SPHysics – development of a free-surface fluid solver – Part 1: Theory and formulations

Balsara, 1995, von Neumann stability analysis of smooth particle hydrodynamics – suggestions for optimal algorithms, Journal of Computational Physics, 121, 357, 10.1016/S0021-9991(95)90221-X Batchelor, 1974 Beeman, 1976, Some multistep methods for use in molecular dynamics calculations, Journal of Computational Physics, 20, 130, 10.1016/0021-9991(76)90059-0 Benz, 1990, Smoothed particle hydrodynamics: a review, 269 Bonet, 1999, Variational and momentum preservation aspects of smoothed particle hydrodynamic formulations, Computer Methods in Applied Mechanical Engeneering, 180, 97, 10.1016/S0045-7825(99)00051-1 Cha, 2003, Implementations and tests of Godunov-particle hydrodynamics, Monthly Notices of the Royal Astronomical Society, 340, 73, 10.1046/j.1365-8711.2003.06266.x Colagrossi, 2003, Numerical simulation of interfacial flows by smoothed particle hydrodynamics, Journal of Computational Physics, 191, 448, 10.1016/S0021-9991(03)00324-3 Crespo, 2007, Boundary conditions generated by dynamic particles in SPH methods, Computers, Materials & Continua, 5, 173 Crespo, 2007, 3D SPH Simulation of large waves mitigation with a dike, Journal of Hydraulic Research, 45, 631, 10.1080/00221686.2007.9521799 Crespo, 2008, Modeling dam break behavior over a wet bed by a SPH technique, Journal of Waterway Port, Coastal, and Ocean Engineering, 134, 313, 10.1061/(ASCE)0733-950X(2008)134:6(313) Crespo, 2011, GPUs, a new tool of acceleration in CFD: efficiency and reliability on smoothed particle hydrodynamics methods, PLoS ONE, 6, e20685, 10.1371/journal.pone.0020685 Dalrymple, 2006, Numerical modeling of water waves with the SPH method, Coastal Engineering, 53, 141, 10.1016/j.coastaleng.2005.10.004 Dilts, 1999, Moving-least-squares-particle hydrodynamics – I. Consistency and stability, International Journal for Numerical Methods in Engineering, 44, 1115, 10.1002/(SICI)1097-0207(19990320)44:8<1115::AID-NME547>3.0.CO;2-L Gingold, 1977, Smoothed particle hydrodynamics: theory and application to non-spherical stars, Monthly Notices of the Royal Astronomical Society, 181, 375, 10.1093/mnras/181.3.375 Gómez-Gesteira, 2004, Using a 3D SPH method for wave impact on a tall structure, Journal of Waterway Port, Coastal, and Ocean Engineering, 130, 63, 10.1061/(ASCE)0733-950X(2004)130:2(63) Gómez-Gesteira, 2005, Green water overtopping analyzed with a SPH model, Ocean Engineering, 32, 223, 10.1016/j.oceaneng.2004.08.003 Gómez-Gesteira, 2010, State-of-the-art of classical SPH for free-surface flows, Journal of Hydraulic Research, 48, 6, 10.1080/00221686.2010.9641242 Gotoh, 2001, Subparticle-scale model for the mps method-Lagrangian flow model for hydraulic engineering, Computational Fluid Dynamics Journal, 9, 339 Hirsch, 1998, Vol. 1 Hughes, 2010, Comparison of incompressible and weakly-compressible SPH models for free-surface water flows, Journal of Hydraulic Research, 48, 105, 10.1080/00221686.2010.9641251 Khayyer, 2010, On particle-based simulation of a dam break over a wet bed, Journal of Hydraulic Research, 48, 238, 10.1080/00221681003726361 Leimkuhler, 1996 Liu, 2003 Liu, 1997, Moving least square Kernel Galerkin method (I) methodology and convergence, Computer Methods in Applied Mechanics and Engineering, 143, 113, 10.1016/S0045-7825(96)01132-2 Lo, 2002, Simulation of near-shore solitary wave mechanics by an incompressible SPH method, Applied Ocean Research, 24, 275, 10.1016/S0141-1187(03)00002-6 Monaghan, 1982, Why particle methods work, SIAM Journal on Scientific and Statistical Computing, 3, 422, 10.1137/0903027 Monaghan, 1989, On the problem of penetration in particle methods, Journal of Computational Physics, 82, 1, 10.1016/0021-9991(89)90032-6 Monaghan, 1992, Smoothed particle hydrodynamics, Annual Review of Astronomy and Astrophysics, 30, 543, 10.1146/annurev.aa.30.090192.002551 Monaghan, 1994, Simulating free surface flows with SPH, Journal of Computational Physics, 110, 399, 10.1006/jcph.1994.1034 Monaghan, 2000, SPH without tensile instability, Journal of Computational Physics, 159, 290, 10.1006/jcph.2000.6439 Monaghan, 2005, Smoothed particle hydrodynamics, Reports on Progress in Physics, 68, 1703, 10.1088/0034-4885/68/8/R01 Monaghan, 1999, Solitary waves on a Cretan beach, Journal of Waterway Port, Coastal, and Ocean Engineering, 125, 145, 10.1061/(ASCE)0733-950X(1999)125:3(145) Monaghan, 1999, Gravity currents descending a ramp in a stratified tank, Journal of Fluid Mechanics, 379, 39, 10.1017/S0022112098003280 Monaghan, 2003, Fluid motion generated by impact, Journal of Waterway Port, Coastal, and Ocean Engineering, 129, 250, 10.1061/(ASCE)0733-950X(2003)129:6(250) Narayanaswamy, 2010, SPHysics-Funwave hybrid model for coastal wave propagation, Journal of Hydraulic Research, 48, 85, 10.1080/00221686.2010.9641249 Omidvar, P., Stansby, P.K., Rogers, B.D., 2011. Wave body interaction in 2D using Smoothed Particle Hydrodynamics (SPH) with variable particle mass. International Journal for Numerical Methods in Fluids. 10.1002/fld.2528. Parshikov, 1999, Application of a solution of the Riemann problem to the SPH method, Computational Mathematics and Mathematical Physics, 39, 1173 Parshikov, 2000, Improvements in SPH method by means of interparticle contact algorithm and analysis of perforation tests at moderate projectile velocities, International Journal of Impact Engineering, 24, 779, 10.1016/S0734-743X(99)00168-2 Parshikov, 2002, Smoothed particle hydrodynamics usingInterparticle contact algorithms, Journal of Computational Physics, 180, 358, 10.1006/jcph.2002.7099 Rogers, 2008, SPH modeling of tsunami waves: Advances in coastal and ocean engineering, Vol. 10. Rogers, 2010, Simulation of caisson breakwater movement using SPH, Journal of Hydraulic Research, 48, 135, 10.1080/00221686.2010.9641254 Toro, 1994, Restoration of the contact surface in the HLL-Riemann solver, Shock Waves, 4, 25, 10.1007/BF01414629 Toro, 2001 Vacondio, R., Rogers, B.D., Stansby, P.K., Mignosa, P. SPH modeling of shallow flow with open boundaries for practical flood simulation. Journal of Hydraulic Engineering, doi:10.1061/(ASCE)HY.1943-7900.0000543, in press. Verlet, 1967, Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules, Physical Review, 159, 98, 10.1103/PhysRev.159.98 Vila, 1999, On particle weighted methods and smooth particle hydrodynamics, Mathematical Models and Methods in Applied Sciences, 9, 161, 10.1142/S0218202599000117 Wendland, 1995, Piecewiese polynomial, positive definite and compactly supported radial functions of minimal degree, Advances in Computational Mathematics, 4, 389, 10.1007/BF02123482