Evaluating the effect of the kernel function and its influence radius on the SPH accuracy andconvergence

In recent years, due to the difficulties of the mesh basedmethods in hydrodynamic numerical simulations,researchers are more attracted by the mesh free methods[۱]. Development of these methods in hydraulicengineering and computational fluid dynamic (CFD)problems such as oil leakage in ocean, simulating wavesin coastal engineering and simulating different kinds offlows in civil and mechanical engineering, increases theimportance of studying their accuracy and convergence.One of the most widely used mesh free methods isSmoothed Particle Hydrodynamics (SPH). In thisresearch the effects of the kernel function and itssmoothing length on accuracy of the weaklycompressible SPH (WCSPH) model are evaluated. Byusing DualSPHysics codes and modifying some parts ofits equations and boundary conditions hydrostaticpressure in a reservoir at rest and laminar and turbulenceflow in an open channel is modeled. For these cases acomparison between two kernel functions (Wendlandand Cubic-Spline) and two influence radiuses (۲ and ۳times the particle dimension) of the Wendland Kernel isperformed considering the accuracy and convergence ofthe results. In addition, the accuracy of these two kernelfunctions in approximating variables is compared in onedimensional condition.According to the results of the simulations, a kernelfunction and its smoothing length for variablesapproximation should be carefully selected due to theproblem conditions. It will be shown that althoughincreasing the influence radius of the kernel increases theconvergence in the laminar case, it will cause someinconsistencies near the boundaries in the turbulence casewith high flow velocity. In addition, it is shown thatselecting an appropriate kernel function in the SPHcalculations have significant effects on the accuracy ofthe results.

کلیدواژه ها:

Numerical Modeling ، Smoothed ParticleHydrodynamics (SPH) ، Kernel function ، Accuracy ، Convergence.