Subsonic turbulence in smoothed particle hydrodynamics and moving-mesh simulations

Highly supersonic, compressible turbulence is thought to be of tantamount importance for star formation processes in the interstellar medium. Likewise, cosmic structure formation is expected to give rise to subsonic turbulence in the intergalactic medium, which may substantially modify the thermodynamic structure of gas in virialized dark matter halos and affect small-scale mixing processes in the gas. Numerical simulations have played a key role in characterizing the properties of astrophysical turbulence, but thus far systematic code comparisons have been restricted to the supersonic regime, leaving it unclear whether subsonic turbulence is faithfully represented by the numerical techniques commonly employed in astrophysics. Here we focus on comparing the accuracy of smoothed particle hydrodynamics (SPH) and our new moving-mesh technique AREPO in simulations of driven subsonic turbulence. To make contact with previous results, we also analyze simulations of transsonic and highly supersonic turbulence. We find that the widely employed standard formulation of SPH yields problematic results in the subsonic regime. Instead of building up a Kolmogorov-like turbulent cascade, large-scale eddies are quickly damped close to the driving scale and decay into small-scale velocity noise. Reduced viscosity settings improve the situation, but the shape of the dissipation range differs compared with expectations for a Kolmogorov cascade. In contrast, our moving-mesh technique does yield power-law scaling laws for the power spectra of velocity, vorticity and density, consistent with expectations for fully developed isotropic turbulence. We show that large errors in SPH's gradient estimate and the associated subsonic velocity noise are ultimately responsible for producing inaccurate results in the subsonic regime. In contrast, SPH's performance is much better for supersonic turbulence. [Abridged]Comment: 22 pages, 20 figures, accepted in MNRAS. Includes a rebuttal to arXiv:1111.1255 of D. Price and significant revisions to address referee comments. Conclusions of original submission unchange

Analysis of the particle relaxation method for generating uniform particle distributions in smoothed particle hydrodynamics

We establish a theoretical framework of the particle relaxation method for uniform particle generation of Smoothed Particle Hydrodynamics. We achieve this by reformulating the particle relaxation as an optimization problem. The objective function is an integral difference between discrete particle-based and smoothed-analytical volume fractions. The analysis demonstrates that the particle relaxation method in the domain interior is essentially equivalent to employing a gradient descent approach to solve this optimization problem, and we can extend such an equivalence to the bounded domain by introducing a proper boundary term. Additionally, each periodic particle distribution has a spatially uniform particle volume, denoted as characteristic volume. The relaxed particle distribution has the largest characteristic volume, and the kernel cut-off radius determines this volume. This insight enables us to control the relaxed particle distribution by selecting the target kernel cut-off radius for a given kernel function

Simulating liquids on dynamically warping grids

We introduce dynamically warping grids for adaptive liquid simulation. Our primary contributions are a strategy for dynamically deforming regular grids over the course of a simulation and a method for efficiently utilizing these deforming grids for liquid simulation. Prior work has shown that unstructured grids are very effective for adaptive fluid simulations. However, unstructured grids often lead to complicated implementations and a poor cache hit rate due to inconsistent memory access. Regular grids, on the other hand, provide a fast, fixed memory access pattern and straightforward implementation. Our method combines the advantages of both: we leverage the simplicity of regular grids while still achieving practical and controllable spatial adaptivity. We demonstrate that our method enables adaptive simulations that are fast, flexible, and robust to null-space issues. At the same time, our method is simple to implement and takes advantage of existing highly-tuned algorithms

Visuelle Analyse großer Partikeldaten

Partikelsimulationen sind eine bewährte und weit verbreitete numerische Methode in der Forschung und Technik. Beispielsweise werden Partikelsimulationen zur Erforschung der Kraftstoffzerstäubung in Flugzeugturbinen eingesetzt. Auch die Entstehung des Universums wird durch die Simulation von dunkler Materiepartikeln untersucht. Die hierbei produzierten Datenmengen sind immens. So enthalten aktuelle Simulationen Billionen von Partikeln, die sich über die Zeit bewegen und miteinander interagieren. Die Visualisierung bietet ein großes Potenzial zur Exploration, Validation und Analyse wissenschaftlicher Datensätze sowie der zugrundeliegenden Modelle. Allerdings liegt der Fokus meist auf strukturierten Daten mit einer regulären Topologie. Im Gegensatz hierzu bewegen sich Partikel frei durch Raum und Zeit. Diese Betrachtungsweise ist aus der Physik als das lagrange Bezugssystem bekannt. Zwar können Partikel aus dem lagrangen in ein reguläres eulersches Bezugssystem, wie beispielsweise in ein uniformes Gitter, konvertiert werden. Dies ist bei einer großen Menge an Partikeln jedoch mit einem erheblichen Aufwand verbunden. Darüber hinaus führt diese Konversion meist zu einem Verlust der Präzision bei gleichzeitig erhöhtem Speicherverbrauch. Im Rahmen dieser Dissertation werde ich neue Visualisierungstechniken erforschen, welche speziell auf der lagrangen Sichtweise basieren. Diese ermöglichen eine effiziente und effektive visuelle Analyse großer Partikeldaten

Adaptive Physically Based Models in Computer Graphics

International audienceOne of the major challenges in physically-based modeling is making simulations efficient. Adaptive models provide an essential solution to these efficiency goals. These models are able to self-adapt in space and time, attempting to provide the best possible compromise between accuracy and speed. This survey reviews the adaptive solutions proposed so far in computer graphics. Models are classified according to the strategy they use for adaptation, from time-stepping and freezing techniques to geometric adaptivity in the form of structured grids, meshes, and particles. Applications range from fluids, through deformable bodies, to articulated solids

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

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