A Particle Method Based on a Generalized Finite Difference Scheme to Solve Weakly Compressible Viscous Flow Problems
Abstract
:1. Introduction
2. Finite Difference Particle Method for Weakly Compressible Flow
2.1. Lagrangian Form of the Governing Equations for Weakly Compressible Viscous Flow
2.2. Generalized Finite Difference Scheme
2.3. Particle Representation for Governing Equations
2.4. Artificial Particle Displacement
2.5. Boundary Conditions
3. Applications of the Finite Difference Particle Method
3.1. Fundamental Definition
3.2. Unsteady Flow in a Pipeline
3.3. Poisseuille Flow
3.4. Couette Flow
3.5. Flow in Porous Media
3.6. Lid-Driven Cavity Flow
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Time (s) | Particle Method: x (m) | Theoretical Solution: u (m/s) | Particle Method: u (m/s) | Error (10−8) |
---|---|---|---|---|
0.25 | 2.48 | 30.16201462 | 30.16201544 | 2.74 |
0.50 | 10.08 | 30.64615858 | 30.64615942 | 2.75 |
0.75 | 17.80 | 31.11956025 | 31.11956110 | 2.75 |
1.00 | 25.64 | 31.58265402 | 31.58265470 | 2.13 |
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Zhang, Y.; Xiong, A. A Particle Method Based on a Generalized Finite Difference Scheme to Solve Weakly Compressible Viscous Flow Problems. Symmetry 2019, 11, 1086. https://doi.org/10.3390/sym11091086
Zhang Y, Xiong A. A Particle Method Based on a Generalized Finite Difference Scheme to Solve Weakly Compressible Viscous Flow Problems. Symmetry. 2019; 11(9):1086. https://doi.org/10.3390/sym11091086
Chicago/Turabian StyleZhang, Yongou, and Aokui Xiong. 2019. "A Particle Method Based on a Generalized Finite Difference Scheme to Solve Weakly Compressible Viscous Flow Problems" Symmetry 11, no. 9: 1086. https://doi.org/10.3390/sym11091086