Abstract
We present unified and consistent boundary conditions for the 2D smoothed particle hydrodynamics (SPH) weakly compressible numerical method, including (1) pressure (wall impermeability), (2) wall shear stress (for laminar and turbulent flows), (3) wall turbulent conditions (k–ε model) and (4) inlet–outlet open boundaries. The first three conditions (wall conditions) are based on modified discrete differential operators, using a proper renormalising function at the wall, which is calculated by solving a governing equation. The last condition (inlet/outlet) is prescribed through the Riemann invariants of Euler equations, leading to absorbing conditions which avoid spurious waves. Validations (fish pass, open and closed channels, hydraulic jump, Creager weir) proved that the proposed models perform well.
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Abbreviations
- A a :
-
Value of A at the point occupied by the particle a
- A ab :
-
Difference A a –A b
- c, c 0 :
-
Speed of sound and reference speed of sound
- g :
-
Gravity acceleration
- k :
-
Turbulent kinetic energy
- P :
-
Production of turbulent kinetic energy
- p :
-
Pressure
- r a :
-
Particle position vector
- R +, R − :
-
Riemann invariants
- S :
-
Rate-of-strain tensor
- U, u :
-
Velocity vector and longitudinal velocity
- u τ :
-
Shear velocity vector
- w :
-
SPH kernel
- γ a :
-
Renormalising factor
- ε:
-
Dissipation of turbulent kinetic energy
- ξ:
-
Exponent of the state equation
- μ, μ T :
-
Molecular viscosity and eddy viscosity
- ρ, ρ0 :
-
Density and reference density
- τ :
-
Wall shear stress
References
Pope, S. B. (2000). Turbulent flows. Cambridge: Cambridge University Press.
Monaghan, J. J. (1992). Smoothed Particle Hydrodynamics. Annual Review of Astronomy and Astrophysics, 30, 543–574.
Lee, E.-S., Moulinec, C., Xu, R., Violeau, D., Laurence, D., & Stansby, P. (2008). Comparisons of weakly compressible and truly incompressible SPH algorithms for 2D flows. Journal of Computational Physics, 227, 8417–8436.
Ferrand, M., Violeau, D., Rogers, B. D., Laurence, D. (2011). Consistent wall boundary treatment for laminar and turbulent flows in SPH. Proceedings of 6th Spheric International Workshop (pp. 275–282). Hamburg, Germany.
Ferrari, A., Dumbser, M., Toro, E. F., & Armanini, A. (2009). A new 3D parallel SPH scheme for free surface flows. Computers and Fluids, 38, 1203–1217.
Mahmood, O., Kassiotis, C., Violeau, D., Ferrand, M., Denis, C. (2011). Effect of wall boundary treatment in SPH for modelling turbulent flows with inlet/outlet. Proceedings of 6th Spheric International Workshop (pp. 333–339), Hamburg, Germany.
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© 2014 Springer Science+Business Media Singapore
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Ferrand, M., Violeau, D., Mayrhofer, A., Mahmood, O. (2014). Correct Boundary Conditions for Turbulent SPH. In: Gourbesville, P., Cunge, J., Caignaert, G. (eds) Advances in Hydroinformatics. Springer Hydrogeology. Springer, Singapore. https://doi.org/10.1007/978-981-4451-42-0_21
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DOI: https://doi.org/10.1007/978-981-4451-42-0_21
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