Smoothed Particle Hydrodynamics (SPH) 를 이용한 유동 시뮬레이션 연구

송재경(Jaekyung Song),남정호(Jeong Ho Nam),임채호(Chae Ho Lim) (사)한국CDE학회 2015 한국 CAD/CAM 학회 학술발표회 논문집 Vol.2015 No.하계

Grid-based method such as Finite Difference Method(FDM), Finite Volume Method(FVM) have been mainly used for flow simulation. Furthermore, particle-based method (Smoothed Particle Hydrodynamics(SPH), Moving Particle Semi-Implicit(MPS) and Discrete Element Method(DEM) etc.) is recently being treated by many researchers. Particle-based methods were introduced long ago but it has not studied enough because there were some problems like as expensive run-time. However, it is currently being applied in various engineering fields because of highly enhanced hardware performance and many parallel techniques (OpenMP, CUDA, OpenCL, etc.). In this paper, we implement the flow simulation using GPU-based(CUDA) SPH and we show simulation results by using SPH compared with the experiment and by using FDM.

Importance of Initial Particle Distribution in Modeling Dam Break Analysis with SPH

Mahyar Pourlak,Hassan Akbari,Ehsan Jabbari 대한토목학회 2023 KSCE Journal of Civil Engineering Vol.27 No.1

Smoothed-Particle Hydrodynamics (SPH) has drawn a great deal of attention in recent years to model various phenomena in engineering and science. SPH is a Lagrangian model in which moving particles represent the fluid body during simulation. Therefore, the initial distribution of particles may affect the model results along with the simulation, and a good initial condition can minimize numerical errors or increase the computational efficiency. Since SPH model particle distributions need a flow pattern, the dam break flow as a classic benchmark SPH problem is selected in this study, and the best initial particle distribution for this case has to be found. Different results, including the mean density of particles, hydrostatic and dynamic pressures and surge front position, are considered the main model results for the adequacy of different initial particle distributions to be discussed. All models are verified at first by simulating different test cases and comparing the results with analytical and experimental data. Acceptable agreements between these data show the model's capability in well predicting the dam break flows. Then, the effects of initial particle distribution on the results are investigated by considering five different particle distributions. For this purpose, Body-Centered Cubic (BCC), Simple Cubic (SC), Greedy, Voronoi Tessellation and Fibonacci algorithms for particle distributions have been modeled. To get reliable conclusions, these distributions have been utilized in models with different kernel functions as well as with different particle spacings. Based on the results, irregular arrangements such as Greedy distribution perform better than regular SC and BCC distributions in modeling dam-break flow. In addition, both Voronoi and Fibonacci distributions perform almost the same with a moderate level of accuracy. Regarding mentioned arrangements, the main outcome of this study, is that the initial particle distribution is an important issue in SPH models, which clearly affects the results.

CONVEX HULL 알고리즘 개발

이진성(Jin Sung Lee),박정수(Jung-Soo Park),이영신(Young Shin Lee) 대한기계학회 2010 대한기계학회 춘추학술대회 Vol.2010 No.3

Smoothed Particle Hydrodynamics(입자완화 유동법)는 고속 충돌시 발생되는 대변형 문제를 효율적으로 계산하기 위하여 연구되고 있는 무요소 수치해석 방법중의 하나로서 해석의 정확성을 높이기 위해서는 주변입자(neighbour particle)의 선택이 매우 중요하다. 이에 본 연구에서는 기존에 많이 사용되었던 방법에서 발생되는 문제점을 보완할 수 있는 새로운 형태의 neighbour particle 선택방법인 convex hull 알고리즘에 대하여 연구하였다. 연구된 convex hull 알고리즘의 구성내용은 생성된 입자에 대하여 각각의 입자들에 대한 주변의 candidate neighbour particle set(이웃입자 후보군)을 지정하고 이들을 inverse mapping을 통하여 convex hull을 이루도록 새로운 공간으로 투영시킨 후 convex hull을 구성하는 최외곽점을 찾으면 이들이 가장 근접되어 있는 neighbour particle이 되며 이러한 과정들을 작성된 프로그램을 통하여 실제 문제에 적용해 보았으며 본 연구에서 개발된 convex hull 알고리즘은 앞으로 수행될 SPH 해석방법 연구에서 neighbour particle을 선택하는 방법으로 적용이 기대된다. SPH(Smoothed Particle Hydrodynamics) is a grid less Lagrangian technique that is useful as an alternative numerical analysis method used to analyze high deformation problems as well as astrophysical and cosmological problems. In SPH, All points within the support of the kernel are taken as neighbours. The accuracy of the SHP is highly influenced by the method for choosing neighbours from all particle points considered. Typically a linked-list method or tree search method has been used as an effective tool because of its conceptual simplicity, but these methods have some liability in anisotropy situations. In this study, convex hull algorithm is presented as an improved method to eliminate this artifact. A convex hull is the smallest convex set that contains a certain set of points or a polygon. The selected candidate neighbours set are mapped into the new space by an inverse square mapping, and extract a convex hull. The neighbours are selected from the shell of the convex hull. This algorithm is proved by Fortran programs. The program is expected to use as a searching algorithm in the future SPH program development.

Total Lagrangian 기반 음해적 입자법을 이용한 외팔보 동적 거동 해석

이완기(Wan Ki Lee),주영석(Young Suk Joo),김진현(Jin Kim) 대한기계학회 2022 大韓機械學會論文集A Vol.46 No.5

SPH(smoothed particle hydrodynamics)는 Lagrangian 기반 수치해석 기법이며 입자를 단위로 사용하는 무격자 방식이다. 기존 SPH 기법으로 구현된 구조해석은 두 가지 문제점을 가지고 있다. 대변형 지점에서 인장불안정으로 인한 입자 겹침 문제와 수치적 민감성으로 인하여 작은 해석간격을 사용하는 문제이다. 본 연구에서는 total Lagrangian 기반 SPH 기법으로 구조해석을 구현하여 인장불안정 문제를 해소한다. 그리고 동회전성 커널함수를 사용하고 탄성력 연산을 음해적으로 수행하여 보다 큰 해석간격을 사용하여도 해석이 발산하지 않도록 한다. 외팔보 동적 거동 해석을 수행하여 수치모델 정확성을 검증하고 구조해석 적용 가능성을 확인한다. Smoothed particle hydrodynamics (SPH) is a particle-based meshless Lagrangian numerical method. The status quo SPH-based structural analysis has two problems: overlapping particles at large deformation points owing to tensile instability and marginal limits on the time-step size owing to the inherent numerical sensitivity. In this study, a total Lagrangian SPH method is employed in the structural analysis to solve the tensile instability problem. In addition, simulation divergence is prevented even when a relatively larger time-step is used by performing a numerical analysis implicitly and using a corotated kernel function. Dynamic analyses of cantilever beams are performed to verify the accuracy of the numerical model presented in this study and its applicability to structure analysis.

SPH 기법 기반의 파동수조 시뮬레이션

이상민,김무종,고권환,홍정욱 한국전산구조공학회 2021 한국전산구조공학회논문집 Vol.34 No.1

Recently, large-scale offshore and coastal structures have been constructed owing to the increasing interest in eco-friendly energy development. To achieve this, the precise simulations of waves are necessary to ensure the safe operations of marine structures. Several experiments are required in the field to understand the offshore wave; however, in terms of scale, it is difficult to control variables, and the cost is significant. In this study, numerical waves under various wave conditions are produced using a piston-type wavemaker, and the produced wave profiles are verified by comparing with the results from a numerical wave tank (NWT) modeled using the smoothed particle hydrodynamics (SPH) method and theoretical equations. To minimize the effect by the reflected wave, a mass-weighted damping zone is set at the right end of the NWT, and therefore, stable and uniform waves are simulated. The waves are generated using the linear and Stokes wave theories, and it is observed that the numerical wave profiles calculated by the Stokes wave theory yield high accuracy. When the relative depth is smaller than two, the results show good agreement irrespective of the wave steepness. However, when the relative depth and wave steepness are larger than 2 and 0.04, respectively, the errors are negligible if the measurement position is close to the excitation plate. However, the error is 10% or larger if the measurement position is away from the excitation location. Applicable target wave ranges are confirmed through various case studies. 최근 친환경 에너지 개발에 대한 관심의 증가로 해상 및 연안 지역에서 대규모 해양구조물들이 건설되고 있다. 해양구조물은 항상 파랑 하중에 노출되어 있으므로 구조적인 안전성을 확보하기 위해서는 파랑에 대한 정확한 이해와 분석이 필수적이다. 실해역에서 수행되는 실험은 해양파를 이해하기 위한 가장 정확한 방법이지만, 변수의 통제가 어렵고 비용과 규모 측면에서 실험이 제한되는 경우가 많다. 본 연구에서는 수치파동수조를 이용하여 다양한 조건의 파를 생성하고 및 이론식과 비교를 통해 파랑 생성 능력을 검증하였다. 입자 기반 수치해석법인 SPH(Smoothed Particle Hydrodynamics) 기법을 이용하여 3차원 수조 및 피스톤 조파기를 모델링하였으며, 반사파에 대한 영향을 최소화하기 위해 수로 끝단에 질량 가중 감쇠 영역을 설정하여 안정적인 파고 및 유속 계산이 수행될 수 있게 하였다. 목표 파랑 조건에서 상대 수심이 2 이하를 만족하는 경우 파형경사에 관계없이 파고와 유속을 계산한 결과가 이론값과 높은 정확도를 보였다. 그러나 상대수심과 파형경사의 목표값이 증가하고, 측정 위치가 멀어짐에 따라서 최대 10% 이상의 오차가 발생하였다. 수치해석을 이용하여 정확한 계산이 가능한 파랑 범위를 무차원 변수를 이용하여 제안하였으며, 차후 수치해석을 이용한 수치파동수조 검증기준과 유체-구조물 상호작용 해석분야 연구에 효과적으로 활용될 수 있다.

Application of mesh-free smoothed particle hydrodynamics (SPH) for study of soil behavior

Niroumand, Hamed,Mehrizi, Mohammad Emad Mahmoudi,Saaly, Maryam Techno-Press 2016 Geomechanics & engineering Vol.11 No.1

The finite element method (FEM), discrete element method (DEM), and Discontinuous deformation analysis (DDA) are among the standard numerical techniques applied in computational geo-mechanics. However, in some cases there no possibility for modelling by traditional finite analytical techniques or other mesh-based techniques. The solution presented in the current study as a completely Lagrangian and mesh-free technique is smoothed particle hydrodynamics (SPH). This method was basically applied for simulation of fluid flow by dividing the fluid into several particles. However, several researchers attempted to simulate soil-water interaction, landslides, and failure of soil by SPH method. In fact, this method is able to deal with behavior and interaction of different states of materials (liquid and solid) and multiphase soil models and their large deformations. Soil indicates different behaviors when interacting with water, structure, instrumentations, or different layers. Thus, study into these interactions using the mesh based grids has been facilitated by mesh-less SPH technique in this work. It has been revealed that the fast development, computational sophistication, and emerge of mesh-less particle modeling techniques offer solutions for problems which are not modeled by the traditional mesh-based techniques. Also it has been found that the smoothed particle hydrodynamic provides advanced techniques for simulation of soil materials as compared to the current traditional numerical methods. Besides, findings indicate that the advantages of applying this method are its high power, simplicity of concept, relative simplicity in combination of modern physics, and particularly its potential in study of large deformations and failures.

화학 교반기 디지털 트윈을 위한 시뮬레이션 기법 비교 연구: Eulerian 기반 격자법과 Lagrangian 기반 입자법

김준서(Jun-Seo Kim), 박형준(Hyung-Jun Park) 한국전자통신학회 2025 한국전자통신학회 논문지 Vol.20 No.6

본 연구는 화학 교반기의 시뮬레이션에서 널리 활용되는 두 수치 기법, 유한체적법(FVM, Finite Volume Method)과 완화입자유체동역학(SPH, Smoothed Particle Hydrodynamics)을 동일 조건에서 비교하여 디지털 트윈적용 가능성을 평가하였다. 동일한 형상과 경계 조건에서 수행된 시뮬레이션 결과, 압력장과 속도장 예측치는 두 기법 간 유사한 경향을 보였다. 계산 효율성 측면에서는 GPU 병렬화 기반의 SPH가 자유수면을 포함한 과도 다상유동 해석에서 FVM보다 최대 54배 빠른 계산 속도를 나타냈다. 이러한 결과는 디지털 트윈 구현과 같이 실시간성이 요구되는 응용에서 SPH가 효과적인 대안이 될 수 있음을 시사한다. This study compares two numerical methods widely used for chemical stirrer simulations—the Finite Volume Method (FVM) and Smoothed Particle Hydrodynamics (SPH)—under identical conditions to evaluate their applicability to digital twin development. The predicted pressure and velocity fields showed close agreement between the two methods. In terms of computational efficiency, the GPU-parallelized SPH achieved up to 54 times faster performance in transient multiphase flow simulations involving free surfaces. These findings indicate that SPH can serve as an effective alternative for real-time digital twin applications where computational speed is a key requirement.

Parametric studies on smoothed particle hydrodynamic simulations for accurate estimation of open surface flow force

Lee, Sangmin,Hong, Jung-Wuk The Society of Naval Architects of Korea 2020 International Journal of Naval Architecture and Oc Vol.12 No.-

The optimal parameters for the fluid-structure interaction analysis using the Smoothed Particle Hydrodynamics (SPH) for fluids and finite elements for structures, respectively, are explored, and the effectiveness of the simulations with those parameters is validated by solving several open surface fluid problems. For the optimization of the Equation of State (EOS) and the simulation parameters such as the time step, initial particle spacing, and smoothing length factor, a dam-break problem and deflection of an elastic plate is selected, and the least squares analysis is performed on the simulation results. With the optimal values of the pivotal parameters, the accuracy of the simulation is validated by calculating the exerted force on a moving solid column in the open surface fluid. Overall, the SPH-FEM coupled simulation is very effective to calculate the fluid-structure interaction. However, the relevant parameters should be carefully selected to obtain accurate results.

SPH을 활용한 3차원 비선형 파랑모형 개발

조용준(Cho Yong Jun),김권수(Kim Gweon Soo) 대한토목학회 2008 대한토목학회논문집 B Vol.28 No.5B

Navier-Stokes식, Gaussian 분포형 용출함수를 이용한 내부조파, energy absorbing layer로 삼차원 파랑모형을 새롭게 구성하였다. Navier-Stokes식의 수치적분에는 정교한 수치기법인 SPH(Smoothed Particle Hydrodynamics)가 활용된다. 제안된 파랑모형의 검증은 삼차원 포물형 용기에서의 solshing현상과 Thacker(1981)의 해석해를 토대로 수행되었다. 초기 수면 형상이 Gaussian hump인 경우와 일방향으로 경사진 경우에 대해 수치모의 하였다. 수치모의 결과 수면이 융기되도록 구속한 외부조건이 해제되면서 시작되는 자유진동의 정성적 거동은 비교적 정확히 모의되었으나 시간이 경과될수록 위상차, 침수선이 퇴각하는 등 초기 수면과는 상당히 다른 결과를 보였다. 최종적인 검증은 쐐기모양 해안에서의 비선형 천수, 굴절거동의 수치모의를 토대로 진행되었다. 수치모의 결과 굴절되는 양이 Hamiltonian ray theory가 제공하는 수치보다 전반적으로 작게 나타났다. 이러한 현상은 이상유체와 선형 이론에 기초한 Hamiltonian ray theory에서 간과된 비선형성, 점성으로 인한 양안과 저면에서의 에너지 감쇄, 쇄파 과정에 유동계에 도입되는 에너지 감쇄, 선행파랑에 의한 down-rush와 조우시 발생하는 도수 등에 기인하는 것으로 판단된다. In this study, we newly proposed 3-D nonlinear wave driver utilizing the Navier-Stokes Eq. the numerical integration of which is carried out using SPH (Smoothed Particle Hydrodynamics), an internal wave generation with the source function of Gaussian distribution and an energy absorbing layer. For the verification of new 3-D nonlinear wave driver, we numerically simulate the sloshing problem within a parabolic water basin triggered by a Gaussian bump and uniformly inclined water surface by Thacker (1981). It turns out that the qualitative behavior of sloshing caused by relaxing the external force which makes a free surface convex or uniformly inclined is successfully simulated even though phase error is visible and an inundation height shrinks as numerical simulation more proceeds. For the more severe test, we also simulate the nonlinear shoaling and refraction over uniform beach of wedge shape. It is shown that numerically simulated waves are less refracted than the linear counterpart by Hamiltonian ray theory due to nonlinearity, energy dissipation at the bottom and side walls, energy loss induced by breaking, and the hydraulic jump occurring when breaking waves encounter a down-rush by the preceding wave.

SPH법을 이용한 해안에서의 2차원 비선형파 수치시뮬레이션

김철호(Cheol-Ho Kim),이영길(Young-Gill Lee),정광열(Kwang-Leol Jeong) 대한조선학회 2010 대한조선학회 논문집 Vol.47 No.4

In this paper, wave breakers which occur in two dimensional coasts are simulated using a SPH(Smoothed Particle Hydrodynamics) method which represents the movement of fluidic physical volume with particles. As continuative fluid is approximated to the particles, the simulations are performed using fully Lagrangian method without any grid system. Two-dimensional Navier-Stokes equations and continuity equation are used for the numerical simulations. To generate incident waves, a piston type wavemaker is employed. The accuracy of the wave which is numerically generated by the wavemaker is verified by comparing with analytical results. The computations are carried out with various wave heights and slopes. The wave patterns generated through the numerical simulations are compared with several existing experimental and computational results. Agreement between the experimental data and the computation results is comparatively good. Also, the breaker depth index and the breaker height index from the present calculations are compared with the existing experimental results, and the tendency is very similar.