Document Type : Research Article

**Abstract**

Mesh-free particle (Lagrangian) methods, such as moving-particle semi-implicit (MPS) and smoothed particle hydrodynamics (SPH), are the newest methods in computational fluid dynamics, which have been applied in flow problems with large deformations and inconsistency. The aim of this research was to develop and improve the simulation of open-boundary free-surface flows, using the new method of weakly compressible MPS (WC-MPS) .Most studies in the field of Lagrangian models are concerned with closed boundary conditions. This study, introduces a comprehensive method for MPS modeling of cases with inflow and outflow boundaries. Inflow and outflow boundaries are considered and the boundary conditions and recycling of particles are prescribed. The algorithm not only improves the inlet and outlet boundary conditions, but also reduces the pressure fluctuations at boundaries. To evaluate the proposed method, the famous applied flow problem of ogee spillway and steady shallow flow over curved bed is analyzed. The program is written in C language and validations are performed for this code. Comparison of the results of proposed model and physical models showed acceptable accuracy in modeling the free surface flows with open boundary conditions.

**Keywords**

Adami, S. X, Hu,Y. and Adams, N. A.(2012). “Simulating three-dimensional turbulence with SPH”. In Proceedings of the *Summer Program*, p. 177.

Ataie-Ashtiani, B. and Farhadi, L. (2006). “A stable moving–particle semi-implicit method for free surface flows”, Fluid Dyn. Res., 38, pp. 241-256.

Chatila, J. and Tabbara, M. (2004). “Computational modeling of flow over an ogee spillway”, J. Comput. Struc. 82, pp. 1805-1812.

Deville, M. O. and Gatski, T. B. (2012). *Mathematical modeling for complex fluids and flows*. Springer Science and Business Media, 364225294X, p. 294.

Gotoh, H. and Sakai, T. (1999). “Lagrangian simulation of breaking wave using particle method”, Coastal Eng. J., 41(3-4), pp. 303-326.

Gotoh, H. and Sakai, T. (2006). “Key issues in the particle method for computation of wave breaking”, Coastal Eng. J., 53, pp. 171-179.

Gotoh, H., Shibahara, T. and Saka, T. (2001). “Sub-particle scale turbulence model for the MPS method- Lagrangian flow model for hydraulic engineering”, Comput. Fluid Dyn. J., 9(4), pp. 331-347.

Hirt, C.W. and Nichols, B.D. (1981). “Volume of fluid (VOF) method for the dynamics of free boundaries”, J. Comput. Phys., 39(1), pp. 201-225.

Khayyer, A. and Gotoh, H. (2009). “Modified moving particle semi-implicit methods for the prediction of 2D wave impact pressure”, Coastal Eng., 56, pp. 419-440.

Khayyer, A. and Gotoh, H. (2010). “A higher order Laplacian model for enhancement and stabilization of pressure calculation by the MPS method”, Appl. Ocean Res., 32, pp. 124-131.

Kim, D. G. and park J. H, (2005). “Analysis of flow structure over ogee_spillway in consideration of scale and roughness effects by using CFD model”. KSCE Journal of Civil Engineering; Vol. 9, No. 2, pp. 161~169.

Kondo, M. and Koshizuka, S. (2011). Improvement of stability in moving particle semi-implicit method. Int. J. Numer. Methods in Fluids, 65(6), pp. 638-654.

Koshizuka, S. and Oka, Y. (1996). “Moving particle semi-implicit method for fragmentation of incompressible fluid”, Nucl. Sci. Eng., 123(3), pp. 421-434.

Koshizuka, S., Nobe, A. and Oka, Y. (1998). “Numerical analysis of breaking waves using the moving particle semi-implicit method”, Int. J. Numer. Methods in Fluids, 26(7), pp. 751-769.

Liu, J., Koshizuka, S. and Oka, Y. (2005). “A hybrid particle-mesh method for viscous, incompressible, multiphase flows” J. Comput. Phys., 202(1), pp. 65-93.

Shakibaeinia, A. and Jin, Y.C. (2010). “A weakly compressible MPS method for modeling of open-boundary free-surface flow”, Int. J. Numer. Methods in Fluids, 63(10), 1208-1232.

Shakibaeinia, A. and Jin, Y.C. (2011a). “A mesh-free particle model for simulation of mobile-bed dam break”, Adv. Water Resour., 34(6), pp. 794-807.

Shakibaeinia, A. and Jin, Y.C. (2011b). “MPS-based mesh-free particle method for modeling open-channel flows”, J. Hyd. Eng. 137(11), pp. 1375-1384.

Shakibaeinia, A. and Jin, Y.C. (2012a). “MPS meshfree particle method for multiphase flows”, Comput. Methods Appl. Mech. Eng., 229-232: pp. 13-26.

Shibata, K. and Koshizuka, S. (2007). “Numerical analysis of shipping water impact on a deck using a particle method”, Ocean Eng., 34, pp. 585-593.

Shibata, K., Koshizuka, S. and Oka, Y. (2004). “Numerical analysis of jet breakup using particle method”, J. Nucl. Sci. Technol., 41(7), pp. 715-722.

Sivakumaran, N.S., Tingsanchali, T. and Hosking, R.J. (1983). “Steady shallow flow over curved beds”, J. Fluid Mech., 128, pp. 469-487.

June 2015

Pages 37-52

**Receive Date:**20 February 2015**Revise Date:**01 August 2015**Accept Date:**31 August 2015