Incompressibility Enforcement for Multiple-fluid SPH Using Deformation Gradient

To maintain incompressibility in SPH fluid simulations is important for visual plausibility. However, it remains an outstanding challenge to enforce incompressibility in such recent multiple-fluid simulators as the mixture-model SPH framework. To tackle this problem, we propose a novel incompressible SPH solver, where the compressibility of fluid is directly measured by the deformation gradient. By disconnecting the incompressibility of fluid from the conditions of constant density and divergence-free velocity, the new incompressible SPH solver is applicable to both single- and multiple-fluid simulations. The proposed algorithm can be readily integrated into existing incompressible SPH frameworks developed for single-fluid, and is fully parallelizable on GPU. Applied to multiple-fluid simulations, the new incompressible SPH scheme significantly improves the visual effects of the mixture-model simulation, and it also allows exploitation for artistic controlling

Monolith: a monolithic pressure-viscosity-contact solver for strong two-way rigid-rigid rigid-fluid coupling

We propose Monolith, a monolithic pressure-viscosity-contact solver for more accurately, robustly, and efficiently simulating non-trivial two-way interactions of rigid bodies with inviscid, viscous, or non-Newtonian liquids. Our solver simultaneously handles incompressibility and (optionally) implicit viscosity integration for liquids, contact resolution for rigid bodies, and mutual interactions between liquids and rigid bodies by carefully formulating these as a single unified minimization problem. This monolithic approach reduces or eliminates an array of problematic artifacts, including liquid volume loss, solid interpenetrations, simulation instabilities, artificial "melting" of viscous liquid, and incorrect slip at liquid-solid interfaces. In the absence of solid-solid friction, our minimization problem is a Quadratic Program (QP) with a symmetric positive definite (SPD) matrix and can be treated with a single Linear Complementarity Problem (LCP) solve. When friction is present, we decouple the unified minimization problem into two subproblems so that it can be effectively handled via staggered projections with alternating LCP solves. We also propose a complementary approach for non-Newtonian fluids which can be seamlessly integrated and addressed during the staggered projections. We demonstrate the critical importance of a contact-aware, unified treatment of fluid-solid coupling and the effectiveness of our proposed Monolith solver in a wide range of practical scenarios.This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (Grant RGPIN-04360-2014)

FrictionalMonolith: A Monolithic Optimization-based Approach for Granular Flow with Contact-Aware Rigid-Body Coupling

We propose FrictionalMonolith, a monolithic pressure-friction-contact solver for more accurately, robustly, and efficiently simulating two-way interactions of rigid bodies with continuum granular materials or inviscid liquids. By carefully formulating the components of such systems within a single unified minimization problem, our solver can simultaneously handle unilateral incompressibility and implicit integration of friction for the interior of the continuum, frictional contact resolution among the rigid bodies, and mutual force exchanges between the continuum and rigid bodies. Our monolithic approach eliminates various problematic artifacts in existing weakly coupled approaches, including loss of volume in the continuum material, artificial drift and slip of the continuum at solid boundaries, interpenetrations of rigid bodies, and simulation instabilities. To efficiently handle this challenging monolithic minimization problem, we present a customized solver for the resulting quadratically constrained quadratic program that combines elements of staggered projections, augmented Lagrangian methods, inexact projected Newton, and active-set methods. We demonstrate the critical importance of a unified treatment and the effectiveness of our proposed solver in a range of practical scenarios.Natural Sciences and Engineering Research Council of Canada, Grant RGPIN-2021-02524

Lagrangian Neural Style Transfer for Fluids

Artistically controlling the shape, motion and appearance of fluid simulations pose major challenges in visual effects production. In this paper, we present a neural style transfer approach from images to 3D fluids formulated in a Lagrangian viewpoint. Using particles for style transfer has unique benefits compared to grid-based techniques. Attributes are stored on the particles and hence are trivially transported by the particle motion. This intrinsically ensures temporal consistency of the optimized stylized structure and notably improves the resulting quality. Simultaneously, the expensive, recursive alignment of stylization velocity fields of grid approaches is unnecessary, reducing the computation time to less than an hour and rendering neural flow stylization practical in production settings. Moreover, the Lagrangian representation improves artistic control as it allows for multi-fluid stylization and consistent color transfer from images, and the generality of the method enables stylization of smoke and liquids likewise.Comment: ACM Transaction on Graphics (SIGGRAPH 2020), additional materials: http://www.byungsoo.me/project/lnst/index.htm

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

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

Numerical modelling of aeration and hydroelasticity in slamming loads and responses of marine structures

Slamming plays a significant role in the ultimate and fatigue limit state design of marine structures. Despite a relatively long history of investigations, there are still gaps in knowledge and open questions in understanding the slamming phenomenon and the approach it needs in the design phase due to its complex nature and limitations of research tools. The so-called hydroelasticity effect, which is the coupled interaction of structural responses with the body of fluid on both global and local scales, is one of the main complex aspects of slamming. Variation of fluid compressibility due to the mixing of air bubbles with the fluid, called aeration, alters the slamming loads and could also affect the hydroelastic coupling. The possible interaction of the two mentioned processes affecting the slamming physics and how to approach it in the analysis of slamming is still not well understood and is the focus of investigation in this thesis. The research methodology of this work is based on studying the details of pressure and the flow field around the slamming area and the evolution of slamming force and structural response employing numerical modeling. A numerical tool for this purpose was developed and validated against benchmark experimental data available in the literature. In the study of hydroelasticity, local shell deformations, as well as global deformations of the structure, were studied. The interlinked effects of local hydroelasticity and aeration were investigated by performing two sets of numerical simulation campaigns on the water entry of elastic flat plates and cylindrical shell sections. Both studies revealed that local flexibility has a noticeable reducing effect on peak values of slamming pressure and forces. This reduction effect of flexibility disappears for plates in the presence of aeration, which shows a significant indication of interdependence in the roles of aeration and hydroelasticity in slamming dynamics. In plate entry and cylinder entry simulations, aeration shows a damping effect on the response strain oscillations, strengthening with increasing aeration. Both water entry studies present new insights with valuable details on slamming load's major characteristics and local structural response of plates and cylinders. Noticeable differences between plate and cylinder entries were observed; for instance, aeration causes a substantial extension of slamming load duration in plate entries, but no meaningful change is observed in cylinder entries. Extensive parameter studies led to new functional relations to determine peak slamming pressure/force in pure and aerated water entries in terms of relatively simple power-law approximations, which have been derived for plates and cylinders. The study shows that hydroelasticity may not be an essential issue for locally stiff structures, but considering air entrainment and entrapment processes is important to determine local loading characteristics. This thesis also presents a novel simplified model of wave slamming on an SDOF cylindrical structure. The model could reproduce the experimental slamming force and pressure time series of the large-scale wave slamming on a vertical monopile with a reasonable accuracy level. The validation study shows that the introduced simplified model could present valuable data on the physics of the interaction of a flexible cylindrical structure with impacting body of water. The simplified model was applied in a parameter study to investigate the effect of global structural vibration characteristics and aeration on wave slamming loads and structural response characteristics. The parameter study indicates that processes related to compressibility, such as aeration and air entrapment, are far more important than the structure's global flexibility. Since wave impact events in natural conditions may incorporate variable aeration levels in the water, which is shown to alter the structural response and duration of vibration, in both deterministic and stochastic studies of wave impact dynamics, the compressibility parameter is important and should be considered in the analysis

SURFSUP: Learning Fluid Simulation for Novel Surfaces

Modeling the mechanics of fluid in complex scenes is vital to applications in design, graphics, and robotics. Learning-based methods provide fast and differentiable fluid simulators, however most prior work is unable to accurately model how fluids interact with genuinely novel surfaces not seen during training. We introduce SURFSUP, a framework that represents objects implicitly using signed distance functions (SDFs), rather than an explicit representation of meshes or particles. This continuous representation of geometry enables more accurate simulation of fluid-object interactions over long time periods while simultaneously making computation more efficient. Moreover, SURFSUP trained on simple shape primitives generalizes considerably out-of-distribution, even to complex real-world scenes and objects. Finally, we show we can invert our model to design simple objects to manipulate fluid flow.Comment: Website: https://surfsup.cs.columbia.edu

Implementation and Study of Optimal Parameters by Taichi of Particle-Based Simulation with Stable Fluid-Rigid Interaction

The author implements of the interlinked SPH method with the Taichi programming language and investigates of optimal parameters for simulations considering fluid-rigid-body interactions. The author implements of the interlinked SPH method proposed by Gissler et al. with the Taichi data-oriented programming language proposed by Hu et al. for particle-based simulations that simultaneously handle fluid and rigid interactions, to stabilize and speed up the simulation. Taichi is a programming language that uses hierarchical data structures to accelerate operations by utilizing the sparsity of particle data. The optimal values for the parameters of the hierarchical data structure differ from scene to scene. Therefore, the author investigates the optimal parameters for hierarchical data structures by measuring the processing speed of multiple scenes for each number of layers