Stability Improvement of the Immersed Boundary–Lattice Boltzmann Coupling Scheme by Semi-Implicit Weighting of External Force
Abstract
:1. Introduction
2. Immersed Boundary–Lattice Boltzmann Coupling Scheme
2.1. Immersed Boundary Method
2.2. The LB Method for the Fluid Flow
2.2.1. Basic Formulation of LBM with Multi-Relaxation-Time Collision
2.2.2. Introducing the External Force into the LB Model
3. Presentation of the Averagely Weighted Iteration Approach
3.1. Effectiveness of the DI Approach in Improving the Stability
- (1)
- With the explicit method, the executable program begins to run stably only at , when the membrane relaxes to a circular curve.
- (2)
- With the DI approach (the iteration time per evolution step is set as 10), the critical value is . In addition, the stability rapidly decreases with increasing iteration time (in Figure 2 the IB knots in four diagonal regions).
3.2. Averagely Weighted Iteration (AWI) Approach
4. Verification and Validation
4.1. Verification of the Accuracy of the Averagely Weighted Iteration (AWI) Approach
4.2. Validation of the Stability Improvement
4.2.1. Tension Stiffness
4.2.2. Fastening Stiffness
4.2.3. Bending Rigidity
4.2.4. Density of the Flexible Structure
4.2.5. Fluid Viscosity
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
LBM | Lattice Boltzmann method |
IBM | Immersed boundary method |
AWI | Averagely weighted iteration |
DI | Directly iterative |
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Parameters | Enclosed Area, A | Pressure Jump, Δp | |||
---|---|---|---|---|---|
t = 30,000 | t = 100,000 | t = 30,000 | t = 100,000 | ||
Simulated | (Explicit) | 1.1532 | 1.1461 | 0.00607 | 0.00596 |
(AWI) | 1.1544 | 1.1469 | 0.00601 | 0.00581 | |
Analytical | 1.1576 | 1.1576 | 0.00589 | 0.00589 | |
Relative error (%) | (Explicit) | 0.38 | 0.99 | 3.1 | 1.2 |
(AWI) | 0.28 | 0.92 | 2 | 1.4 |
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Zhang, C.; Li, T.; Hou, J.; Zhou, Q.; Meng, W.; Ma, Q.; Peng, P. Stability Improvement of the Immersed Boundary–Lattice Boltzmann Coupling Scheme by Semi-Implicit Weighting of External Force. Appl. Sci. 2023, 13, 9995. https://doi.org/10.3390/app13189995
Zhang C, Li T, Hou J, Zhou Q, Meng W, Ma Q, Peng P. Stability Improvement of the Immersed Boundary–Lattice Boltzmann Coupling Scheme by Semi-Implicit Weighting of External Force. Applied Sciences. 2023; 13(18):9995. https://doi.org/10.3390/app13189995
Chicago/Turabian StyleZhang, Chunze, Tao Li, Ji Hou, Qin Zhou, Wanwan Meng, Qian Ma, and Peiyi Peng. 2023. "Stability Improvement of the Immersed Boundary–Lattice Boltzmann Coupling Scheme by Semi-Implicit Weighting of External Force" Applied Sciences 13, no. 18: 9995. https://doi.org/10.3390/app13189995
APA StyleZhang, C., Li, T., Hou, J., Zhou, Q., Meng, W., Ma, Q., & Peng, P. (2023). Stability Improvement of the Immersed Boundary–Lattice Boltzmann Coupling Scheme by Semi-Implicit Weighting of External Force. Applied Sciences, 13(18), 9995. https://doi.org/10.3390/app13189995