A Pressure-Based Fully-Coupled Flow Algorithm for the Control Volume Finite Element Method
Abstract
:1. Introduction
2. Governing Equations
3. The Control Volume Finite Element Method
4. The Pressure-Based Coupled Solution Procedure
4.1. Discretized Momentum Conservation Equation
4.2. Discretized Mass Conservation Equation
4.3. Discretized Energy Conservation Equation
5. Boundary Conditions
5.1. Boundary Conditions for the Momentum Conservation Equation
5.1.1. No-Slip Wall
5.1.2. Inlet
5.1.3. Outlet
5.1.4. Opening
5.1.5. Symmetry Plane
5.2. Boundary Conditions for the Mass Conservation Equation
5.2.1. No-Slip Walls
5.2.2. Inlet
5.2.3. Outlet
5.2.4. Opening
5.2.5. Symmetry Plane
5.3. Boundary Conditions for the Energy Conservation Equation
5.3.1. No-Slip Wall
5.3.2. Inlet
5.3.3. Outlet
5.3.4. Opening
5.3.5. Symmetry Plane
6. Parallelization Strategy
7. Test Cases
7.1. Turbulent Flow over a Flat Plate
7.2. Buice 2D Diffuser
7.3. 3D NACA0012 Wing Wind Tunnel Test
7.4. Transonic Turbulent Flow over ONERA Wing
8. Closing Remarks
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
Fields and Parameters | |
Velocity | |
v | Velocity magnitude |
p | Pressure |
Specific total enthalpy | |
T | Temperature |
Density | |
Viscosity | |
Turbulent viscosity | |
Effective viscosity | |
Thermal conductivity | |
Turbulent thermal conductivity | |
Effective thermal conductivity | |
Specific heat at constant pressure | |
R | Gas constant |
k | Turbulent kinetic energy |
Turbulent dissipation frequency | |
Ratio of specific heats | |
t | Time |
Pressure coefficient | |
Stress tensor | |
Surface vector | |
S | Surface area |
V | Volume |
N | Shape function |
Mass flux | |
Scalar quantity | |
Distance vector | |
n | Number of nodes of an element |
Number of nodes of a side | |
Number of nodes of the whole mesh | |
r | Residual |
Identity matrix | |
Pressure coefficient | |
Super- and Subscripts | |
* | Latest available value |
∘ | Previous time step value |
Cartesian components of a vector | |
i | Node index |
j | Neighboring/adjacent node index to i |
C | Control volume associated with the node of index i |
F | Neighboring/adjacent control volume to C |
Neighboring/adjacent control volume to C with no s shared | |
Integration point | |
Boundary integration point | |
k | Index of a node which straddles the integration point |
Specified | |
∞ | Free-stream condition |
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Mangani, L.; Alloush, M.M.; Lindegger, R.; Hanimann, L.; Darwish, M. A Pressure-Based Fully-Coupled Flow Algorithm for the Control Volume Finite Element Method. Appl. Sci. 2022, 12, 4633. https://doi.org/10.3390/app12094633
Mangani L, Alloush MM, Lindegger R, Hanimann L, Darwish M. A Pressure-Based Fully-Coupled Flow Algorithm for the Control Volume Finite Element Method. Applied Sciences. 2022; 12(9):4633. https://doi.org/10.3390/app12094633
Chicago/Turabian StyleMangani, Luca, Mhamad Mahdi Alloush, Raphael Lindegger, Lucian Hanimann, and Marwan Darwish. 2022. "A Pressure-Based Fully-Coupled Flow Algorithm for the Control Volume Finite Element Method" Applied Sciences 12, no. 9: 4633. https://doi.org/10.3390/app12094633
APA StyleMangani, L., Alloush, M. M., Lindegger, R., Hanimann, L., & Darwish, M. (2022). A Pressure-Based Fully-Coupled Flow Algorithm for the Control Volume Finite Element Method. Applied Sciences, 12(9), 4633. https://doi.org/10.3390/app12094633