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In this paper we implement a simple strategy, based on Jin and Braza's method, to deal with nonreflecting outlet boundary conditions for incompressible Navier-Stokes flows using the method of smoothed particle hydrodynamics (SPH). The outflow boundary conditions are implemented using an outflow zone downstream of the outlet, where particles are moved using an outgoing wave equation for the velocity field so that feedback noise from the outlet boundary is greatly reduced. For unidirectional flow across the outlet, this condition reduces to Orlanski's wave equation. The performance of the method is demonstrated through several two-dimensional test problems, arXiv:1709.09141v1 [physics.flu-dyn] 26 Sep 2017 including unsteady, plane Poiseuille flow, flow between two inclined plates, the Kelvin-Helmholtz instability in a channel, and flow in a constricted conduit, and in three-dimensions for turbulent flow in a 90 • section of a curved square pipe. The results show that spurious waves incident from the outlet are effectively absorbed and that steady-state laminar flows can be maintained for much longer times compared to periodic boundary conditions. In addition, time-dependent anisotropies in the flow, like fluid recirculations, are convected across the outlet in a very stable and accurate manner.

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This work presents a new multiphase SPH model that includes the shifting algorithm and a variable smoothing length formalism to simulate multiphase flows with accuracy and proper interphase management. The implementation was performed in the DualSPHysics code, and validated for different canonical experiments, such as the single-phase and multiphase Poiseuille and Couette test cases. The method is accurate even for the multiphase case for which two phases are simulated. The shifting algorithm and the variable smoothing length formalism has been applied in the multiphase SPH model to improve the numerical results at the interphase even when it is highly deformed and non-linear effects become important. The obtained accuracy in the validation tests and the good interphase definition in the instability cases, indicate an important improvement in the numerical results compared with single-phase and multiphase models where the shifting algorithm and the variable smoothing length formalism are not applied.

The flow through pipe bends and elbows occurs in a wide range of applications. While many experimental data are available for such flows in the literature, their numerical simulation is less abundant. Here, we present highly-resolved simulations of laminar and turbulent water flow in a 90° pipe bend using Smoothed Particle Hydrodynamics (SPH) methods coupled to a Large-Eddy Simulation (LES) model for turbulence. Direct comparison with available experimental data is provided in terms of streamwise velocity profiles, turbulence intensity profiles and cross-sectional velocity maps at different stations upstream, inside and downstream of the pipe bend. The numerical results are in good agreement with the experimental data. In particular, maximum root-mean-square deviations from the experimental velocity profiles are always less than ∼1.4%. Convergence to the experimental measurements of the turbulent fluctuations is achieved by quadrupling the resolution necessary to guarantee convergence of the velocity profiles. At such resolution, the deviations from the experimental data are ∼0.8%. In addition, the cross-sectional velocity maps inside and downstream of the bend shows that the experimentally observed details of the secondary flow are also very well predicted by the numerical simulations.

The swirling secondary flow in curved pipes is studied in three-space dimensions using a weakly compressible Smoothed Particle Hydrodynamics (WCSPH) formulation coupled to new non-reflecting outflow boundary conditions. A large eddy simulation (LES) model for turbulence is benchmarked with existing experimental data. After validation of the present model against experimental results for a $90^{\circ}$ pipe bend, a detailed numerical study aimed at reproducing experimental flow measurements for a wide range of Reynolds numbers has been performed for different pipe geometries, including U pipe bends, S-shaped pipes and helically coiled pipes. In all cases, the SPH calculated behavior shows reasonably good agreement with the measurements across and downstream the bend in terms of streamwise velocity profiles and cross-sectional contours. Maximum mean-root- square deviations from the experimentally obtained profiles are always less than $\sim 1.8$\%. This combined with the very good matching between the SPH and the experimental cross-sectional contours shows the uprising capabilities of the present scheme for handling engineering applications with streamline curvature, such as flows in bends and manifolds.

We present numerical simulations of blood flow through a brain vascular aneurysm with an artificial stent using Smoothed Particle Hydrodynamics (SPH). The aim of this work is to analyze how the flow into an aneurysm changes using different stent configurations. The initial conditions for the simulations were constructed from angiographic images of a real patient with an aneurysm. The wall shear stresses, pressure and highest velocity within the artery, and other particular quantities are calculated which are of medical specific interest. The numerical simulations of the cerebral circulation help doctors to determine if the patient's own vascular anatomy has the conditions to allow arterial stenting by endovascular method before the surgery or even evaluate the effect of different stent structure and materials. The results show that the flow downstream the aneurysm is highly modified by the stent configuration and that the best choice for reducing the flow in the aneurysm is to use a completely extended Endeavor stent.