Particle methods in Computational Fluid Dynamics

Particle methods in Computational Fluid Dynamics (CFD) are numerical tools for the solution of the equations of f luid dynamics obtained by replacing the fluuid continuum with a finite set of particles. For mathematicians, particles are just points from which properties of the uid can be interpolated. For physicists the particles are material points, which can be treated like any other particle system. Either way, particle methods have a number of attractive features. One of the key attributes is that pure advection is treated exactly. For example, if the particles are given a determined colour and the velocity is specified, the transport of colours by the particle system is exact. The convection of properties also eases the solution of multi material problems, simplifying the detection of interfaces. The use of particles also allows to bridge the gap between the continuum and fragmentation in a natural way, for example in fracture or droplets problems. Since the computation domain, the particles, matches exactly the material domain of interest, the computational resources are optimized with the corresponding reduction in storage and calculation time compared to other methods. Finally, because of the close similarity between particle methods and the physics of the problems to be solved, it is often possible to account for complex physics more easily than with other methods

A compressible Lagrangian framework for the simulation of underwater implosion problems

The development of efficient algorithms to understand implosion dynamics presents a number of challenges. The foremost challenge is to efficiently represent the coupled compressible fluid dynamics of internal air and surrounding water. Secondly, the method must allow one to accurately detect or follow the interface between the phases. Finally, it must be capable of resolving any shock waves which may be created in air or water during the final stage of the collapse. We present a fully Lagrangian compressible numerical framework for the simulation of underwater implosion. Both air and water are considered compressible and the equations for the Lagrangian shock hydrodynamics are stabilized via a variationally consistent multiscale method. A nodally perfect matched definition of the interface is used and then the kinetic variables, pressure and density, are duplicated at the interface level. An adaptive mesh generation procedure, which respects the interface connectivities, is applied to provide enough refinement at the interface level. This framework is then used to simulate the underwater implosion of a large cylindrical bubble, with a size in the order of cm. Rapid collapse and growth of the bubble occurred on very small spatial (0.3mm), and time (0.1ms) scales followed by Rayleigh-Taylor instabilities at the interface, in addition to the shock waves traveling in the fluid domains are among the phenomena that are observed in the simulation. We then extend our framework to model the underwater implosion of a cylindrical aluminum container considering a monolithic fluid-structure interaction (FSI). The aluminum cylinder, which separates the internal atmospheric-pressure air from the external high-pressure water, is modeled by a three node rotation-free shell element. The cylinder undergoes fast transient deformations, large enough to produce self-contact along it. A novel elastic frictionless contact model is used to detect contact and compute the non-penetrating forces in the discretized domain between the mid-planes of the shell. Two schemes are tested, implicit using the predictor/multi-corrector Bossak scheme, and explicit, using the forward Euler scheme. The results of the two simulations are compared with experimental data

Solución numérica del problema de transmisión de calor con cambio de fase

Este trabajo resume el estado del arte de la solución numérica de los problemas de transmisión de calor con cambio de fase. Su objetivo consiste en presentar algoritmos en función de su capacidad de encarar problemas ingenieriles, dejando de lado los aspectos teóricos referidos a la convergencia de la solución numérica a-la solución matemática clásica del problema. Se detallan las ventajas y desventajas de los diferentes esquemas para que se pueda efectuar la selección del método más conveniente para un problema determinado. Asimismo se indican cuáles son las tendencias de investigación actuales y las posibilidades futuras en el área. Se incluye una serie de ejemplos numéricos para remarcar los aspectos destacables de los métodos tratados en el trabajo

A conservative coupling algorithm between a compressible flow and a rigid body using an Embedded Boundary method

This paper deals with a new solid-fluid coupling algorithm between a rigid body and an unsteady compressible fluid flow, using an Embedded Boundary method. The coupling with a rigid body is a first step towards the coupling with a Discrete Element method. The flow is computed using a Finite Volume approach on a Cartesian grid. The expression of numerical fluxes does not affect the general coupling algorithm and we use a one-step high-order scheme proposed by Daru and Tenaud [Daru V,Tenaud C., J. Comput. Phys. 2004]. The Embedded Boundary method is used to integrate the presence of a solid boundary in the fluid. The coupling algorithm is totally explicit and ensures exact mass conservation and a balance of momentum and energy between the fluid and the solid. It is shown that the scheme preserves uniform movement of both fluid and solid and introduces no numerical boundary roughness. The effciency of the method is demonstrated on challenging one- and two-dimensional benchmarks

NURBS distance fields for extremely curved cracks

This paper presents the first methodology that combines a meshless method and the exact representation of cracks using Non-Uniform Rational B-Splines (NURBS). The methodology consists on developing an enrichment function based on distance functions to NURBS curves.The examples show the potential of the proposed approach and demonstrate the applicability to problems involving complex cracks that appear in sol-gel films

A State of the Art Review of the Particle Finite Element Method (PFEM)

The particle finite element method (PFEM) is a powerful and robust numerical tool for the simulation of multi-physics problems in evolving domains. The PFEM exploits the Lagrangian framework to automatically identify and follow interfaces between different materials (e.g. fluid–fluid, fluid–solid or free surfaces). The method solves the governing equations with the standard finite element method and overcomes mesh distortion issues using a fast and efficient remeshing procedure. The flexibility and robustness of the method together with its capability for dealing with large topological variations of the computational domains, explain its success for solving a wide range of industrial and engineering problems. This paper provides an extended overview of the theory and applications of the method, giving the tools required to understand the PFEM from its basic ideas to the more advanced applications. Moreover, this work aims to confirm the flexibility and robustness of the PFEM for a broad range of engineering applications. Furthermore, presenting the advantages and disadvantages of the method, this overview can be the starting point for improvements of PFEM technology and for widening its application fields

Flow behaviour of negatively buoyant jets in immiscible ambient fluid

In this paper we investigate experimentally the injection of a negatively buoyant jet into a homogenous immiscible ambient fluid. Experiments are carried out by injecting a jet of dyed fresh water through a nozzle in the base of a cylindrical tank containing rapeseed oil. The fountain inlet flow rate and nozzle diameter were varied to cover a wide range of Richardson Ri (8 × 10 -4 < Ri < 1.98), Reynolds Re (467 < Re < 5,928) and Weber We (2.40 < We < 308.56) numbers. Based on the Re, Ri and We values for the experiments, we have determined a regime map to define how these values may control the occurrence of the observed flow types. Whereas Ri plays a stronger role when determining the maximum penetration height, the effect of the Reynolds number is stronger predicting the flow behaviour for a specific nozzle diameter and injection velocity. © 2011 Springer-Verlag.M. Mier-Torrecilla thanks the Catalan Agency for Administration of University and Research Grants (AGAUR), the European Social Fund and CIMNE for their support. AG is grateful for her post-doctoral Beatriu de Pino´s Grant (2008 BP B 00318) and her Juan de la Cierva Grant (JCI-2010-06092). We thank three anonymous reviewers for their interesting comments that have helped us to improve the previous version of this manuscript. This work was partially supported by the European Research Council under the Advanced Grant: ERC-2009-AdG ‘‘Real Time Computational Mechanics Techniques for Multi-Fluid Problems’’.Peer Reviewe

Una formulación Petrov-Galerkin para la ecuación de reacción-advención-difusión

Presentamos un esquema de discretización basado en la formulación Petrov-Galerkin para, problemas de reacción-advección-difusión. El esquema presentado exhibe superconvergencia, (valores exactos en los nodos) para una cierta clase restringida de problemas unidimensionales, de la misma forma que ocurre con SUBG cuando el parámetro de upwind es elegido a través de la "función mágica". Estos resultados son extendidos a sistemas de ecuaciones. Como caso particular mostramos la aplicación a las ecuaciones simplificadas que rigen los flujos viscosos en sistemas de rotación (capa límite de Eckman). Se presentan ejemplos numéricos uni- y bidimensionales, con y sin fuente, y también en el contexto de la capa límete de Eckman