A 3D Fully Non-Hydrostatic Model for Free-Surface Flows with Complex Immersed Boundaries
Abstract
:1. Introduction
2. Numerical Model
2.1. Governing Equations
2.2. Numerical Solution by FDM
2.3. Numerical Solution with FDM and VOS-Based Immersed Boundary Method
2.4. Volume Fraction Transport Equation
2.5. Solution Procedure
- Propose the initial and the boundary conditions for a given time-step and use the VOF reconstruction method via Equation (23) to compute a cell-center estimate of the volume fraction and free-surface position.
- Solve the , and using Equations (10)–(12) via FDM.
- Solve the right-hand side D of pressure Poisson equation (Equation 16) using iterative method to obtain the pressure, Pn+1/2 based on point-successive over relaxation iteration.
- Solve the velocity, u, v, and w using Equations (7)–(9) via a split operating step FDM.
- Using the via Equation (20) to calculate the forcing function, , , and in Equations (7)–(9) include the effect of immersed body.
- In the fractional time-step, the values of velocities, forcing functions, and pressure variables calculated from the previous time-step were used to resolve the steps 1 to 5 to obtain new values. The above numerical procedure was reiterated until the prescribed time was reached.
3. Results and Discussion
3.1. Dam-Break Flow Passing a Cylinder
3.2. Partial Dam-Break Flow
3.3. Dam-Break Surge Passing Four Aligned Square or Circular Cylinders
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Δt (s) | Grid Size (m) | ||
---|---|---|---|
0.02 | 0.01 | 0.005 | |
0.001 | 48 | 156 | 508 |
0.0005 | 75 | 226 | 711 |
0.00025 | 105 | 306 | 938 |
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Lo, D.-C.; Tsai, Y.-S. A 3D Fully Non-Hydrostatic Model for Free-Surface Flows with Complex Immersed Boundaries. Water 2022, 14, 3803. https://doi.org/10.3390/w14233803
Lo D-C, Tsai Y-S. A 3D Fully Non-Hydrostatic Model for Free-Surface Flows with Complex Immersed Boundaries. Water. 2022; 14(23):3803. https://doi.org/10.3390/w14233803
Chicago/Turabian StyleLo, Der-Chang, and Yuan-Shiang Tsai. 2022. "A 3D Fully Non-Hydrostatic Model for Free-Surface Flows with Complex Immersed Boundaries" Water 14, no. 23: 3803. https://doi.org/10.3390/w14233803