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Register a new userModified mass-conservative curved boundary scheme for lattice Boltzmann simulations
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The lattice Boltzmann (LB) method has gained much success in a variety of fields involving fluid flow and/or heat transfer. In this method, the bounce-back scheme is a popular boundary scheme for treating nonslip boundaries. However, this scheme leads to staircase-shaped boundaries for curved walls. Therefore many curved boundary schemes have been proposed, but mostly suffer from mass leakage at the curved boundaries. Several correction schemes have been suggested for simulating single-phase flows, but very few discussions or studies have been made for two-phase LB simulations with curved boundaries. In this paper, the performance of three well-known types of curved boundary schemes in two-phase LB simulations is investigated through modeling a droplet resting on a circular cylinder. For all of the investigated schemes, the results show that the simulated droplet rapidly evaporates under the nonslip and isothermal conditions, owing to the imbalance between the mass streamed out of the system by the outgoing distribution functions and the mass streamed into the system by the incoming distribution functions at each boundary node. Based on the numerical investigation, we formulate two modified mass-conservative curved boundary schemes for two-phase LB simulations. The accuracy of the modified curved boundary schemes and their capability of conserving mass in two-phase LB simulations are numerically demonstrated.
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This paper proposes an improved lattice Boltzmann scheme for incompressible axisymmetric flows. The scheme has the following features. First, it is still within the framework of the standard lattice Boltzmann method using the single-particle density distribution function and consistent with the philosophy of the lattice Boltzmann method. Second, the source term of the scheme is simple and contains no velocity gradient terms. Owing to this feature, the scheme is easy to implement. In addition, the singularity problem at the axis can be appropriately handled without affecting an important advantage of the lattice Boltzmann method: the easy treatment of boundary conditions. The scheme is tested by simulating Hagen-Poiseuille flow, three-dimensional Womersley flow, Wheeler benchmark problem in crystal growth, and lid-driven rotational flow in cylindrical cavities. It is found that the numerical results agree well with the analytical solutions and/or the results reported in previous studies.
The pseudopotential multiphase lattice Boltzmann (LB) model is a very popular model in the LB community for simulating multiphase flows. When the multiphase modeling involves a solid boundary, a numerical scheme is required to simulate the contact angle at the solid boundary. In this work, we aim at investigating the implementation of contact angles in the pseudopotential LB simulations with curved boundaries. In the pseudopotential LB model, the contact angle is usually realized by employing a solid-fluid interaction or specifying a constant virtual wall density. However, it is shown that the solid-fluid interaction scheme yields very large spurious currents in the simulations involving curved boundaries, while the virtual-density scheme produces an unphysical thick mass-transfer layer near the solid boundary although it gives much smaller spurious currents. We also extend the geometric-formulation scheme in the phase-field method to the pseudopotential LB model. Nevertheless, in comparison with the solid-fluid interaction scheme and the virtual-density scheme, the geometric-formulation scheme is relatively difficult to implement for curved boundaries and cannot be directly applied to three-dimensional space. By analyzing the features of these three schemes, we propose an improved virtual-density scheme to implement contact angles in the pseudopotential LB simulations with curved boundaries, which does not suffer from a thick mass-transfer layer near the solid boundary and retains the advantages of the original virtual-density scheme, i.e., simplicity, easiness for implementation, and low spurious currents.
We present a novel method for fluid structure interaction (FSI) simulations where an original 2nd-order curved space lattice Boltzmann fluid solver (LBM) is coupled to a finite element method (FEM) for thin shells. The LBM can work independently on a standard lattice in curved coordinates without the need for interpolation, re-meshing or an immersed boundary. The LBM distribution functions are transformed dynamically under coordinate change. In addition, force and momentum can be calculated on the nodes exactly in any geometry. Furthermore, the FEM shell is a complete numerical tool with implementations such as growth, self-contact and strong external forces. We show resolution convergent error for standard tests under metric deformation. Mass and volume conservation, momentum transfer, boundary-slip and pressure maintenance are verified through specific examples. Additionally, a brief deformation stability analysis is carried out. Next, we study the interaction of a square fluid flow channel to a deformable shell. Finally, we simulate a flag at moderate Reynolds number, air flow channel. The scheme is limited to small deformations of O(10%) relative to domain size, by improving its stability the method can be naturally extended to multiple applications without further implementations.
We develop and implement a novel lattice Boltzmann scheme to study multicomponent flows on curved surfaces, coupling the continuity and Navier-Stokes equations with the Cahn-Hilliard equation to track the evolution of the binary fluid interfaces. Standard lattice Boltzmann method relies on regular Cartesian grids, which makes it generally unsuitable to study flow problems on curved surfaces. To alleviate this limitation, we use a vielbein formalism to write down the Boltzmann equation on an arbitrary geometry, and solve the evolution of the fluid distribution functions using a finite difference method. Focussing on the torus geometry as an example of a curved surface, we demonstrate drift motions of fluid droplets and stripes embedded on the surface of a torus. Interestingly, they migrate in opposite directions: fluid droplets to the outer side while fluid stripes to the inner side of the torus. For the latter we demonstrate that the global minimum configuration is unique for small stripe widths, but it becomes bistable for large stripe widths. Our simulations are also in agreement with analytical predictions for the Laplace pressure of the fluid stripes, and their damped oscillatory motion as they approach equilibrium configurations, capturing the corresponding decay timescale and oscillation frequency. Finally, we simulate the coarsening dynamics of phase separating binary fluids in the hydrodynamics and diffusive regimes for tori of various shapes, and compare the results against those for a flat two-dimensional surface. Our lattice Boltzmann scheme can be extended to other surfaces and coupled to other dynamical equations, opening up a vast range of applications involving complex flows on curved geometries.
We show that, when a single relaxation time lattice Boltzmann algorithm is used to solve the hydrodynamic equations of a binary fluid for which the two components have different viscosities, strong spurious velocities in the steady state lead to incorrect results for the equilibrium contact angle. We identify the origins of these spurious currents, and demonstrate how the results can be greatly improved by using a lattice Boltzmann method based on a multiple-relaxation-time algorithm. By considering capillary filling we describe the dependence of the advancing contact angle on the interface velocity.
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