Computational Modeling of Individual Red Blood Cell Dynamics Using Discrete Flow Composition and Adaptive Time-Stepping Strategies
Abstract
:1. Introduction
2. Mathematical Framework
2.1. Preliminaries
2.2. Membrane Model
2.3. Interface Tracking: Level-Set Representation
2.4. Non-Newtonian Fluid Model
Dimensionless Nonlinear Coupled Problem
3. Composition Technique Applied to the Second-Order BDF Scheme
3.1. Second-Order Backward Differentiation BDF-2
- Step 1:
- Step 2:
3.2. Step 1: Calculation of an Intermediate Solution
3.3. Step 2 and Solution Method
3.4. Algorithm of Composed BDF-2 Scheme with Fixed Time Step
Algorithm 1 Composed BDF-2 with fixed time step. |
|
3.5. Algorithm for Composing BDF-2 with Adaptive Time Step
Algorithm 2 Composed BDF-2 with adaptive time steps. |
|
4. Numerical Approximation of the Fluid/Membrane Problem
4.1. Time Discretization of the Fluid Problem
4.2. Penalty Method
4.3. Level Set Problem
5. Numerical Results
5.1. Example 1: One-Dimensional Test Case—Accuracy-Order Analysis
5.2. Example 2: Membrane Dynamics in a Newtonian Fluid under Simple Shear Flow
5.2.1. Tank-Treading Regime
5.2.2. Tumbling Regime
5.2.3. Calibration of the Penalty Parameter
5.2.4. Quantitative Validation with Respect to Existing Results
5.3. Example 3: Membrane Dynamics in a Casson Shear Flow
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Note on the Composition Technique for the Level-Set Problem
References
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20 | 40 | 80 | 160 | 320 | 720 | |
1.65 | 1.83 | 1.92 | 1.96 | 1.98 | 1.99 | |
2.777 | 2.925 | 2.975 | 2.991 | 2.996 | 2.998 |
0.0022 | 0.021 | 0.0138 | 0.0082 | 0.03692 | 0.0512 | 0.0675 | |
0.036 | 0.0013 | 0.0027 | 0.0057 | 0.0199 | 0.0309 | 0.0458 |
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Laadhari, A.; Deeb, A. Computational Modeling of Individual Red Blood Cell Dynamics Using Discrete Flow Composition and Adaptive Time-Stepping Strategies. Symmetry 2023, 15, 1138. https://doi.org/10.3390/sym15061138
Laadhari A, Deeb A. Computational Modeling of Individual Red Blood Cell Dynamics Using Discrete Flow Composition and Adaptive Time-Stepping Strategies. Symmetry. 2023; 15(6):1138. https://doi.org/10.3390/sym15061138
Chicago/Turabian StyleLaadhari, Aymen, and Ahmad Deeb. 2023. "Computational Modeling of Individual Red Blood Cell Dynamics Using Discrete Flow Composition and Adaptive Time-Stepping Strategies" Symmetry 15, no. 6: 1138. https://doi.org/10.3390/sym15061138
APA StyleLaadhari, A., & Deeb, A. (2023). Computational Modeling of Individual Red Blood Cell Dynamics Using Discrete Flow Composition and Adaptive Time-Stepping Strategies. Symmetry, 15(6), 1138. https://doi.org/10.3390/sym15061138