Multiphase SPH simulation for interactive fluids and solids

This work extends existing multiphase-fluid SPH frameworks to cover solid phases, including deformable bodies and granular materials. In our extended multiphase SPH framework, the distribution and shapes of all phases, both fluids and solids, are uniformly represented by their volume fraction functions. The dynamics of the multiphase system is governed by conservation of mass and momentum within different phases. The behavior of individual phases and the interactions between them are represented by corresponding constitutive laws, which are functions of the volume fraction fields and the velocity fields. Our generalized multiphase SPH framework does not require separate equations for specific phases or tedious interface tracking. As the distribution, shape and motion of each phase is represented and resolved in the same way, the proposed approach is robust, efficient and easy to implement. Various simulation results are presented to demonstrate the capabilities of our new multiphase SPH framework, including deformable bodies, granular materials, interaction between multiple fluids and deformable solids, flow in porous media, and dissolution of deformable solids

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

Simulation of Fluid Structure Inte actions by using High Order FEM and SPH

The investigation of fluid structure interactions is crucial in many areas of science and technology. This study presents a robust methodology for studying fluid structure interactions, which is characterized by high convergence behavior and is insensitive to distortion and stiffening effects. Therefore, the Smoothed Particle Hydodynamicy is coupled with the high order FEM. After various coupling methods for linear and quadratic elements from the literature have been described, a variant with higher-value approach functions is implemented. The two methods can be meshed independend without loss of accuracy. After successful validation, it is shown that only a few finite elements are necessary to obtain a convergent solution. The presented method is promising especially for thin-walled structures where significantly fewer degrees of freedom are required than for linear elements

A Unified Particle System Framework for Multi-Phase, Multi-Material Visual Simulations

We introduce a unified particle framework which integrates the phase-field method with multi-material simulation to allow modeling of both liquids and solids, as well as phase transitions between them. A simple elasto-plastic model is used to capture the behavior of various kinds of solids, including deformable bodies, granular materials, and cohesive soils. States of matter or phases, particularly liquids and solids, are modeled using the non-conservative Allen-Cahn equation. In contrast, materials---made of different substances---are advected by the conservative Cahn-Hilliard equation. The distributions of phases and materials are represented by a phase variable and a concentration variable, respectively, allowing us to represent commonly observed fluid-solid interactions. Our multi-phase, multi-material system is governed by a unified Helmholtz free energy density. This framework provides the first method in computer graphics capable of modeling a continuous interface between phases. It is versatile and can be readily used in many scenarios that are challenging to simulate. Examples are provided to demonstrate the capabilities and effectiveness of this approach

A moving least square reproducing kernel particle method for unified multiphase continuum simulation

In physically based-based animation, pure particle methods are popular due to their simple data structure, easy implementation, and convenient parallelization. As a pure particle-based method and using Galerkin discretization, the Moving Least Square Reproducing Kernel Method (MLSRK) was developed in engineering computation as a general numerical tool for solving PDEs. The basic idea of Moving Least Square (MLS) has also been used in computer graphics to estimate deformation gradient for deformable solids. Based on these previous studies, we propose a multiphase MLSRK framework that animates complex and coupled fluids and solids in a unified manner. Specifically, we use the Cauchy momentum equation and phase field model to uniformly capture the momentum balance and phase evolution/interaction in a multiphase system, and systematically formulate the MLSRK discretization to support general multiphase constitutive models. A series of animation examples are presented to demonstrate the performance of our new multiphase MLSRK framework, including hyperelastic, elastoplastic, viscous, fracturing and multiphase coupling behaviours etc

Multi-level adaptive particle refinement method with large refinement scale ratio and new free-surface detection algorithm for complex fluid-structure interaction problems

Fluid-Structure Interaction (FSI) is a crucial problem in ocean engineering. The smoothed particle hydrodynamics (SPH) method has been employed recently for FSI problems in light of its Lagrangian nature and its advantage in handling multi-physics problems. The efficiency of SPH can be greatly improved with the Adaptive Particle Refinement (APR) method, which refines particles in the regions of interest while deploying coarse particles in the left areas. In this study, the APR method is further improved by developing several new algorithms. Firstly, a new particle refinement strategy with the refinement scale ratio of 4 is employed for multi-level resolutions, and this dramatically decreases the computational costs compared to the standard APR method. Secondly, the regularized transition sub-zone is deployed to render an isotropic particle distribution, which makes the solutions between the refinement zone and the non-refinement zone smoother and consequently results in a more accurate prediction. Thirdly, for complex FSI problems with free surface, a new free-surface detection method based on the Voronoi diagram is proposed, and the performance is validated in comparison to the conventional method. The improved APR method is then applied to a set of challenging FSI cases. Numerical simulations demonstrate that the results from the refinement with scale ratio 4 are consistent with other studies and experimental data, and also agree well with those employing the refinement scale ratio 2. A significant reduction in the computational time is observed for all the considered cases. Overall, the improved APR method with a large refinement scale ratio and the new free-surface detection strategy shows great potential in simulating complex FSI problems efficiently and accurately.Comment: 47 pages, 26 figures, accepted to be published by Journal of Computational Physic

Fluid Simulation by the Smoothed Particle Hydrodynamics Method: A Survey.

This paper presents a survey of Smoothed Particle Hydrodynamics (SPH) and its use in computational fluid dynamics. As a truly mesh-free particle method based upon the Lagrangian formulation, SPH has been applied to a variety of different areas in science, computer graphics and engineering. It has been established as a popular technique for fluid based simulations, and has been extended to successfully simulate various phenomena such as multi-phase flows, rigid and elastic solids, and fluid features such as air bubbles and foam. Various aspects of the method will be discussed: Similarities, advantages and disadvantages in comparison to Eulerian methods; Fundamentals of the SPH method; The use of SPH in fluid simulation; The current trends in SPH. The paper ends with some concluding remarks about the use of SPH in fluid simulations, including some of the more apparent problems, and a discussion on prospects for future work