A local lattice Boltzmann method for multiple immiscible fluids and dense suspensions of drops

The lattice Boltzmann method (LBM) for computational fluid dynamics benefits from a simple, explicit, completely local computational algorithm making it highly efficient. We extend LBM to recover hydrodynamics of multi-component immiscible fluids, whilst retaining a completely local, explicit and simple algorithm. Hence, no computationally expensive lattice gradients, interaction potentials or curvatures, that use information from neighbouring lattice sites, need be calculated, which makes the method highly scalable and suitable for high performance parallel computing. The method is analytic and is shown to recover correct continuum hydrodynamic equations of motion and interfacial boundary conditions. This LBM may be further extended to situations containing a high number (O(100)) of individually immiscible drops. We make comparisons of the emergent non-Newtonian behaviour with a power-law fluid model. We anticipate our method will have a range applications in engineering, industrial and biological sciences

The development and use of strategic business performance improvement frameworks for rapid prototyping and tooling : executive summary

Increasing global competition within industry has forced businesses to respond by reducing costs and product development lead times in order to survive. In the automotive industry, these strategic responses include the specific exploitation of new technologies and mergers with other companies to gain economies of scale. BMW AG purchased Rover Group in 1994 but it wasn't until 1998 that competitive pressure led to the completion of the merger through the creation of a single "Group Function" structure within BMW Group. The BMW Board stated high-level objectives for the process but provided no mechanism to convert them into reality. Similarly, the BMW Group Board initiated a business process "Re-engineering" programme in 1997/8 and stated cost, time and other objectives that would have to be met. The technical and process changes that would help to achieve the business improvements were being largely driven from the bottom of the organisation but there were no frameworks available to guide strategic technology introduction. The principal innovations generated during the course of this research are frameworks for: • Maximising the business benefits from the creation of 'Group Functions' • Internal strategy creation for technology-based business sub-units These two new frameworks have for the first time provided management and staff with the means to develop meaningful strategies and operational action plans from the corporate strategic objectives. The economic and business literature concentrates mainly on whole business strategy and merger activity, neglecting the need for guidance at the sub-corporate level. Although corporate strategy can provide the overall direction of a company, it is the managers that have to drive strategic change within the business. The frameworks were developed by the author based on an in-depth review of the literature and the specific context relating to Rapid Prototyping & Tooling (RP&T) within BMW. The frameworks were validated within the business situation and further enhanced where appropriate. The Group Function framework fills the process gap between the high-level objectives and the need for operational action plans. It provides a straightforward and easy to communicate structure to the process of optimising duplicated business subunits. Use of the framework led to the retention of both RP&T teams and the initiation of beneficial synergistic activities. The framework should be applicable to other similar groups in similar circumstances. The author developed a new strategy creation framework that for the first time combines a range of strategy development approaches from within the literature into a practical framework for sub-corporate strategy development. The framework was matched to the specific context of the RP&T case but could be used in other similar circumstances. The framework was used to successfully develop a new strategy for RP&T in BMW Group and includes new approaches developed by the author that reduce the impact of environmental change and uncertainty. The framework has been described in a stand alone form that can easily be more widely exploited

Chromo-dynamic multi-component lattice Boltzmann equation scheme for axial symmetry

We validate the chromo-dynamic multi-component lattice Boltzmann equation (MCLBE) simulation for immiscible fluids with a density contrast against analytical results for complex flow geometries, with particular emphasis on the fundamentals of the method, i.e. compliance with inter-facial boundary conditions of continuum hydrodynamics. To achieve the necessary regimes for the chosen validations, we develop, from a three-dimensional, axially-symmetric flow formulation, a novel, two-dimensional, pseudo Cartesian, MCLBE scheme. This requires the inclusion in lattice Boltzmann methodology of a continuously distributed source and a velocity-dependent force density (here, the metric force terms of the cylindrical Navier–Stokes equations). Specifically, we apply our model to the problem of flow past a spherical liquid drop in Re = 0, Ca regime and, also, flow past a lightly deformed drop. The resulting simulation data, once corrected for the simulation’s inter-facial micro-current (using a method we also advance herein, based on freezing the phase field) show good agreement with theory over a small range of density contrasts. In particular, our data extend verified compliance with the kinematic condition from flat (Burgin et al 2019 Phys. Rev. E 100 043310) to the case of curved fluid–fluid interfaces. More generally, our results indicate a route to eliminate the influence of the inter-facial micro-current

The shear viscosity of a two-dimensional emulsion of drops using a multiple-relaxation-time-step lattice Boltzmann method

An extended Benzi-Dellar lattice Boltzmann equation scheme (R. Benzi, S. Succi and M. Vergassola, Europhys. Lett. 13, 727 (1990), R. Benzi, S. Succi and M. Vergassola, Phys. Rep. 222, 145 (1992), P. M. Dellar, Phys Rev. E 65 036309 (2002)) is developed and applied to the problem of confirming, at low Re and drop fluid concentration, c, the variation of effective shear viscosity, Data obtained with our enhanced multi-component lattice Boltzmann method, using average shear stress and hydrodynamic dissipation agree well, once appropriate corrections to Landau's volume average shear stress (L. Landau and E. M. Lifshitz, Fluid Mechanics, Sixth Edition, Pergamon Press ) are applied. Simulation results also confirm the expected form for f(_i; _2) and provide a reasonable estimate of its parameters. Most significantly, perhaps the generality of our data support the validity of Taylor's disputed simplification (G. I. Taylor. Proc. R. Soc. Lond. A 1932 138 133-146) to reduce the effect of one hydrodynamic boundary condition (on the continuity of the normal contraction of stress) to an assumption that interfacial tension is sufficiently strong to maintain a spherical drop shape

Benchmarking of three-dimensional multicomponent lattice Boltzmann equation

We present a challenging validation of phase field multi-component lattice Boltzmann equation (MCLBE) simulation against the Re = 0 Stokes flow regime Taylor-Einstein theory of dilute suspension viscosity. By applying a number of recent advances in the understanding and the elimination of the interfacial micro-current artefact, extending to 3D a class of stability-enhancing multiple relaxation time collision models (which require no explicit collision matrix, note) and developing new interfacial interpolation schemes, we are able to obtain data which show that MCLBE may be applied in new flow regimes. Our data represent one of the most stringent tests yet attempted on LBE-one which received wisdom would preclude on grounds of overwhelming artefact flow

Local membrane length conservation in two-dimensional vesicle simulation using multi-component lattice Boltzmann Equation Method.

We present a method for applying a class of velocity-dependant forces within a multi-component lattice Boltzmann equation simulation which is designed to recover continuum regime incompressible hydrodynamics. This method is applied to the problem, in two dimensions, of constraining to uniformity the tangential velocity of a vesicle membrane implemented within a recent multi-component lattice Boltzmann simulation method, which avoids the use of Lagrangian boundary tracers. The constraint of uniform tangential velocity is carried by an additional contribution to an immersed boundary force, which we derive here from physical arguments. The result of this enhanced immersed boundary force is to apply a physically appropriate boundary condition at the interface between separated lattice fluids, defined as that region over which the phase-field varies most rapidly. Data from this enhanced vesicle boundary method are in agreement with other data obtained using related methods (e.g. T. Krüger, S, Frijters, F. Günther, B. Kaoui and J. Harting, Eur. Phys. J. 222, 177 (2013)) ) and underscore the importance of a correct vesicle membrane condition

Chromodynamic multirelaxation-time lattice Boltzmann scheme for fluids with density difference

We develop, after Dellar ( P. J. Dellar, Phys. Rev. E. 65, 036309 (2002), J. Comput. Phys. 190, pp351 (2003)), a multiple-relaxation time (MRT), chromodynamic, multi-component lattice Boltzmann equation (MCLBE) scheme for simulation of isothermal, immiscible fluid flow with a density contrast. It is based on Lishchuk’s method (J. U. Brackbill, D. B. Kothe and C. Zemach, J. Comp. Phys. 100, 335-354 (1992), S. V. Lishchuk, C. M. Care and I. Halliday, Phys. Rev. E. 67(3), 036701(2), (2003)) and the segregation of d’Ortona et al. (U. D’Ortona, D. Salin, M. Cieplak, R. B. Rybka and J. R. Banavar Phys. Rev. E. 51, 3718, (1995)). We focus on fundamental model verifiability but do relate some of our data to that from previous approaches, due to Ba et al. (Y. Ba, H. Liu, Q. Li, Q. Kang and J. Sun, Phys. Rev. E 94, 023310 (2016)) and earlier Liu et al. (H. Liu, A. J. Valocchi and Q. Kang, Phys. Rev. E 85, 046309 (2012)), who pioneered large density difference chromodynamic MCLBE and showed the practical benefits of a MRT collision model. Specifically, we test the extent to which chromodynamic MCLBE MRT schemes comply with the kinematic condition of mutual impenetrability and the continuous traction condition by developing analytical benchmarking flows. We conclude that our data, taken with those of Ba et al., verify the utility of MRT chromodynamic MCLBE