An Unstructured Finite-volume Technique for Shallow-water Flows with Wetting and Drying Fronts
An unstructured finite volume numerical model is
presented here for simulating shallow-water flows with wetting and
drying fronts. The model is based on the Green-s theorem in
combination with Chorin-s projection method. A 2nd-order upwind
scheme coupled with a Least Square technique is used to handle
convection terms. An Wetting and drying treatment is used in the
present model to ensures the total mass conservation. To test it-s
capacity and reliability, the present model is used to solve the
Parabolic Bowl problem. We compare our numerical solutions with
the corresponding analytical and existing standard numerical results.
Excellent agreements are found in all the cases.
[1] S. F. Bradford and B. F. Sanders, "Finite-volume model for shallowwater
flooding of arbitrary topography," J. Hydraul. Eng., ASCE, vol
128, no. 3, pp. 289-298, 2002.
[2] P. Brufau, M. E. Vázquez-Cendon and P. García-Navarro, "A numerical
model for the flooding and drying of irregular domains," Int. J. Numer.
Meth. Fluids, vol 39, pp. 247-275, 2002.
[3] S. Bunya, E. J. Kubatko, J. J. Westerink and Dawson C, "A wetting and
drying treatment for the Runge-Kutta discontinuous Galerkin solution to
the shallow water equations, " Comput. Methods Appl. Mech. Engrg.,
vol 198, pp. 1548-1562, 2009.
[4] A. J. Chorin, "Numerical solution of the Navier-Stokes equations,"
Math. Comput., vol 22, pp. 745-762, 1968.
[5] A. Ern, S. Piperno and K. Djadel, "A well-balanced Runge-Kutta
discontinuous Galerkin method for the shallow-water equations with
flooding and drying," Int. J. Numer. Meth. Fluids, vol 58, pp. 1-25,
2008.
[6] S. Guillou and K. D. Nguyen, "An improved technique for solving twodimensional
shallow water problems," Int. J. Numer. Meth. Fluids, vol
29, p. 465-483, 1999.
[7] M. H. Kobayashi, J. M. C. Pereira and J. C. F. Pereira, J.C.F, "A
conservative finite-volume second-order accurate projection method on
hybrid unstructured grids," J. Comp. Phys., vol 150, pp. 40-75, 1999.
[8] K. D. Nguyen and A. Ouahsine, "2D numerical study on tidal circulation
in strait of Dover," J. of Waterway, Port, Coastal and Ocean
Engineering, vol 123, no. 1, pp. 8-15, 1997.
[9] K. D. Nguyen, Y-E Shi, S. Wang and T. H. Nguyen, "2D Shallow-Water
Model Using Unstructured Finite-Volumes Methods," Journal of
Hydaulic Engineering, ASCE, vol 132 (3) , pp. 258-269, 2006.
[10] C. M. Rhie and W. L. Chow, "Numerical study of the turbulent flow past
an airfoil with trailing edge separation," American Institute of
Aeronautics and Astronautics (AIAA) Journal, vol 21, no. 11, pp. 1525-
1532, 1983.
[11] J. C. Tannehill, D. A. Anderson and R. H. Pletcher Computational Fluid
Mechanics and Heat Transfer. Washington D.C.: Taylor & Francis,
1997, ch. IV.
[12] W. C. Thacker, "Some Exact Solutions to the Nonlinear Shallow-water
Wave Equations," J. Fluid Mech., vol 107, p. 499 - 508, 1981.
[1] S. F. Bradford and B. F. Sanders, "Finite-volume model for shallowwater
flooding of arbitrary topography," J. Hydraul. Eng., ASCE, vol
128, no. 3, pp. 289-298, 2002.
[2] P. Brufau, M. E. Vázquez-Cendon and P. García-Navarro, "A numerical
model for the flooding and drying of irregular domains," Int. J. Numer.
Meth. Fluids, vol 39, pp. 247-275, 2002.
[3] S. Bunya, E. J. Kubatko, J. J. Westerink and Dawson C, "A wetting and
drying treatment for the Runge-Kutta discontinuous Galerkin solution to
the shallow water equations, " Comput. Methods Appl. Mech. Engrg.,
vol 198, pp. 1548-1562, 2009.
[4] A. J. Chorin, "Numerical solution of the Navier-Stokes equations,"
Math. Comput., vol 22, pp. 745-762, 1968.
[5] A. Ern, S. Piperno and K. Djadel, "A well-balanced Runge-Kutta
discontinuous Galerkin method for the shallow-water equations with
flooding and drying," Int. J. Numer. Meth. Fluids, vol 58, pp. 1-25,
2008.
[6] S. Guillou and K. D. Nguyen, "An improved technique for solving twodimensional
shallow water problems," Int. J. Numer. Meth. Fluids, vol
29, p. 465-483, 1999.
[7] M. H. Kobayashi, J. M. C. Pereira and J. C. F. Pereira, J.C.F, "A
conservative finite-volume second-order accurate projection method on
hybrid unstructured grids," J. Comp. Phys., vol 150, pp. 40-75, 1999.
[8] K. D. Nguyen and A. Ouahsine, "2D numerical study on tidal circulation
in strait of Dover," J. of Waterway, Port, Coastal and Ocean
Engineering, vol 123, no. 1, pp. 8-15, 1997.
[9] K. D. Nguyen, Y-E Shi, S. Wang and T. H. Nguyen, "2D Shallow-Water
Model Using Unstructured Finite-Volumes Methods," Journal of
Hydaulic Engineering, ASCE, vol 132 (3) , pp. 258-269, 2006.
[10] C. M. Rhie and W. L. Chow, "Numerical study of the turbulent flow past
an airfoil with trailing edge separation," American Institute of
Aeronautics and Astronautics (AIAA) Journal, vol 21, no. 11, pp. 1525-
1532, 1983.
[11] J. C. Tannehill, D. A. Anderson and R. H. Pletcher Computational Fluid
Mechanics and Heat Transfer. Washington D.C.: Taylor & Francis,
1997, ch. IV.
[12] W. C. Thacker, "Some Exact Solutions to the Nonlinear Shallow-water
Wave Equations," J. Fluid Mech., vol 107, p. 499 - 508, 1981.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:52742", author = "Rajendra K. Ray and Kim Dan Nguyen", title = "An Unstructured Finite-volume Technique for Shallow-water Flows with Wetting and Drying Fronts", abstract = "An unstructured finite volume numerical model is
presented here for simulating shallow-water flows with wetting and
drying fronts. The model is based on the Green-s theorem in
combination with Chorin-s projection method. A 2nd-order upwind
scheme coupled with a Least Square technique is used to handle
convection terms. An Wetting and drying treatment is used in the
present model to ensures the total mass conservation. To test it-s
capacity and reliability, the present model is used to solve the
Parabolic Bowl problem. We compare our numerical solutions with
the corresponding analytical and existing standard numerical results.
Excellent agreements are found in all the cases.", keywords = "Finite volume method, Projection method, Shallow
water, Unstructured grid, wetting/drying fronts.", volume = "4", number = "11", pages = "1194-6", }