Detailed analysis of the lattice Boltzmann method on unstructured grids

The lattice Boltzmann method has become a standard for efficiently solving problems in fluid dynamics. While unstructured grids allow for a more efficient geometrical representation of complex boundaries, the lattice Boltzmann methods is often implemented using regular grids. Here we analyze two implementations of the lattice Boltzmann method on unstructured grids, the standard forward Euler method and the operator splitting method. We derive the evolution of the macroscopic variables by means of the Chapman-Enskog expansion, and we prove that it yields the Navier-Stokes equation and is first order accurate in terms of the temporal discretization and second order in terms of the spatial discretization. Relations between the kinetic viscosity and the integration time step are derived for both the Euler method and the operator splitting method. Finally we suggest an improved version of the bounce-back boundary condition. We test our implementations in both standard benchmark geometries and in the pore network of a real sample of a porous rock.Comment: 42 page

Modelling of high pressure binary droplet collisions

AbstractDroplet collision efficiency is a rather uncharted area for real hydrocarbon systems under non-atmospheric conditions. It is also of great interest in many industrial applications. In this work binary head-on droplet collisions at high pressure have been simulated using the lattice Boltzmann method. A model that captures the physics of the coalescence process is used where no external criterion for coalescence is needed. The collision process is described in terms of hydrodynamic variables and through a quantitative study of energy loss. At high pressures, low inertia collisions are the most frequent. Distinguishing between bouncing and coalescence under these conditions is needed in order to provide closure conditions for macroscopic CFD models. A limit of Re<170ρlg is found to predict coalescence in all the cases simulated. In addition this paper explains the stochastic behaviour of low inertia coalescence at high pressure. This has major implications both when building macroscopic models for predicting industrial process efficiencies and in the optimization of equipment internals working with droplets at high pressure as is the case for combustion chambers and gas–liquid separators

Computational fluid dynamics using Graphics Processing Units: Challenges and opportunities

A new paradigm for computing fluid flows is the use of Graphics Processing Units (GPU), which have recently become very powerful and convenient to use. In the past three years, we have implemented five different fluid flow algorithms on GPUs and have obtained significant speed-ups over a single CPU. Typically, it is possible to achieve a factor of 50-100 over a single CPU. In this review paper, we describe our experiences on the various algorithms developed and the speeds achieved

A random projection method for sharp phase boundaries in lattice Boltzmann simulations

Existing lattice Boltzmann models that have been designed to recover a macroscopic description of immiscible liquids are only able to make predictions that are quantitatively correct when the interface that exists between the fluids is smeared over several nodal points. Attempts to minimise the thickness of this interface generally leads to a phenomenon known as lattice pinning, the precise cause of which is not well understood. This spurious behaviour is remarkably similar to that associated with the numerical simulation of hyperbolic partial differential equations coupled with a stiff source term. Inspired by the seminal work in this field, we derive a lattice Boltzmann implementation of a model equation used to investigate such peculiarities. This implementation is extended to different spacial discretisations in one and two dimensions. We shown that the inclusion of a quasi-random threshold dramatically delays the onset of pinning and facetting

Simulating anomalous dispersion in porous media using the unstructured lattice Boltzmann method

Flow in porous media is a significant challenge to many computational fluid dynamics methods because of the complex boundaries separating pore fluid and host medium. However, the rapid development of the lattice Boltzmann methods and experimental imaging techniques now allow us to efficiently and robustly simulate flows in the pore space of porous rocks. Here we study the flow and dispersion in the pore space of limestone samples using the unstructured, characteristic based off-lattice Boltzmann method. We use the method to investigate the anomalous dispersion of particles in the pore space. We further show that the complex pore network limits the effectivity by which pollutants in the pore space can be removed by continuous flushing. In the smallest pores, diffusive transport dominates over advective transport and therefore cycles of flushing and no flushing, respectively, might be a more efficient strategy for pollutant removal

A Pragmatic Approach of Computational Methods for Simulation of Multiphase Flows

In this paper we study the numerical simulation of multiphase flows which is a powerful tool for investigating and understanding the multiphase flows and to provide insight on the physics of free surface and interfacial flows such as bubble droplet dynamics, ocean wave motion, among others. The advanced in computational fluid dynamics and its extension to multi-fluid flows which is computational multifluid dynamics (CMFD) together with the increasing capacity of parallel computers have made possible to tackle such complex problems by using high performance numerical techniques such as direct numerical simulation (DNS).  Direct numerical simulation is an important research area in modern CMFD. Moreover, DNS has a key role for improving the understanding of the multiphase phenomena and for using this technique for the simulation of flows in complex geometricians. The results from DNS is useful for developing better Eulerian-Eulerian and Eulerian-Lagrange methods. Furthermore, most of the DNS methods discussed in the literature have been restricted to Cartesian meshes and academic configurations. Thus the reasons are mainly due to the limited computational resources and because the standards algorithms are very complex to be efficient implemented on unstructured grids. Keywords:Conservative level set method, Bubbly flow, Computational multi fluid dynamics, Navier Stoke’s equation, Direct numerical simulation