A Divergence‐free Mixture Model for Multiphase Fluids

We present a novel divergence free mixture model for multiphase flows and the related fluid-solid coupling. The new mixture model is built upon a volume-weighted mixture velocity so that the divergence free condition is satisfied for miscible and immiscible multiphase fluids. The proposed mixture velocity can be solved efficiently by adapted single phase incompressible solvers, allowing for larger time steps and smaller volume deviations. Besides, the drift velocity formulation is corrected to ensure mass conservation during the simulation. The new approach increases the accuracy of multiphase fluid simulation by several orders. The capability of the new divergence-free mixture model is demonstrated by simulating different multiphase flow phenomena including mixing and unmixing of multiple fluids, fluid-solid coupling involving deformable solids and granular materials

MPM based simulation for various solid deformation

Solid materials are responsible for many interesting phenomena. There are various types of them such as deformable objects and granular materials. In this paper, we present an MPM based framework to simulate the wide range of solid materials. In this framework, solid mechanics is based on the elastoplastic model, where we use von Mises criterion for deformable objects, and the Drucker-Prager model with non-associated plastic flow rules for granular materials. As a result, we can simulate different kinds of deformation of deformable objects and sloping failure for granular materials

Implicit smoothed particle hydrodynamics model for simulating incompressible fluid-elastic coupling

Fluid simulation has been one of the most critical topics in computer graphics for its capacity to produce visually realistic effects. The intricacy of fluid simulation manifests most with interacting dynamic elements. The coupling for such scenarios has always been challenging to manage due to the numerical instability arising from the coupling boundary between different elements. Therefore, we propose an implicit smoothed particle hydrodynamics fluid-elastic coupling approach to reduce the instability issue for fluid-fluid, fluid-elastic, and elastic-elastic coupling circumstances. By deriving the relationship between the universal pressure field with the incompressible attribute of the fluid, we apply the number density scheme to solve the pressure Poisson equation for both fluid and elastic material to avoid the density error for multi-material coupling and conserve the non-penetration condition for elastic objects interacting with fluid particles. Experiments show that our method can effectively handle the multiphase fluids simulation with elastic objects under various physical properties

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

파티클 시뮬레이션을 이용한 물리 기반 비강체 정합 기술

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2013. 8. 신영길.Recent advances in computing hardware have enabled the application of physically based simulation techniques to various research fields for improved accuracy. In this paper, we present a novel physically based non-rigid registration method using smoothed particle hydrodynamics (SPH) for hepatic metastasis volume-preserving registration between follow-up liver CT images. Our method models the liver and hepatic metastasis as a set of particles carrying their own physical properties. Based on the fact that the hepatic metastasis is stiffer than other normal cells in the liver parenchyma, the candidate regions of hepatic metastasis are modeled with particles of higher stiffness compared to the liver parenchyma. Particles placed in the liver and candidate regions of hepatic metastasis in the source image are transformed along a gradient vector flow (GVF)-based force field calculated in the target image. In this transformation, the particles are physically interacted and deformed by a novel deformable particle method which is proposed to preserve the hepatic metastasis to the best. In experimental results using 10 clinical datasets, our method matches the liver effectively between follow-up CT images as well as preserves the volume of hepatic metastasis almost completely, enabling the accurate assessment of the volume change of the hepatic metastasis. These results demonstrated a potential of the proposed method that it can deliver a substantial aid in measuring the size change of index lesion (i.e., hepatic metastasis) after the chemotheraphy of metastasis patients in radiation oncology.최근 컴퓨팅 하드웨어의 발달은 정확도 향상을 위해 물리 기반의 시뮬레이션 기술을 다양한 연구 분야에 적용할 수 있게 하였다. 본 논문에서는 입자를 이용하여 시뮬레이션하는 방법 중 하나인 입자 보간 방식의 유체역학(smoothed particle hydrodynamics) 기술을 이용하여, 후속 컴퓨터 단층촬영 영상(computed tomography) 사이에 간전이(hepatic metastasis) 체적을 보전하는 물리 기반의 비정형체 정합 기술을 제안한다. 제안 방법은 간과 간전이를 물리적 속성을 동반하는 일련의 입자로 표현하며, 간전이가 정상 간에 비해 강한 탄성을 보인다는 사실에 기반하여 간전이로 짐작되는 부위를 상대적으로 강한 탄성을 갖는 입자로 표현하였다. 초기에 간과 간전이 후보 영역을 나타내는 입자들은 입력 영상의 해당 영역에 위치되며, 정합하고자 하는 대상 영상으로 부터 경사도 벡터 흐름(gradient vector flow) 방법으로 계산된 힘의 장을 따라 이동된다. 이 때, 각 입자는 간전이의 체적을 최대한 보존하기 위해 제안된 변형 가능 입자 방식에 따라 서로 물리적으로 상호작용하며 변형된다. 10명의 환자 데이터를 이용한 실험 결과에 따르면, 후속 컴퓨터 단층촬영(CT) 영상 간의 정합 과정에서 간의 모양을 효과적으로 일치시킬 뿐만 아니라 간전이의 체적을 거의 완벽하게 보존하여 간전이의 체적 변화를 정확하게 진단할 수 있게 하였다. 이 결과는 간전이 환자가 화학 요법을 시행 한 후 암의 진행 상태를 판단하기 위해 간전이의 크기 변화를 측정하는데 도움을 줄 수 있는 방법임을 시사한다.I. Introduction 1.1 Motivation 1 1.2 Dissertation Goals 3 1.3 Main Contribution 4 1.4 Organization of the Dissertation 5 II. Background 2.1 Medical Image Registration 6 2.1.1 Transformation Models 8 2.1.2 Similarity Metrics 18 2.1.3 Optimization 23 2.1.4 Physically Based Non-Rigid Registration 25 2.2 Smoothed Particle Hydrodynamics 29 2.2.1 Formulation of SPH 30 2.2.2 Kernels 33 2.2.3 Applications 35 III. Volume-Preserving Deformation of Particles 3.1 SPH for Deformable Objects 40 3.2 Volume-Preserving Deformable Particle 44 IV. Non-Rigid Registration with the Deformable Particles 4.1 Automatic Detection of Liver and Candidate Regions of Metastasis 50 4.2 Placement of Initial Particles in Source Image 53 4.3 Generation of GVF-based Force Field in Target Image 55 4.4 Non-Rigid Registration with Particles 58 4.5 Computation of Deformation Field 60 V. Implementation 5.1 Workflow 62 5.2 Neighbor Search 65 5.3 Time Integrator and Time Step 67 5.4 Terminating Condition 69 VI. Results 6.1 Phantom Study 71 6.2 General Observations based on Visual Assessment 73 6.3 Evaluation of Registration Performance 74 6.4 Evaluation of Metastasis Detection Accuracy 77 6.5 Evaluation of Volume Preservation 79 6.6 Parameter Study 80 VII. Conclusion 86 Bibliography 89Docto

Solid deformation by material point method

Solid materials are responsible for many interesting phenomena. There are various types of them, such as deformable objects and granular materials. In this paper, we present an MPM based framework to simulate the wide range of solid materials. In this framework, solid mechanics is based on the elastoplastic model following small deformation theory. We use von Mises criterion for deformable objects, and the Drucker–Prager model with nonassociated plastic flow rules for granular materials. As a result, we can simulate different kinds of deformation of deformable objects and sloping failure for granular materials

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

Nouvelles méthodes numériques pour la simulation temps-réel des déformations des tissus mous dans le cadre de l’assistance peropératoire

This thesis addresses the problem soft tissue simulation for augmented reality applications in liver surgery assistance and, more specifically, the implementation of a non-rigid registration pipeline to be used by the medical staff to generate interactive deformations of a patient specific liver three-dimensional virtual representation. A formal physics-based framework is first defined and used as the basis for the construction of a biomechanical model capable of producing realistic deformations. Four basic requirements guided the development of the model: accuracy, speed, stability and simplicity of implementation. Meshless and immersed-boundary methods are both considered as alternatives to the traditional finite element method. A formal non-rigid registration algorithm is finally documented and tested with real-life scenarios. A comparison with new and rising machine learning and neural network solutions is also provided.Cette thèse aborde le problème de simulation des tissus mous pour les applications de réalité augmentée en assistance peropératoire du foie et, plus précisément, la mise en oeuvre d'une procédure automatique de recalage non rigide entre une reconstruction préopératoire du foie d'un patient et les données acquises en temps réel pendant la chirurgie. Un cadre formel basé sur la physique est d'abord défini et utilisé comme base pour la construction d'un modèle biomécanique capable de reproduire les déformations du foie. Quatre directives de recherche ont guidé le développement du modèle : la précision, la rapidité, la stabilité et la simplicité de mise en oeuvre. Les méthodes sans maillage et les méthodes aux frontières immergées sont deux considérées comme des alternatives à la méthode traditionnelle des éléments finis. Un algorithme complet de recalage non rigide est documenté et testé avec des scénarios réels. Finalement, une introduction des émergentes en apprentissage automatique et réseaux de neurones est également fournie

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

Conformation constraints for efficient viscoelastic fluid simulation

The simulation of high viscoelasticity poses important computational challenges. One is the difficulty to robustly measure strain and its derivatives in a medium without permanent structure. Another is the high stiffness of the governing differential equations. Solutions that tackle these challenges exist, but they are computationally slow. We propose a constraint-based model of viscoelasticity that enables efficient simulation of highly viscous and viscoelastic phenomena. Our model reformulates, in a constraint-based fashion, a constitutive model of viscoelasticity for polymeric fluids, which defines simple governing equations for a conformation tensor. The model can represent a diverse palette of materials, spanning elastoplastic, highly viscous, and inviscid liquid behaviors. In addition, we have designed a constrained dynamics solver that extends the position-based dynamics method to handle efficiently both position-based and velocity-based constraints. We show results that range from interactive simulation of viscoelastic effects to large-scale simulation of high viscosity with competitive performance