799 research outputs found

    Multiphase flow of immiscible fluids on unstructured moving meshes

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    Figure 1: Multiple fluids with different viscosity coefficients and surface tension densities splashing on the bottom of a cylindrical container. Observe that the simulation has no problem dealing with thin sheets. In this paper, we present a method for animating multiphase flow of immiscible fluids using unstructured moving meshes. Our underlying discretization is an unstructured tetrahedral mesh, the deformable simplicial complex (DSC), that moves with the flow in a Lagrangian manner. Mesh optimization operations improve element quality and avoid element inversion. In the context of multiphase flow, we guarantee that every element is occupied by a single fluid and, consequently, the interface between fluids is represented by a set of faces in the simplicial complex. This approach ensures that the underlying discretization matches the physics and avoids the additional book-keeping required in grid-based methods where multiple fluids may occupy the same cell. Our Lagrangian approach naturally leads us to adopt a finite element approach to simulation, in contrast to the finite volume approaches adopted by a majority of fluid simulation techniques that use tetrahedral meshes. We characterize fluid simulation as an optimization problem allowing for full coupling of the pressure and velocity fields and the incorporation of a second-order surface energy. We introduce a preconditioner based on the diagonal Schur complement and solve our optimization on the GPU. We provide the results of parameter studies as well as

    Multiphase flow of immiscible fluids on unstructured moving meshes

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    pre-printIn this paper, we present a method for animating multiphase flow of immiscible fluids using unstructured moving meshes. Our underlying discretization is an unstructured tetrahedral mesh, the deformable simplicial complex (DSC), that moves with the flow in a Lagrangian manner. Mesh optimization operations improve element quality and avoid element inversion. In the context of multiphase flow, we guarantee that every element is occupied by a single fluid and, consequently, the interface between fluids is represented by a set of faces in the simplicial complex. This approach ensures that the underlying discretization matches the physics and avoids the additional book-keeping required in grid-based methods where multiple fluids may occupy the same cell. Our Lagrangian approach naturally leads us to adopt a finite element approach to simulation, in contrast to the finite volume approaches adopted by a majority of fluid simulation techniques that use tetrahedral meshes. We characterize fluid simulation as an optimization problem allowing for full coupling of the pressure and velocity fields and the incorporation of a second-order surface energy. We introduce a preconditioner based on the diagonal Schur complement and solve our optimization on the GPU. We provide the results of parameter studies as well as a performance analysis of our method, together with suggestions for performance optimization

    Parallel load balancing strategy for Volume-of-Fluid methods on 3-D unstructured meshes

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    © 2016. This version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/l Volume-of-Fluid (VOF) is one of the methods of choice to reproduce the interface motion in the simulation of multi-fluid flows. One of its main strengths is its accuracy in capturing sharp interface geometries, although requiring for it a number of geometric calculations. Under these circumstances, achieving parallel performance on current supercomputers is a must. The main obstacle for the parallelization is that the computing costs are concentrated only in the discrete elements that lie on the interface between fluids. Consequently, if the interface is not homogeneously distributed throughout the domain, standard domain decomposition (DD) strategies lead to imbalanced workload distributions. In this paper, we present a new parallelization strategy for general unstructured VOF solvers, based on a dynamic load balancing process complementary to the underlying DD. Its parallel efficiency has been analyzed and compared to the DD one using up to 1024 CPU-cores on an Intel SandyBridge based supercomputer. The results obtained on the solution of several artificially generated test cases show a speedup of up to similar to 12x with respect to the standard DD, depending on the interface size, the initial distribution and the number of parallel processes engaged. Moreover, the new parallelization strategy presented is of general purpose, therefore, it could be used to parallelize any VOF solver without requiring changes on the coupled flow solver. Finally, note that although designed for the VOF method, our approach could be easily adapted to other interface-capturing methods, such as the Level-Set, which may present similar workload imbalances. (C) 2014 Elsevier Inc. Allrights reserved.Peer ReviewedPostprint (author's final draft

    Modelling the Interfacial Flow of Two Immiscible Liquids in Mixing Processes

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    This paper presents an interface tracking method for modelling the flow of immiscible metallic liquids in mixing processes. The methodology can provide an insight into mixing processes for studying the fundamental morphology development mechanisms for immiscible interfaces. The volume-of-fluid (VOF) method is adopted in the present study, following a review of various modelling approaches for immiscible fluid systems. The VOF method employed here utilises the piecewise linear for interface construction scheme as well as the continuum surface force algorithm for surface force modelling. A model coupling numerical and experimental data is established. The main flow features in the mixing process are investigated. It is observed that the mixing of immiscible metallic liquids is strongly influenced by the viscosity of the system, shear forces and turbulence. The numerical results show good qualitative agreement with experimental results, and are useful for optimisating the design of mixing casting processes

    Numerical simulation of multiphase immiscible flow on unstructured meshes

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    The present thesis aims at developing a basis for the numerical simulation of multiphase flows of immiscible fluids. This approach, although limited by the computational power of the present computers, is potentially very important, since most of the physical phenomena of these flows often happen on space and time scales where experimental techniques are impossible to be utilized in practice. In particular, this research is focused on developing numerical discretizations suitable for three-dimensional (3-D) unstructured meshes. In detail, the first chapter delimits the considered multiphase flows to the case in which the components are immiscible fluids. In particular, the focus is placed on those cases where two or more continuous streams of different fluids are separated by interfaces, and hence, correspondingly named separated flows. Additionally, once the type of flow is determined, the chapter introduces the physical characteristics and the models available to predict its behavior, as well as the mathematical formulation that sustains the numerical techniques developed within this thesis. The second chapter introduces and analyzes a new geometrical Volume-of-Fluid (VOF) method for capturing interfaces on 3-D Cartesian and unstructured meshes. The method reconstructs interfaces as first- and second-order piecewise planar approximations (PLIC), and advects volumes in a single unsplit Lagrangian-Eulerian (LE) geometrical algorithm based on constructing flux polyhedrons by tracing back the Lagrangian trajectories of the cell-vertex velocities. In this way, the situations of overlapping between flux polyhedrons are minimized. Complementing the previous chapter, the third one proposes a parallelization strategy for the VOF method. The main obstacle is that the computing costs are concentrated in the interface between fluids. Consequently, if the interface is not homogeneously distributed, standard domain decomposition (DD) strategies lead to imbalanced workload distributions. Hence, the new strategy is based on a load balancing process complementary to the underlying domain decomposition. Its parallel efficiency has been analyzed using up to 1024 CPU-cores, and the results obtained show a gain with respect to the standard DD strategy up to 12x, depending on the size of the interface and the initial distribution. The fourth chapter describes the discretization of the single-phase Navier-Stokes equations to later extend it to the case of multiphase immiscible flow. One of the most important characteristics of the discretization schemes, aside from accuracy, is their capacity to discretely conserve kinetic energy, specially when solving turbulent flow. Hence, this chapter analyzes the accuracy and conservation properties of two particular collocated and staggered mesh schemes. The extension of the numerical schemes suitable for the single-phase Navier-Stokes equations to the case of multiphase immiscible flow is developed in the fifth chapter. Particularly, while the numerical techniques for the simulation of turbulent flow have evolved to discretely preserve mass, momentum and, specially, kinetic energy, the mesh schemes for the discretization of multiphase immiscible flow have evolved to improve their stability and robustness. Therefore, this chapter presents and analyzes two particular collocated and staggered mesh discretizations, able to simulate multiphase immiscible flow, which favor the discrete conservation of mass, momentum and kinetic energy. Finally, the sixth chapter numerically simulates the Richtmyer-Meshkov (RM) instability of two incompressible immiscible liquids. This chapter is a general assessment of the numerical methods developed along this thesis. In particular, the instability has been simulated by means of a VOF method and a staggered mesh scheme. The corresponding numerical results have shown the capacity of the discrete system to obtain accurate results for the RM instability.Aquesta tesi té com a objectiu desenvolupar una base per a la simulació numèrica de fluids multi-fase immiscibles. Aquesta estratègia, encara que limitada per la potència computacional dels computadors actuals, és potencialment molt important, ja que la majoria de la fenomenologia d'aquests fluids sovint passa en escales temporals i especials on les tècniques experimentals no poden ser utilitzades. En particular, aquest treball es centra en desenvolupar discretitzacions numèriques aptes per a malles no-estructurades en tres dimensions (3-D). En detall, el primer capítol delimita els casos multifásics considerats al cas en que els components són fluids immiscibles. En particular, la tesi es centra en aquells casos en que dos o més fluids diferents són separats per interfases, i per tant, corresponentment anomenats fluxos separats. A més a més, un cop el tipus de flux es determinat, el capítol introdueix les característiques físiques i els models disponibles per predir el seu comportament, així com també la formulació matemàtica i les tècniques numèriques desenvolupades en aquesta tesi. El segon capítol introdueix i analitza un nou mètode "Volume-of-Fluid" (VOF) apte per a capturar interfases en malles Cartesianes i no-estructurades 3-D. El mètode reconstrueix les interfases com aproximacions "piecewise planar approximations" (PLIC) de primer i segon ordre, i advecciona els volums amb un algoritme geomètric "unsplit Lagrangian-Eulerian" (LE) basat en construïr els poliedres a partir de les velocitats dels vèrtexs de les celdes. D'aquesta manera, les situacions de sobre-solapament entre poliedres són minimitzades. Complementant el capítol anterior, el tercer proposa una estratègia de paral·lelització pel mètode VOF. L'obstacle principal és que els costos computacionals estan concentrats en les celdes de l'interfase entre fluids. En conseqüència, si la interfase no està ben distribuïda, les estratègies de "domain decomposition" (DD) resulten en distribucions de càrrega desequilibrades. Per tant, la nova estratègia està basada en un procés de balanceig de càrrega complementària a la DD. La seva eficiència en paral·lel ha sigut analitzada utilitzant fins a 1024 CPU-cores, i els resultats obtinguts mostren uns guanys respecte l'estratègia DD de fins a 12x, depenent del tamany de la interfase i de la distribució inicial. El quart capítol descriu la discretització de les equacions de Navier-Stokes per a una sola fase, per després estendre-ho al cas multi-fase. Una de les característiques més importants dels esquemes de discretització, a part de la precisió, és la seva capacitat per conservar discretament l'energia cinètica, específicament en el cas de fluxos turbulents. Per tant, aquest capítol analitza la precisió i propietats de conservació de dos esquemes de malla diferents: "collocated" i "staggered". L'extensió dels esquemes de malla aptes per els casos de una sola fase als casos multi-fase es desenvolupa en el cinquè capítol. En particular, així com en el cas de la simulació de la turbulència les tècniques numèriques han evolucionat per a preservar discretament massa, moment i energia cinètica, els esquemes de malla per a la discretització de fluxos multi-fase han evolucionat per millorar la seva estabilitat i robustesa. Per lo tant, aquest capítol presenta i analitza dos discretitzacions de malla "collocated" i "staggered" particulars, aptes per simular fluxos multi-fase, que afavoreixen la conservació discreta de massa, moment i energia cinètica. Finalment, el capítol sis simula numèricament la inestabilitat de Richtmyer-Meshkov (RM) de dos fluids immiscibles i incompressibles. Aquest capítol es una prova general dels mètodes numèrics desenvolupats al llarg de la tesi. En particular, la inestabilitat ha sigut simulada mitjançant un mètode VOF i un esquema de malla "staggered". Els resultats numèrics corresponents han demostrat la capacitat del sistema discret en obtenir bons resultats per la inestabilitat RM

    Interface Tracking and Solid-Fluid Coupling Techniques with Coastal Engineering Applications

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    Multi-material physics arise in an innumerable amount of engineering problems. A broadly scoped numerical model is developed and described in this thesis to simulate the dynamic interaction of multi-fluid and solid systems. It is particularly aimed at modelling the interaction of two immiscible fluids with solid structures in a coastal engineering context; however it can be extended to other similar areas of research. The Navier Stokes equations governing the fluids are solved using a combination of finite element (FEM) and control volume finite element (CVFE) discretisations. The sharp interface between the fluids is obtained through the compressive transport of material properties (e.g. material concentration). This behaviour is achieved through the CVFE method and a conveniently limited flux calculation scheme based on the Hyper-C method by Leonard (1991). Analytical and validation test cases are provided, consisting of steady and unsteady flows. To further enhance the method, improve accuracy, and exploit Lagrangian benefits, a novel moving mesh method is also introduced and tested. It is essentially an Arbitrary Lagrangian Eulerian method in which the grid velocity is defined by semi-explicitly solving an iterative functional minimisation problem. A multi-phase approach is used to introduce solid structure modelling. In this approach, solution of the velocity field for the fluid phase is obtained using Model B as explained by Gidaspow (1994, page 151). Interaction between the fluid phase and the solids is achieved through the means of a source term included in the fluid momentum equations. The interacting force is calculated through integration of this source term and adding a buoyancy contribution. The resulting force is passed to an external solid-dynamics model such as the Discrete Element Method (DEM), or the combined Finite Discrete Element Method (FEMDEM). The versatility and novelty of this combined modelling approach stems from its ability to capture the fluid interaction with particles of random size and shape. Each of the three main components of this thesis: the advection scheme, the moving mesh method, and the solid interaction are individually validated, and examples of randomly shaped and sized particles are shown. To conclude the work, the methods are combined together in the context of coastal engineering applications, where the complex coupled problem of waves impacting on breakwater amour units is chosen to demonstrate the simulation possibilities. The three components developed in this thesis significantly extend the application range of already powerful tools, such as Fluidity, for fluids-modelling and finite discrete element solids-modelling tools by bringing them together for the first time
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