Simulation of Viscous Flows with a Gridless Particle Method FOTIOS G. STAMATELOS and JOHN S. ANAGNOSTOPOULOS School of Mechanical Engineering / Fluids Section National Technical University of Athens 9, Iroon Polytechniou ave., Zografou, 15780 Athens GREECE sfotis@fluid.mech.ntua.gr j.anagno@fluid.mech.ntua.gr Abstract: The aim of this paper is to present the numerical simulation of the evolution of the viscous, low Reynolds flows in two-dimensional cases with the use of the Smoothed Particle Hydrodynamics (SPH) method. This work is considered as the first step towards the simulation of complex three-dimensional flows, which occur in impulse water turbines. The method was originally developed for solving problems of astrophysical nature and belongs to the meshless methods, as it does not require any computational grid. A set of descrete fluid particles is used to represent the continuous fluid, and their trajectories are being calculated in a Lagrangian sense through time. The 2- D test cases examined in this paper are the Couette and the Poiseuille Flow, and the basic problem of the liquid column collapse (Dam Break). For the first two test cases the numerical results were tested against analytical solutions from the literature, while for the third test case experimental measurements were used for the validation of the calculations. The agreement of the numerical results with the corresponding analytical and experimental data is quite good and encouraging towards the use of the SPH method in modelling of more complex, unsteady and multiphase flow fields, while the performance of the algorithm referring to the speed of the calculations and the qualitative results is remarkable. Key-Words: - Smoothed Particle Hydrodynamics (SPH), Dam Break, Couette and Poiseuille Flow, Numerical Modelling 1 Introduction Initially the SPH method was expressed by Lucy [1] and then used in astrophysical problems, such as the movement of the stars and the asteroids by Gingold and Monaghan [2], while later it was applied for problems of continuum solid and fluid mechanics. Monaghan in [3] presents an extended review on the SPH method. The method was initially developed for compressible flows and then it was extended to be applied in free surface flows [4], [5] through an artificial fluid which can be considered slightly compressible. Such an assumption was necessary in order to overcome the problem of large sonic velocities and allowed the use of larger computational time step. The SPH method is characterised as a mesh- free particle method since it does not involve any mesh during the calculation procedure and its aim is only to track the trajectories of the particles that represent the moving fluid [3]. The mesh-free nature of the method allows overcoming problems such as the generation of the grid, which sometimes can be very time consuming, or the simulation of the flow field near complex boundary geometries or even the simulation of free surface flows, as no special conditions are required at the interface. It also gives the opportunity to model flows with moving or deforming boundaries or simulate the interaction of several fluid phases [6]. Apart from the above the main advantages of the SPH method are that pure advection can be treated accurately and that when more than one materials are involved in the calculations then the interface problems may be solved easily. Moreover the resolution of the problem can be made easily adapted to the location and to the time while due to the close similarity between SPH and molecular dynamics it is permitted to include complex physics as well [3]. It should also be noted that the SPH is quickly approaching its mature stage, which means that it can be applied for micro-scale to macro-scale problems and from discrete to continuum systems. Some of the fields that the SPH method is already been applied are the modelling of