Moving particle simulation with solid-solid contact

Problems of fluid-structure interaction with free surface flow and multi-body interactions are highly nonlinear and complex phenomena, which is challenging for computational modeling and simulation. In the presence of contact or collision between solids, numerical modeling to detect collision and prevent penetration between bodies is required. The objective of this work is to study a numerical model for solid-solid contact and/or collision, based on contact mechanics theories, to reproduce the macroscopic properties of the multi-body interactions in Moving Particle Simulation (MPS) method. MPS is a fully Lagrangian meshfree particle-based approach that is suitable for the modeling complex geometries with large displacements and deformation, including free surface flow with fragmentation and merging and interaction of fluid with multi-bodies. Analytical results are used to perform the calibration of the numerical friction coefficient. The model is applied to a case of free solid transport in free surface flow, modeled as a 3D experimental dam breaking event, in which free solids interact each other and fixed walls. The numerical results from MPS are compared with numerical and experimental results

An ODE control system of a rigid body on an ocean wave for a surfer simulation in the SPH method

In this work we use a smoothed particle hydrodynamics (SPH) method coupledwith a rigid body simulation to simulate a surfing board on top of an ocean wave. Externalforces are applied to the board to represent a surfer trying to control a surfing board. Anordinary differential equation (ODE) control is used to manipulate the external forces basedon a position, velocity, and an inclination angle of the surfing board. The control systemsuccessfully helps the surfing board to move to and maintain its desired position

Development of GPU-based SPH Framework for Hydrodynamic Interactions With Non-spherical Solid Debris

일본의 후쿠시마 사고 이후 원자로 중대 사고에 대한 연구의 필요성과 대처 능력 확보에 대한 중요성이 점점 증가하고 있다. 사고 시 발생할 수 있는 노심 용융물 거동에 대한 평가는 용융물-콘크리트 상호작용(MCCI, Molten Core Concrete Interaction)과 증기 폭발로부터의 원자로 노심 냉각성 및 건전성에 따른 재임계 측면에서 매우 중요하다. 특히 OPR 1000의 경우, 사전 충수 조건(Wet cavity condition)을 기본적인 원자로 외벽 냉각 대응 전략으로 채택함으로써 핵연료-냉각재 상호작용(FCI, Fuel Coolant Interaction) 반응이 필연적으로 발생하는 것으로 알려져 있다. [Jin, 2014] FCI 현상은 임의 형태의 핵연료 고체 파편물과 냉각재의 상호작용뿐만 아니라, 냉각재 비등 현상 등도 포함하는 다유체, 다상 현상으로 그 현상이 매우 복잡하다. 이 과정에서 원자로 건물 하부에 고체 파편물이 퇴적되어 잔해 층이 형성되고, 그 냉각성에 따라 사고의 다음 진행 상황에 영향을 줄 수 있다. 이러한 비구형 고체 파편물 거동에 대한 이해를 위해 강체 개념을 적용한 고체 해석 체계는 좋은 접근법이 될 수 있다. 따라서 본 연구에서는 유체와 고체 간 수력학적 상호작용 해석을 위해 입자유체동역학(SPH, Smoothed Particle Hydrodynamics) 기법과 강체역학(RBD, Rigid Body Dynamics) 기법을 연계하여 라그랑지안 해석 체계를 구축하였다. 완화입자유체동역학 기법은 해석 유체를 유한개의 입자로 표현함으로써 유동을 해석하는 라그랑지안 해석 기법 중 하나이다. 개별 입자들의 움직임으로 유동을 해석하므로 비선형의 대류항에 대한 계산이 필요 없으며, 입자가 추가되거나 사라지지 않는 한 해석 계의 전체 질량은 자동으로 보존된다. 이러한 라그랑지안 기법의 특성으로 SPH 방법은 자유 표면 유동, 다유체 유동, 다상 유동, 형태 변화가 큰 유동 등에 대해 해석 장점을 갖는다. 본 연구에서는 SPH 기법을 적용한 in-house SOPHIA 코드를 사용하여 비압축 다상 유동 해석을 수행하였으며, 벤치마크 데이터와의 비교에서 좋은 검증 해석 결과를 보였다. 강체역학은 외력에 의해 형태가 변하지 않는 강체의 개념을 이용하여 고체의 병진 운동과 회전 운동을 해석하는 연구 분야이다. 본 연구에서는 이산요소법(DEM, Discrete Element Method) 분야에서 오랜 시간 동안 널리 사용되고 검증되었던 Hertz-Mindlin 충돌 모델을 적용하여 강체 간 충돌 해석을 구현하였다. 강체는 유한개의 입자들로 표현할 수 있으며, 강체 간 충돌은 각 강체를 구성하고 있는 입자쌍의 작은 중첩을 기반으로 계산된다. 본 연구에서는 입자기반의 강체역학 해석 코드를 이용하여 단일 강체 및 다중 강체 충돌에 대해 검증 해석을 수행하였으며, 해석해 및 벤치마크 데이터 결과와 잘 일치함을 확인하였다. 원자력 분야에서 발생할 수 있는 비구형 고체와 유체간 상호작용 해석을 위해 앞서 설명한 SPH 기법과 강체역학 연계 해석 코드를 개발하였다. 본 연구에서 적용한 완전 해상 방식(Fully resolved approach)은 유체-고체의 상이 분리되어 있고, 제 1 원리를 만족하므로 고체의 형상에 따른 상관식과 표면 적분이 필요하지 않다는 장점이 있다. 또한 고체 경계면에서의 정확한 압력 계산을 위해 유체 입자 정보를 기반으로 노이만 압력 경계 조건을 적용하였다. 본 연구에서는 이러한 해상 방식의 유체-강체 연계 해석 코드를 이용하여 비구형 고체와 유체의 수력학적 상호작용에 대한 검증 해석을 수행하였으며, 선행된 실험과의 비교에서 좋은 결과를 보였다. 유동 해석을 위해 본 연구에 적용한 SPH 방법에서는 수식들이 매우 선형적이고 외연적(Explicit)으로 계산을 수행하기 때문에 각 입자에 대한 계산이 독립적으로 수행되어도 문제가 없다. 따라서 SPH 방법은 계산 병렬화에 최적화된 방법으로 잘 알려져 있으며, 대규모 고해상도 해석을 위해 이는 필수적이다. 또한 입자 기반의 강체 계산을 위해서는 효율적인 계산 알고리즘이 필요하다. 따라서 본 연구에서는 대규모 계산과 높은 연산 효율성을 위해 그래픽처리장치(GPU, Graphic Processing Unit)를 이용하여 계산 병렬화를 수행하였으며, 이를 이용한 다중 고체와 유체의 상호작용 해석에서 좋은 계산 성능을 확인하였다. 본 연구에서 수행한 비구형 고체와 유체의 수력학적 상호작용을 위한 GPU 기반의 SPH 해석 코드 개발 연구를 통해 원자로 중대사고 시 발생할 수 있는 냉각재와 핵연료 고체 파편물의 수력학적 상호작용 뿐만 아니라, 고체 파편물 간 역학적 상호작용에 대해 효율적인 해석 체계를 개발하였다. 이를 통해 습식 공동(wet cavity)에서 발생하는 핵연료 고체 파편물의 퇴적 작용, 쓰나미 사고로 인한 해안 구조물의 수력학적 상호작용, 그리고 침수 사고 시 원자로 건물 내 부유물의 거동 등 원자력 분야에서 발생할 수 있는 다양한 고체-유체의 수력학적 상호작용에 대한 해석적 연구에 적용하고 기여할 수 있을 것으로 기대한다.Since the Fukushima accident, the necessity for researches on severe accidents and the importance of securing the ability to cope with the accidents have been increasing. The evaluation of the molten core behavior that may occur during the accident is very important in terms of re-criticality according to the coolability and integrity of the reactor core from the MCCI (Molten Core Concrete Interaction) and steam explosion. In the case of OPR 1000, especially, FCI (Fuel Coolant Interaction) is known to occur unconditionally because the wet cavity condition has been adopted as a basic strategy for ex-vessel cooling. [Jin, 2014] FCI is a highly complicated phenomenon, which includes multi-fluid, multi-phase interaction between the arbitrary shape of solid debris and coolant as well as coolant boiling. In this process, the debris bed is formed at the bottom of the containment, and its coolability influences the next phase of the accident. For the understanding on the solid debris behavior, a solid system with a rigid body can be a good approach for the non-spherical solid debris analysis. Therefore, in this study, Smoothed Particle Hydrodynamics (SPH) method and Rigid Body Dynamics (RBD) are coupled in a fully Lagrangian manner for the hydrodynamic interactions between fluid and solid. Smoothed Particle Hydrodynamics (SPH) is one of the Lagrangian-based analysis methods which represents the fluid flow as a finite number of particles. Since the flow is analyzed by the motion of individual particles, there is no need to calculate the nonlinear convective term, and the total mass of the system is automatically conserved as long as particles are not added or removed. Through these Lagrangian nature, it is well known that the SPH method is effective for the free surface flow, multi-fluid and multi-phase flow, and highly deformable flow. In this study, the incompressible multi-phase flow analysis has been performed using the in-house SPH code, SOPHIA code, and V&V simulation results showed good agreement with the benchmark data. Rigid Body Dynamics (RBD) is a research field that analyses the translation and rotation of a solid body by using the concept that a rigid body doesn’t change its shape by external forces. In this study, the collision calculation between rigid bodies is implemented by applying the Hertz-Mindlin contact force model commonly used and verified for a long time in the Discrete Element Method (DEM) field. A rigid body can be expressed as a group of finite particles, and the contact forces between solid bodies are calculated based on the small overlap of the particle pairs. Using the particle-based RBD analysis code implemented in this study, V&V simulations on single- and multi- rigid body collisions have been performed and showed good agreement with the analytical solution and the benchmark data. To analyze the hydrodynamic interactions between non-spherical solids and fluids that can occur in the nuclear field, the integrated code has been developed by coupling RBD with SPH code. Since a fully resolved approach adopted in this study as a phase coupling method satisfies the 1st principle and the fluid-solid phase is entirely separated from each other, there is no need for the surface integral and empirical correlations depending on the solid geometry. In addition, the Neumann pressure boundary condition is implemented for accurate pressure estimation at the solid interface using the fluid particle properties. By applying the resolved SPH-RBD coupled code, V&V simulations were carried out on the hydrodynamic interactions of non-spherical solid-fluid and showed good agreement with the experimental data. In the SPH method, since the numerical expression are highly linear and the calculations are performed explicitly, there is no problem even if the calculations for each particle are performed independently. Therefore, the SPH is well known as an optimized method for parallelization, and it is essential for large scale high-resolution simulations. In addition, an efficient computational algorithm is required for particle-based rigid body calculation. In this study, therefore, the parallelization was performed using a Graphical Processing Unit (GPU) for large-scale calculations and high computational efficiency, and it showed a good performance in analyzing the interactions of a large number of solids and fluids particles. Through the researches on the development of a GPU-based SPH framework for the hydrodynamic interaction of non-spherical solids and fluids in this study, an efficient analysis system has been developed for not only the hydrodynamic interaction of solid corium debris with coolant but also the mechanical interaction between solid debris which can occur at the severe accidents in the nuclear reactor. By using this, it is expected that the integrated code will contribute to analytical researches on various accident scenarios that may occur in the nuclear field such as solid fuel debris sedimentation in the wet cavity, hydrodynamic interactions with coastal structures caused by the Tsunami, and the behavior of floating objects in the reactor building at the flooding accident, etc.Chapter 1 Introduction 1 1.1 Background and Motivation 1 1.2 Previous Studies 3 1.2.1 Numerical Studies on FCI Premixing Jet Breakup 3 1.2.2 Numerical Studies on Fluid-Solid Coupling with RBD 4 1.3 Objectives and Scope 5 Chapter 2 Smoothed Particle Hydrodynamics (SPH) 9 2.1 SPH Overview 9 2.1.1 Basic Concept of SPH 9 2.1.2 SPH Particle Approximation 10 2.1.3 SPH Kernel Function 12 2.1.4 SPH Governing Equations 13 2.2 SPH Multi-phase Models 16 2.2.1 Normalized Density Approach 16 2.2.2 Treatments for Multi-phase Flow 17 2.2.3 Surface Tension Force Model 18 2.3 SPH Code Implementation 20 2.3.1 Nearest Neighbor Particle Search (NNPS) 20 2.3.2 Algorithm of SPH Code 21 2.3.3 Time Integration 21 2.3.4 GPU Parallelization 22 Chapter 3 Rigid Body Dynamics (RBD) 30 3.1 RBD Overview 30 3.2 Collision Models of Rigid Body 31 3.2.1 Monaghan Boundary Force (MBF) Model 31 3.2.2 Ideal Plastic Collision Model 33 3.2.3 Impulse-based Boundary Force (IBF) Model 35 3.2.4 Penalty-based Contact Model 37 3.2.5 Determination of Collision Model 40 3.3 Algorithm of RBD 41 3.3.1 Calculation of Rigid Body Information 41 3.3.2 Contact Detection 42 3.3.3 Contact Normal Calculation 42 3.3.4 Contact Force Calculation 45 3.3.5 Summation of Rigid Body Particles 46 3.3.6 Time Integration 47 3.4 GPU Parallelization 48 3.4.1 Algorithm 1: Atomic Operation 49 3.4.2 Algorithm 2: Sorting 50 3.5 Code V&V Simulations 51 3.5.1 Conservation of Momentum & Angular Momentum 51 3.5.2 Conservation of Kinetic Energy in Elastic Collision 52 3.5.3 Bouncing Block 53 3.5.4 Sliding Block on a Slope 55 3.5.5 Collapse of Stacked Multi-body 57 Chapter 4 Two-way Coupling of SPH-RBD 75 4.1 Resolved Approach 75 4.2 Governing Equations 75 4.2.1 Solid Phase 75 4.2.2 Fluid Phase 78 4.3 Algorithm of SPH-RBD Code 78 4.4 Code V&V Simulations 81 4.4.1 Karman Vortex Problem 81 4.4.2 Water Entry 84 4.4.3 Sinking & Rotating Body 85 4.4.4 Floating & Falling Body 85 4.4.5 Collapse of Stacked Multi-body with Fluid 87 4.4.6 Code Application to Non-spherical Debris Sedimentation 89 Chapter 5 Conclusion 110 5.1 Summary 110 5.2 Recommendations 112 Nomenclature 114 Bibliography 117 국문 초록 127박

On a Coupled SPH-Rigid Body Method for the Surfing Problem

13301甲第4816号博士（理学）金沢大学博士論文本文Full 以下に掲載予定：The Science Reports of Kanazawa University 62 2018. The Institute of Science and Engineering, Kanazawa University. 共著者：Reza Rendian Septiawa

Example Based Caricature Synthesis

The likeness of a caricature to the original face image is an essential and often overlooked part of caricature production. In this paper we present an example based caricature synthesis technique, consisting of shape exaggeration, relationship exaggeration, and optimization for likeness. Rather than relying on a large training set of caricature face pairs, our shape exaggeration step is based on only one or a small number of examples of facial features. The relationship exaggeration step introduces two definitions which facilitate global facial feature synthesis. The first is the T-Shape rule, which describes the relative relationship between the facial elements in an intuitive manner. The second is the so called proportions, which characterizes the facial features in a proportion form. Finally we introduce a similarity metric as the likeness metric based on the Modified Hausdorff Distance (MHD) which allows us to optimize the configuration of facial elements, maximizing likeness while satisfying a number of constraints. The effectiveness of our algorithm is demonstrated with experimental results

Partikelbasierte Strömungssimulation im Anwendungsbereich granularer Materialien und Fluide

Computersimulationen von Strömungen spielen als hilfreiches Werkzeug bei der Lösung rheologischer Fragestellungen eine immer größer werdende Rolle. Ziel ist die Ausarbeitung des Nutzens und der Grenzen von partikelbasierter Strömungssimulation anhand zweier Problemstellungen aus unterschiedlichen Fachbereichen. Zum Einen wird das dynamische Fließverhalten von granularem Material innerhalb einer Dosierwaage mit archimedischer Schraube zur Optimierung des Systems simuliert. Die experimentell bestimmte Durchflussrate im realen Aufbau wird bei angepassten Simulationsparametern rechnerisch modelliert. Zum Zweiten wird für eine spezielle Tumorbehandlung das Verhalten von in Blutgefäßen mitschwimmenden therapeutisch strahlenwirksamen Mikrosphären analysiert. Die entwickelte Methode basiert auf eindimensionalen Volumenstromberechnungen, welche mittels der Ergebnisse einer dreidimensionalen Strömungsanalyse adaptiert werden. Die nötige Blutgefäßgeometrie wird mit angiografischen CT-Aufnahmen und einem zusätzlich implementierten Modell zur Generierung von Blutgefäßen unterhalb der Bildauflösungsgrenze definiert. Die Ergebnisse werden mit experimentellen Daten verglichen. Mittels einer weiteren Analyse wird die Notwendigkeit zur Verbesserung des bildgebenden Systems der Blutgefäße belegt und zu erzielende Bedingungen hierfür ermittelt. Die jeweilige Strömungssimulation hat sich als nützliches Werkzeug bei der Systemoptimierung erwiesen, welche mit rein experimentellen Methoden oder theoretischen Modellen nicht, oder nur unter deutlich größerem Aufwand, erreicht werden kann. Abschließend werden die beiden verwendeten Ansätze vergleichend diskutiert. Die vielseitige Anwendbarkeit von partikelbasierter Strömungssimulation bei physikalisch unterschiedlichen Problemstellungen wird aufgezeigt