Kannan N. Premnath

Multigrid lattice Boltzmann method for accelerated solution of elliptic equations

A new solver for second-order elliptic partial differential equations (PDEs) based on the lattice Boltzmann method (LBM) and the multigrid (MG) technique is presented. Several benchmark elliptic equations are solved numerically with the inclusion of multiple grid-levels in two-dimensional domains at an optimal computational cost within the LB framework. The results are compared with the corresponding analytical solutions and numerical solutions obtained using the Stones strongly implicit procedure. The classical PDEs considered in this article include the Laplace and Poisson equations with Dirichlet boundary conditions, with the latter involving both constant and variable coefficients. A detailed analysis of solution accuracy, convergence and computational efficiency of the proposed solver is given. It is observed that the use of a high-order stencil (for smoothing) improves convergence and accuracy for an equivalent number of smoothing sweeps. The effect of the type of scheduling cycle (V- or W-cycle) on the performance of the MG-LBM is analyzed. Next, a parallel algorithm for the MG-LBM solver is presented and then its parallel performance on a multi-core cluster is analyzed. Lastly, a practical example is provided wherein the proposed elliptic PDE solver is used to compute the electro-static potential encountered in an electro-chemical cell, which demonstrates the effectiveness of this new solver in complex coupled systems. Several orders of magnitude gains in convergence and parallel scaling for the canonical problems, and a factor of 5 reduction for the multiphysics problem are achieved using the MG-LBM.

Comparative Study of the Large Eddy Simulations with the Lattice Boltzmann Method Using the Wall-Adapting Local Eddy-Viscosity and Vreman Subgrid Scale Models

The wall-adapting local eddy-viscosity (WALE) and Vreman subgrid scale models for large eddy simulations are compared within the framework of a generalised lattice Boltzmann method. Fully developed turbulent flows near a flat wall are simulated with the two models for the shear (or friction) Reynolds number of 183.6. Compared to the direct numerical simulation (DNS), damped eddy viscosity in the vicinity of the wall and a correct velocity profile in the transitional region are achieved by both the models without dynamic procedures. The turbulent statistics, including, e.g., root-mean-square velocity fluctuations, also agree well with the DNS results. The comparison also shows that the WALE model predicts excellent damped eddy viscosity near the wall.

ELECTRODEPOSITION MODELING USING COUPLED PHASE-FIELD AND LATTICE BOLTZMANN APPROACH

In this paper, a coupled phase-field (PF) and lattice Boltzmann method (LBM) is presented to model the multiphysics phenomenon involving electro-chemical deposition. The deposition (or dissolution) of the electrode is represented using variations of an order-parameter. The time-evolution of an order-parameter is proportional to the variation of a Ginzburg–Landau free-energy functional. Further, the free-energy densities of the two phases are defined based on a dilute or an ideal solution approximation. An efficient LBM is used to obtain the converged electro-static potential field for each physical time-step of the evolution of the PF variable. The coupled approach demonstrates the applicability of the LBM in a multiphysics scenario. The numerical validation for the coupled approach is performed by the simulation of the electrodeposition process of Cu from CuSO4 solution.

Computation of transitional flow past a circular cylinder using multiblock lattice Boltzmann method with a dynamic subgrid scale model

Lattice Boltzmann method (LBM) is a kinetic based numerical scheme for the simulation of fluid flow. While the approach has attracted considerable attention during the last two decades, there is a need for systematic investigation of its applicability for complex canonical turbulent flow problems of engineering interest, where the nature of the numerical properties of the underlying scheme plays an important role for their accurate solution. In this paper, we discuss and evaluate a LBM based on a multiblock approach for efficient large eddy simulation of three-dimensional external flow past a circular cylinder in the transitional regime characterized by the presence of multiple scales. For enhanced numerical stability at higher Reynolds numbers, a multiple relaxation time formulation is considered. The effect of subgrid scales is represented by means of a Smagorinsky eddy-viscosity model, where the model coefficient is computed locally by means of a dynamic procedure, providing better representation of flow physics with reduced empiricism. Simulations are performed for a Reynolds number of 3900 based on the free stream velocity and cylinder diameter for which prior data is available for comparison. The presence of laminar boundary layer which separates into a pair of shear layers that evolve into turbulent wakes impose particular challenge for numerical methods for this condition. The relatively low numerical dissipation introduced by the inherently parallel and second-order accurate LBM is an important computational asset in this regard. Computations using five different grid levels, where the various blocks are suitably aligned to resolve multiscale flow features show that the structure of the recirculation region is well reproduced and the statistics of the mean flow and turbulent fluctuations are in satisfactory agreement with prior data.

Surfactant effects on interfacial flow and thermal transport processes during phase change in film boiling

The presence of surfactants in two-phase flows results in the transport and adsorption of surfactants to the interface, and the resulting local interfacial concentration significantly influences the surface tension between the liquid and vapor phases in a fluid undergoing phase change. This computational study is aimed at understanding and elucidating the mechanisms of enhanced flows and thermal transport processes in film boiling due to the addition of surfactants. A change in surface tension results in a change in the critical Rayleigh-Taylor wavelength leading to different bubble release patterns and a change in the overall heat transfer rates. Due to the presence of surfactants, an additional transport mechanism of the Marangoni convection arises from the resulting tangential gradients in the surfactant concentration along the phase interface. Our computational approach to study such phenomena consists of representing the interfacial motion by means of the coupled level set-volume-of-fluid method, the fluid motion via the classical marker-and-cell approach, as well as representations for the bulk transport of energy and surfactants, in conjunction with a phase change model and an interfacial surfactant model. Using such an approach, we perform numerical simulations of surfactant-laden single mode as well as multiple mode film boiling and study the effect of surfactants on the transport processes in film boiling, including bubble release patterns, vapor generation rates, and heat transfer rates at different surfactant concentrations. The details of the underlying mechanisms will be investigated and interpreted.The presence of surfactants in two-phase flows results in the transport and adsorption of surfactants to the interface, and the resulting local interfacial concentration significantly influences the surface tension between the liquid and vapor phases in a fluid undergoing phase change. This computational study is aimed at understanding and elucidating the mechanisms of enhanced flows and thermal transport processes in film boiling due to the addition of surfactants. A change in surface tension results in a change in the critical Rayleigh-Taylor wavelength leading to different bubble release patterns and a change in the overall heat transfer rates. Due to the presence of surfactants, an additional transport mechanism of the Marangoni convection arises from the resulting tangential gradients in the surfactant concentration along the phase interface. Our computational approach to study such phenomena consists of representing the interfacial motion by means of the coupled level set-volume-of-fluid method, the...

Application of Coupled Lattice Boltzmann and Phase-Field Methods for Multiphase Flow Simulations

Coupling of lattice Boltzmann (LB) and phase-field (PF) methods is discussed for simulation of a range of multiphase flow problems. The local relaxation and shifting operators make the LB method an attractive candidate for the simulation of the single-phase as well as multiphase flows. For simulating interface dynamics, LB methods require to be coupled with an appropriate scheme representing interfacial dynamics. To this end, we have used a model based on the order parameter, which could be either an index function or a phase-field variable, and coupled it with a LB solver for the simulation of various classes of complex multi-physics and multiphase flows. The LB method is used to compute the flow-field, and, in the case of electrodeposition process modeling, the electro-static potential-field. The application of such a coupled LB-PF is illustrated by the solution of a variety of examples. Finally, fast simulation of such a coupled algorithm is achieved using the state-of-art numerical solution acceleration techniques involving preconditioning and multigrid approaches.Copyright