Derivation of an improved smoothed particle hydrodynamics model for establishing a three-dimensional numerical wave tank overcoming excessive numerical dissipation

In this study, an improved SPH (smoothed particle hydrodynamics) method coupling the κ-ε turbulence model and the wall function is proposed to simulate wall-bounded turbulent flows at medium and high Reynolds numbers. The second-order partial derivative term of the composite function containing the turbulent viscosity coefficient is decomposed into the sum of two terms, which helps SPH to avoid numerical errors and difficulties in dealing with boundary conditions in the nested approximation of first-order partial derivatives. Particle shifting technique, δ-SPH method, and graphics processing unit parallel technology are used in the simulations to ensure uniform particles, smooth pressure field, and high computational efficiency, respectively. The SPH method with the κ-ε turbulence model and the wall function is tested and validated by simulating four classical wall-bounded turbulent flows at medium and high Reynolds numbers, which are the turbulent flat plate boundary layer at Re = 4.2 × 106 and Re = 107, backward step separation flow at ReH = 3025, the flow around the airfoil at Re = 3 × 106, and the flow around the pitching airfoil at Re = 1.35 × 105, respectively. The simulation results are consistent with the references, validating the suitability of the current SPH method for simulating wall-bounded turbulent flows at medium and high Reynolds numbers. Finally, the airfoil motion combining the pitching and deforming at Re = 3 × 106 is investigated by the current SPH method. The results show that the deformation of the airfoil's relative thickness affects the lift coefficients of the pitching airfoil. Furthermore, the increase in the relative thickness increment reduces the amplitude of the lift coefficient, while the increase in the deformation period has little effect on the amplitude of the lift coefficient.

Smoothed particle hydrodynamics with κ-ε closure for simulating wall-bounded turbulent flows at medium and high Reynolds numbers

Bao,

Hu,

Huang

et al. 2023

Direct imposition of the wall boundary condition for weakly compressible flows in three-dimensional smoothed particle hydrodynamics simulations

Kim,

Park

2023

This study introduces a novel method for imposing wall boundary conditions in smoothed particle hydrodynamics (SPH). SPH is a particle method based on the Lagrangian approach, primarily employed in fluid analysis as a part of numerical computation methods. Due to its ability to discretize space using particles, SPH excels in handling analyses of free surface flow or multiphase flow with intricate boundary surfaces. However, there is a drawback in modeling wall boundaries using particles, as resolving the particle deficiency problem necessitates multi-layered boundary particles to be arranged behind the wall boundary. This leads to difficulties in implementing complex shapes and adds computational expense. To address this issue, this study suggests the use of boundary segments for wall boundary modeling and specifically employs triangular segments for three-dimensional expansions. For robust application of boundary conditions, a method considering both Poisson's equation and geometric configurations is proposed. The proposed method is independent of the segment density, which facilitates efficient and flexible modeling. In addition, by imposing accurate boundary conditions from the wall, the stability and accuracy of the solution are enhanced. The performance of the proposed method is validated through numerical examples, compared with various analytical and experimental results.

Establishment and validation of a viscous-potential coupled and graphics processing unit accelerated numerical tank based on smoothed particle hydrodynamics and high-order spectral methods

Lyu,

Sun,

Yang

et al. 2023

The smoothed particle hydrodynamics (SPH) method is an entirely Lagrangian and truly meshless numerical tool that is inherently suitable for simulating violent viscous free-surface flows, whilst it usually renders considerable simulation time when solving large-scale engineering problems. The high-order spectral (HOS) method is an accurate and very efficient numerical tool for modeling a large-scale inviscid gravity wave field, whilst it is hard to tackle complex physical phenomena due to the dependence on the potential flow theory. This paper aims to propose a viscous-potential coupled and graphics processing unit accelerated numerical model for establishing a high-fidelity and high-efficiency numerical wave tank. In this coupling scheme, the SPH method is applied in the near-field where violent physical processes exist to accurately capture complex free-surface behaviors such as overturning and breaking, whilst the HOS method is applied in the far-field where the water undergoes gentle motion to efficiently generate a desired gravity wave. A dedicated SPH–HOS coupling interface is also presented to accurately transmit the flow information from the HOS side to the SPH side. Meanwhile, an SPH–HOS buffer region with several key techniques is also proposed to ensure a successful coupling between the two numerical methods. Different benchmarks demonstrate that the present SPH–HOS coupling method absorbs the respective advantages of the two numerical methods and shows great feasibility and reliability in solving hydrodynamic problems involving gravity wave generation, propagation, deformation, and its interaction with marine structures.