Recalibration of LBM Populations for Construction of Grid Refinement with No Interpolation
Abstract
:1. Introduction
2. Theoretical Background
2.1. Lattice Boltzmann Method and Its Parameters
2.2. Recalibration of Populations
2.2.1. Recalibration with
2.2.2. Recalibration with Both and
2.2.3. Recalibration with a Change in Quadrature
2.2.4. Recalibration with the Change of Stencil
3. Grid Refinement Interface without Interpolation
3.1. Grid Geometry
3.2. Stencils and Recalibration
3.3. Full Grid Transition Algorithm
- 1.
- Perform streaming on the coarse grid with the use of
- (a)
- The D2Q7(1, 1/4) (or D2Q15(1, 25/38)) stencil for the blue nodes;
- (b)
- The D2Q9(1, 1/3) stencil for the dark-green nodes. Here, the incoming populations at the nodes that are exactly on the boundary are saved in a separate temporary buffer to be used in Step 5, because the prestreaming populations are still needed in the next step.
- 2.
- Perform streaming on the fine grid at (Figure 1b) with the use of
- (a)
- The D2Q9(1/2, 1/3) stencil for the light-green nodes;
- (b)
- The D2Q9(1/2, 4/3) stencil for the orange nodes.
- 3.
- Perform collisions on the fine grid at the orange and light-green nodes (Figure 1b).
- 4.
- Perform the second streaming at into the light-green nodes of the fine grid (Figure 1a).
- 5.
- Restore the values of the boundary nodes from the buffer.
- 6.
- Perform collisions on all nodes with the respective stencils depicted in Figure 1a.
4. Benchmarks
4.1. Poiseuille Flow
4.2. Athermal Vortex
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
LBM | Lattice Boltzmann method |
CFD | Computational fluid dynamics |
BGK | Bhatnagar–Gross–Krook |
ZAMR | Zipped Data Structure for Adaptive Mesh Refinement |
IVP | Initial-value problem |
BVP | Boundary-value problem |
HRR | Hybrid-recursive regularized |
Appendix A. Stencils for the Grid Transition
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Berezin, A.; Perepelkina, A.; Ivanov, A.; Levchenko, V. Recalibration of LBM Populations for Construction of Grid Refinement with No Interpolation. Fluids 2023, 8, 179. https://doi.org/10.3390/fluids8060179
Berezin A, Perepelkina A, Ivanov A, Levchenko V. Recalibration of LBM Populations for Construction of Grid Refinement with No Interpolation. Fluids. 2023; 8(6):179. https://doi.org/10.3390/fluids8060179
Chicago/Turabian StyleBerezin, Arseniy, Anastasia Perepelkina, Anton Ivanov, and Vadim Levchenko. 2023. "Recalibration of LBM Populations for Construction of Grid Refinement with No Interpolation" Fluids 8, no. 6: 179. https://doi.org/10.3390/fluids8060179