A numerical refinement study on the SPH modeling of the violent free surface flows

A comparative study of the numerical treatmentsthat are commonly used in Smoothed Particle Hydrodynamics(SPH) together with relatively a new one, namely ArtificialParticle Displacement algorithm is presented. As a benchmark study, two-dimensional dam-break problem is investigated bymeans of weakly compressible SPH approximation using Eu-ler’s equation of motion with artificial viscosity. After adoptingstandard SPH discretization schemes and equations without anynumerical remedies, three different treatments are sequentiallytested on the dam-break problem. In weakly compressible SPHapproximation, the precise calculation of the densities of theparticles is vital for the overall accuracy of the solution. Inorder to have an improved density field, a density correctionalgorithm is incorporated into the numerical algorithm as abasic numerical treatment. Subsequently, XSPH velocity variantalgorithm [1] and artificial particle displacement (APD) algo-rithm [2] are implemented concurrently in conjunction with thedensity correction algorithm. The effects of each treatment onthe calculated free surface profiles, pressure values and the totalmechanical energy of the system are compared methodically. Theeffects of the numerical treatments particularly on the dynamiccharacteristics of the free surface flow in the dam-break testcase are shown. The outcomes of the simulations show thatdensity correction algorithm to large extent circumvents densityfluctuation induced numerical issues in dam-breaking problem.It is further noted that the combined usage of the APD treatmentand the density correction algorithm gives the most compatibleresults with those of the experimental studies.