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

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

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

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

Peridynamic Galerkin methods for nonlinear solid mechanics

Simulation-driven product development is nowadays an essential part in the industrial digitalization. Notably, there is an increasing interest in realistic high-fidelity simulation methods in the fast-growing field of additive and ablative manufacturing processes. Thanks to their flexibility, meshfree solution methods are particularly suitable for simulating the stated processes, often accompanied by large deformations, variable discontinuities, or phase changes. Furthermore, in the industrial domain, the meshing of complex geometries represents a significant workload, which is usually minor for meshfree methods. Over the years, several meshfree schemes have been developed. Nevertheless, along with their flexibility in discretization, meshfree methods often endure a decrease in accuracy, efficiency and stability or suffer from a significantly increased computation time. Peridynamics is an alternative theory to local continuum mechanics for describing partial differential equations in a non-local integro-differential form. The combination of the so-called peridynamic correspondence formulation with a particle discretization yields a flexible meshfree simulation method, though does not lead to reliable results without further treatment.\newline In order to develop a reliable, robust and still flexible meshfree simulation method, the classical correspondence formulation is generalized into the Peridynamic Galerkin (PG) methods in this work. On this basis, conditions on the meshfree shape functions of virtual and actual displacement are presented, which allow an accurate imposition of force and displacement boundary conditions and lead to stability and optimal convergence rates. Based on Taylor expansions moving with the evaluation point, special shape functions are introduced that satisfy all the previously mentioned requirements employing correction schemes. In addition to displacement-based formulations, a variety of stabilized, mixed and enriched variants are developed, which are tailored in their application to the nearly incompressible and elasto-plastic finite deformation of solids, highlighting the broad design scope within the PG methods. Extensive numerical validations and benchmark simulations are performed to show the impact of violating different shape function requirements as well as demonstrating the properties of the different PG formulations. Compared to related Finite Element formulations, the PG methods exhibit similar convergence properties. Furthermore, an increased computation time due to non-locality is counterbalanced by a considerably improved robustness against poorly meshed discretizations

Discrete-continuum hybrid modelling of flowing and static regimes

Bulk handling, transport and processing of granular materials and powders are fundamental operations in a wide range of industrial processes and geophysical phenomena. Particulate materials, which can be found in nature, are usually characterized by grain size which can range across several scales: from nanometre to the order of metre. Depending on the volume fraction and shear strain conditions, granular materials can have different behaviours and often can be expressed as a new state of matter with properties of solids, liquids and gases. For the above reasons both the experimental and the numerical analysis of granular media is still a difficult task and the prediction of their dynamic behaviour still represents nowadays an important challenge. The main goal of the current thesis is the development of a numerical strategy with the objective of studying the macroscopic behaviour of dry granular flows in quasi-static and dense flow regime. The problem is defined in a continuum mechanics framework and the balance laws, which govern the behaviour of a solid body, are solved by using a Lagrangian formalism. The Material Point Method (MPM), a particle-based method, is chosen due to its features which make it very suitable for the solution of large deformation problems involving complex history-dependent constitutive laws. An irreducible formulation using a Mohr-Coulomb constitutive law, which takes into account geometric non-linearities, is implemented within the MPM framework. The numerical strategy is verified and validated against several benchmark tests and experimental results, available in the literature. Further, a mixed formulation is implemented for the solution of granular flows that undergo undrained conditions. Finally, the developed MPM strategy is used and tested against the experimental study performed for the characterization of the flowability of several types of sucrose. The capabilities and limitations of this numerical strategy are observed and discussed and the bases for future research are outlined.El manejo, el transporte y el procesamiento de materiales granulares y polvo son operaciones fundamentales en una amplia gama de procesos industriales y de fenómenos geofísicos. Los materiales particulados, que pueden ser encontrados en la naturaleza, generalmente están caracterizados por el tamaño del grano, que puede variar entre varios órdenes de magnitud: desde el nanómetro hasta el orden de los metros. En función de las condiciones de fracción volumétrica y de deformación de cortante, los materiales granulares pueden tener un comportamiento diferente y a menudo pueden expresarse como un nuevo estado de materia con propiedades de sólidos, de líquidos y de gases. A causa de las observaciones antes mencionadas, tanto el análisis experimental como la simulación numérica de medios granulares es aún una tarea compleja y la predicción de su comportamiento dinámico representa aun hoy día un desafío muy importante. El principal objetivo de esta tesis es el desarrollo de una estrategia numérica con la finalidad de estudiar el comportamiento macroscópico de los flujos de medios granulares secos en régimen cuasiestático y en régimen dinámico. El problema está definido en el contexto de la mecánica de medios continuos y las leyes de equilibrio, que gobiernan el comportamiento del cuerpo sólido, y están resueltas mediante un formalismo Lagrangiano. El Metodo de los Puntos Materiales (MPM), método basado en el concepto de discretización del cuerpo sólido en partículas, está elegido por sus características que lo convierten en una técnica apropiada para resolver problemas de grandes deformaciones donde se tienen que utilizar complejas leyes constitutivas. En el marco del MPM está implementada una formulación irreducible que usa una ley constitutiva de Mohr-Coulomb y que tiene en cuenta no-linealidades geométricas. La estrategia numérica está verificada y validada con respecto a tests de referencia y resultados experimentales disponibles en la literatura. Además, se ha implementado una formulación mixta para resolver casos de flujo granular en condiciones no drenadas. Por último, la estrategia MPM desarrollada está utilizada y evaluada con respecto a un estudio experimental realizado para la caracterización de la fluidez de diferentes tipologías de azúcar. También se presentan unas observaciones y discusión sobre las capacidades y las limitaciones de esta herramienta numérica y se describen las bases de una investigación futura

Discrete-continuum hybrid modelling of flowing and static regimes

Bulk handling, transport and processing of granular materials and powders are fundamental operations in a wide range of industrial processes and geophysical phenomena. Particulate materials, which can be found in nature, are usually characterized by grain size which can range across several scales: from nanometre to the order of metre. Depending on the volume fraction and shear strain conditions, granular materials can have different behaviours and often can be expressed as a new state of matter with properties of solids, liquids and gases. For the above reasons both the experimental and the numerical analysis of granular media is still a difficult task and the prediction of their dynamic behaviour still represents nowadays an important challenge. The main goal of the current thesis is the development of a numerical strategy with the objective of studying the macroscopic behaviour of dry granular flows in quasi-static and dense flow regime. The problem is defined in a continuum mechanics framework and the balance laws, which govern the behaviour of a solid body, are solved by using a Lagrangian formalism. The Material Point Method (MPM), a particle-based method, is chosen due to its features which make it very suitable for the solution of large deformation problems involving complex history-dependent constitutive laws. An irreducible formulation using a Mohr-Coulomb constitutive law, which takes into account geometric non-linearities, is implemented within the MPM framework. The numerical strategy is verified and validated against several benchmark tests and experimental results, available in the literature. Further, a mixed formulation is implemented for the solution of granular flows that undergo undrained conditions. Finally, the developed MPM strategy is used and tested against the experimental study performed for the characterization of the flowability of several types of sucrose. The capabilities and limitations of this numerical strategy are observed and discussed and the bases for future research are outlined.El manejo, el transporte y el procesamiento de materiales granulares y polvo son operaciones fundamentales en una amplia gama de procesos industriales y de fenómenos geofísicos. Los materiales particulados, que pueden ser encontrados en la naturaleza, generalmente están caracterizados por el tamaño del grano, que puede variar entre varios órdenes de magnitud: desde el nanómetro hasta el orden de los metros. En función de las condiciones de fracción volumétrica y de deformación de cortante, los materiales granulares pueden tener un comportamiento diferente y a menudo pueden expresarse como un nuevo estado de materia con propiedades de sólidos, de líquidos y de gases. A causa de las observaciones antes mencionadas, tanto el análisis experimental como la simulación numérica de medios granulares es aún una tarea compleja y la predicción de su comportamiento dinámico representa aun hoy día un desafío muy importante. El principal objetivo de esta tesis es el desarrollo de una estrategia numérica con la finalidad de estudiar el comportamiento macroscópico de los flujos de medios granulares secos en régimen cuasiestático y en régimen dinámico. El problema está definido en el contexto de la mecánica de medios continuos y las leyes de equilibrio, que gobiernan el comportamiento del cuerpo sólido, y están resueltas mediante un formalismo Lagrangiano. El Metodo de los Puntos Materiales (MPM), método basado en el concepto de discretización del cuerpo sólido en partículas, está elegido por sus características que lo convierten en una técnica apropiada para resolver problemas de grandes deformaciones donde se tienen que utilizar complejas leyes constitutivas. En el marco del MPM está implementada una formulación irreducible que usa una ley constitutiva de Mohr-Coulomb y que tiene en cuenta no-linealidades geométricas. La estrategia numérica está verificada y validada con respecto a tests de referencia y resultados experimentales disponibles en la literatura. Además, se ha implementado una formulación mixta para resolver casos de flujo granular en condiciones no drenadas. Por último, la estrategia MPM desarrollada está utilizada y evaluada con respecto a un estudio experimental realizado para la caracterización de la fluidez de diferentes tipologías de azúcar. También se presentan unas observaciones y discusión sobre las capacidades y las limitaciones de esta herramienta numérica y se describen las bases de una investigación futura.Postprint (published version

An explicit Lagrangian finite element method for free-surface weakly compressible flows

In the present work, an explicit finite element approach to the solution of the Lagrangian formulation of the Navier-Stokes equations for weakly compressible fluids or fluid-like materials is investigated. The introduction of a small amount of compressibility is shown to allow for the formulation of a fast and robust explicit solver based on a particle finite element method. Newtonian and Non-Newtonian Bingham laws are considered. A barotropic equation of state completes the model relating pressure and density fields. The approach has been validated through comparison with experimental tests and numerical simulations of free surface fluid problems involving water and waterâ\u80\u93soil mixtures

Numerical methods for the modelling of chip formation

The modeling of metal cutting has proved to be particularly complex due to the diversity of physical phenomena involved, including thermo-mechanical coupling, contact/friction and material failure. During the last few decades, there has been significant progress in the development of numerical methods for modeling machining operations. Furthermore, the most relevant techniques have been implemented in the the relevant commercial codes creating tools for the engineers working in the design of processes and cutting devices. This paper presents a review on the numerical modeling methods and techniques used for the simulation of machining processes. The main purpose is to identify the strengths and weaknesses of each method and strategy developed up-to-now. Moreover the review covers the classical Finite Element Method covering mesh-less methods, particle-based methods and different possibilities of Eulerian and Lagrangian approaches.Postprint (author's final draft