
| collection | DOAJ |
| description | A non-equilibrium scheme and an optimized approximate force are proposed for the immersed boundary–lattice Boltzmann method (IB-LBM) to solve the fluid–structure interaction (FSI) equations. This new IB-LBM uses the discrete velocity distribution function and non-equilibrium distribution function to establish the interpolation operator and the spread operator at the mesoscopic scale. In the interpolation operator, we use the force model of LBM to derive a direct force with a simple form. In the spread operator, we give a theoretical proof with local second-order accuracy of the spread process using the non-equilibrium theory from the LBM. A non-iterative explicit force approximation scheme optimizes the direct force in that the streamlines have no penetration phenomenon, and the no-slip condition is strictly satisfied. Different from other schemes for the IB-LBM, we try to apply the non-equilibrium theory from the LBM to the IB-LBM and obtain good results. The explicit force obtained using the non-equilibrium scheme and then optimized via the non-iterative streamline correction equation simplifies the explicit direct force scheme and the original implicit scheme previously proposed but obtains a similar streamline correction result compared with the implicit method. Numerical tests prove the applicability and accuracy of this method in the simulation of complex conditions such as moving rigid bodies and deforming flexible bodies. |
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| language | English |
| last_indexed | 2024-03-11T06:56:30Z |
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| spelling | doaj.art-71258766d0b54925badcfd7e055ca1e82023-11-17T09:35:33ZengMDPI AGAxioms2075-16802023-03-0112329810.3390/axioms12030298A Non-Equilibrium Interpolation Scheme for IB-LBM Optimized by Approximate ForceBowen Liu0Weiping Shi1School of Mathematics, Jilin University, Changchun 130012, ChinaSchool of Mathematics, Jilin University, Changchun 130012, ChinaA non-equilibrium scheme and an optimized approximate force are proposed for the immersed boundary–lattice Boltzmann method (IB-LBM) to solve the fluid–structure interaction (FSI) equations. This new IB-LBM uses the discrete velocity distribution function and non-equilibrium distribution function to establish the interpolation operator and the spread operator at the mesoscopic scale. In the interpolation operator, we use the force model of LBM to derive a direct force with a simple form. In the spread operator, we give a theoretical proof with local second-order accuracy of the spread process using the non-equilibrium theory from the LBM. A non-iterative explicit force approximation scheme optimizes the direct force in that the streamlines have no penetration phenomenon, and the no-slip condition is strictly satisfied. Different from other schemes for the IB-LBM, we try to apply the non-equilibrium theory from the LBM to the IB-LBM and obtain good results. The explicit force obtained using the non-equilibrium scheme and then optimized via the non-iterative streamline correction equation simplifies the explicit direct force scheme and the original implicit scheme previously proposed but obtains a similar streamline correction result compared with the implicit method. Numerical tests prove the applicability and accuracy of this method in the simulation of complex conditions such as moving rigid bodies and deforming flexible bodies.https://www.mdpi.com/2075-1680/12/3/298immersed boundarylattice Boltzmannfluid–structure interactionnon-equilibriumdeformable bodymoving particles |
| spellingShingle | Bowen Liu Weiping Shi A Non-Equilibrium Interpolation Scheme for IB-LBM Optimized by Approximate Force Axioms immersed boundary lattice Boltzmann fluid–structure interaction non-equilibrium deformable body moving particles |
| title | A Non-Equilibrium Interpolation Scheme for IB-LBM Optimized by Approximate Force |
| title_full | A Non-Equilibrium Interpolation Scheme for IB-LBM Optimized by Approximate Force |
| title_fullStr | A Non-Equilibrium Interpolation Scheme for IB-LBM Optimized by Approximate Force |
| title_full_unstemmed | A Non-Equilibrium Interpolation Scheme for IB-LBM Optimized by Approximate Force |
| title_short | A Non-Equilibrium Interpolation Scheme for IB-LBM Optimized by Approximate Force |
| title_sort | non equilibrium interpolation scheme for ib lbm optimized by approximate force |
| topic | immersed boundary lattice Boltzmann fluid–structure interaction non-equilibrium deformable body moving particles |
| url | https://www.mdpi.com/2075-1680/12/3/298 |
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