Simulation of Sloshing-Shear Mixed Shallow Water Waves (II) Numerical Solutions
This is the second part of the paper. It, aside from the
core subroutine test reported previously, focuses on the simulation of
turbulence governed by the full STF Navier-Stokes equations on a
large scale. Law of the wall is found plausible in this study as a model
of the boundary layer dynamics. Model validations proceed to
include velocity profiles of a stationary turbulent Couette flow, pure
sloshing flow simulations, and the identification of water-surface
inclination due to fluid accelerations. Errors resulting from the
irrotational and hydrostatic assumptions are explored when studying
a wind-driven water circulation with no shakings. Illustrative
examples show that this numerical strategy works for the simulation
of sloshing-shear mixed flow in a 3-D rigid rectangular base tank.
[1] D. K. Lilly, "The representation of small-scale turbulence in numerical
simulation experiments," Proc. IBM Sci. Comput. Symposium Environ.
Sci., IBM Data Process Div., White Plains, N.Y., pp. 195-210, 1967.
[2] J. W. Deardorff, "A numerical study of three-dimensional turbulent
channel flow at large Reynolds numbers," J. Fluid Mech., vol. 41, pp.
453-480, 1970.
[3] P. J. Mason, and N. S. Callen, "On the magnitude of the subgrid-scale
eddy coefficient in large eddy simulations of turbulent channel flow," J.
Fluid Mech., vol. 162, pp. 439-462, 1986.
[4] J. Constantin, M. G. Inclan, and M. Raschendorfer, "The energy budget
of a spruce forest: field measurements and comparison with the
forest-land-atmosphere model (FLAME)," J. of Hydrology, pp. 212-213,
22-35, 1998.
[5] C. Babajimopoulos, and K. Bedford, "Formulating lake models with
preserve spectral statistics," J. Hydr. Div., ASCE, vol. 106, pp. 1-19,
1980.
[6] H. Schmidt, and U. Schumann, "Coherent structure of the convective
boundary layer derived from large-eddy simulations," J. of Fluid Mech.,
vol. 200, pp. 511-565, Great Britain. 1989.
[7] C. B. Liao, M. F. Wu, and M. H. Gou, "Large eddy simulation of a round
jet in a cross flow," Proceedings of the 13th hydraulic engineering
conference, M14-M21, Taiwan. 2002.
[8] W. H. Chung, "Dependence of the Smagorinsky-Lilly-s constant on
inertia, wind stress, and bed roughness for large eddy simulations,"
Journal of Mechanics, vol. 22, No. 2, pp. 125-136, 2006.
[9] G. T. Csanady, "Circulation in the Coastal Ocean," pp. 279, D. Reidel
Pub. Co.., 1982.
[10] J. Amorocho, and J. J. Devries, "A new evaluation of the wind stress
coefficient over water surfaces," J. Geophys. Res., vol. 85, pp. 433-442,
1980.
[11] W. H. Chung, "Dependence of the Smagorinsky-Lilly-s constant on
inertia, wind stress, and bed roughness for large eddy simulations,"
Journal of Mechanics, vol. 22, No. 2, pp. 125-136, 2006.
[12] O. M. Faltinsen, "A numerical non-linear method of sloshing in tanks
with two-dimensional flow," J. of Ship Research, vol. 18(4), pp. 224-241,
1978.
[13] T. M. Okamoto, and M. Kawahara, "Two-dimensional sloshing analysis
by Lagrangian finite element method," International Journal for
Numerical Methods in Fluids, vol. 11, pp. 453-477, 1990.
[14] W. Chen, M. A. Haroun, and F. Liu, "Large amplitude liquid sloshing in
seismically excited tanks," Earthquake Engineering and Structural
Dynamics, vol. 25, pp. 653-669, 1996.
[15] G. X. Wu, Q. W. Ma, and R. E. Taylor, "Numerical simulation of
sloshing waves in a 3D tank based on a finite element method," Applied
Ocean Research, vol. 20, pp. 337-355, 1998.
[16] O. M. Faltinsen, O. F. Rognebakke, and A. N. Imokha, "Resonant
three-dimensional nonlinear sloshing in a square-base basin, Part 2.
Effect of higher modes," J. Fluid Mech, vol. 523, pp. 199-218, 2002.
[17] O. M. Faltinsen, O. F. Rognebakke, and A. N. Timokha, "Transient and
steady-state amplitudes of resonant three-dimensional sloshing in a
square base thank with a finite fluid depth," Physics of Fluids, vol. 18,
012103, pp. 1-14, 2006.
[1] D. K. Lilly, "The representation of small-scale turbulence in numerical
simulation experiments," Proc. IBM Sci. Comput. Symposium Environ.
Sci., IBM Data Process Div., White Plains, N.Y., pp. 195-210, 1967.
[2] J. W. Deardorff, "A numerical study of three-dimensional turbulent
channel flow at large Reynolds numbers," J. Fluid Mech., vol. 41, pp.
453-480, 1970.
[3] P. J. Mason, and N. S. Callen, "On the magnitude of the subgrid-scale
eddy coefficient in large eddy simulations of turbulent channel flow," J.
Fluid Mech., vol. 162, pp. 439-462, 1986.
[4] J. Constantin, M. G. Inclan, and M. Raschendorfer, "The energy budget
of a spruce forest: field measurements and comparison with the
forest-land-atmosphere model (FLAME)," J. of Hydrology, pp. 212-213,
22-35, 1998.
[5] C. Babajimopoulos, and K. Bedford, "Formulating lake models with
preserve spectral statistics," J. Hydr. Div., ASCE, vol. 106, pp. 1-19,
1980.
[6] H. Schmidt, and U. Schumann, "Coherent structure of the convective
boundary layer derived from large-eddy simulations," J. of Fluid Mech.,
vol. 200, pp. 511-565, Great Britain. 1989.
[7] C. B. Liao, M. F. Wu, and M. H. Gou, "Large eddy simulation of a round
jet in a cross flow," Proceedings of the 13th hydraulic engineering
conference, M14-M21, Taiwan. 2002.
[8] W. H. Chung, "Dependence of the Smagorinsky-Lilly-s constant on
inertia, wind stress, and bed roughness for large eddy simulations,"
Journal of Mechanics, vol. 22, No. 2, pp. 125-136, 2006.
[9] G. T. Csanady, "Circulation in the Coastal Ocean," pp. 279, D. Reidel
Pub. Co.., 1982.
[10] J. Amorocho, and J. J. Devries, "A new evaluation of the wind stress
coefficient over water surfaces," J. Geophys. Res., vol. 85, pp. 433-442,
1980.
[11] W. H. Chung, "Dependence of the Smagorinsky-Lilly-s constant on
inertia, wind stress, and bed roughness for large eddy simulations,"
Journal of Mechanics, vol. 22, No. 2, pp. 125-136, 2006.
[12] O. M. Faltinsen, "A numerical non-linear method of sloshing in tanks
with two-dimensional flow," J. of Ship Research, vol. 18(4), pp. 224-241,
1978.
[13] T. M. Okamoto, and M. Kawahara, "Two-dimensional sloshing analysis
by Lagrangian finite element method," International Journal for
Numerical Methods in Fluids, vol. 11, pp. 453-477, 1990.
[14] W. Chen, M. A. Haroun, and F. Liu, "Large amplitude liquid sloshing in
seismically excited tanks," Earthquake Engineering and Structural
Dynamics, vol. 25, pp. 653-669, 1996.
[15] G. X. Wu, Q. W. Ma, and R. E. Taylor, "Numerical simulation of
sloshing waves in a 3D tank based on a finite element method," Applied
Ocean Research, vol. 20, pp. 337-355, 1998.
[16] O. M. Faltinsen, O. F. Rognebakke, and A. N. Imokha, "Resonant
three-dimensional nonlinear sloshing in a square-base basin, Part 2.
Effect of higher modes," J. Fluid Mech, vol. 523, pp. 199-218, 2002.
[17] O. M. Faltinsen, O. F. Rognebakke, and A. N. Timokha, "Transient and
steady-state amplitudes of resonant three-dimensional sloshing in a
square base thank with a finite fluid depth," Physics of Fluids, vol. 18,
012103, pp. 1-14, 2006.
@article{"International Journal of Architectural, Civil and Construction Sciences:53297", author = "Weihao Chung and Iau-Teh Wang and Yu-Hsi Hu", title = "Simulation of Sloshing-Shear Mixed Shallow Water Waves (II) Numerical Solutions", abstract = "This is the second part of the paper. It, aside from the
core subroutine test reported previously, focuses on the simulation of
turbulence governed by the full STF Navier-Stokes equations on a
large scale. Law of the wall is found plausible in this study as a model
of the boundary layer dynamics. Model validations proceed to
include velocity profiles of a stationary turbulent Couette flow, pure
sloshing flow simulations, and the identification of water-surface
inclination due to fluid accelerations. Errors resulting from the
irrotational and hydrostatic assumptions are explored when studying
a wind-driven water circulation with no shakings. Illustrative
examples show that this numerical strategy works for the simulation
of sloshing-shear mixed flow in a 3-D rigid rectangular base tank.", keywords = "potential flow theory, sloshing flow, space-timefiltering, order of accuracy.", volume = "5", number = "2", pages = "71-10", }
