Y. T. Chew

A lattice Boltzmann model for multiphase flows with large density ratio

a lattice Boltzmann model for simulating multiphase flows with large density ratios is described in this paper. The method is easily implemented. It does not require solving the Poisson equation and does not involve the complex treatments of derivative terms. The interface capturing equation is recovered without any additional terms as compared to other methods [M.R. Swift, W.R. Osborn, J.M. Yeomans, Lattice Boltzmann simulation of liquid-gas and binary fluid systems, Phys. Rev. E 54 (1996) 5041-5052; T. Inamuro, T. Ogata, S. Tajima, N. Konishi, A lattice Boltzmann method for incompressible two-phase flows with large density differences, J. Comput. Phys. 198 (2004) 628-644; T. Lee, C.-L. Lin, A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio, J. Comput. Phys. 206 (2005) 16-47]. Besides, it requires less discrete velocities. As a result, its efficiency could be greatly improved, especially in 3D applications. It is validated by several cases: a bubble in a stationary flow and the capillary wave. The numerical surface tension obtained from the Laplace law and the interface profile agrees very well with the respective analytical solution. The method is further verified by its application to capillary wave and the bubble rising under buoyancy with comparison to other methods. All the numerical experiments show that the present approach can be used to model multiphase flows with large density ratios.

A novel immersed boundary velocity correction-lattice Boltzmann method and its application to simulate flow past a circular cylinder

A novel immersed boundary velocity correction-lattice Boltzmann method is presented and validated in this work by its application to simulate the two-dimensional flow over a circular cylinder. The present approach is inspired from the conventional immersed boundary method (IBM). In the conventional IBM, the effect of rigid body on the surrounding flow is modeled through a forcing term, which is in turn used to correct the surrounding velocity field. It was found that this process is actually an iterative procedure, trying to satisfy the non-slip boundary condition at the solid wall. In this work, a new concept of immersed boundary velocity correction approach is proposed, which directly corrects the velocity to enforce the physical boundary condition. The main advantage of the new method is that it is simple in concept and easy for implementation, and the convergence of numerical computation is faster and more stable than the conventional IBM. One challenging issue of conventional IBM is that some streamlines may pass through the solid body since there is no mechanism to enforce the non-slip condition at the boundary. As shown in the present numerical results, this unphysical phenomenon is avoided in our new method since the non-slip condition is enforced. The present results for the steady and unsteady flows compare very well with available data in the literature.

A hybrid method to study flow-induced deformation of three-dimensional capsules

A hybrid method is proposed to study the transient deformation of liquid filled capsules with elastic membranes under flow. In this method, the immersed boundary concept is introduced into the framework of lattice Boltzmann method, and the multi-block strategy is employed to refine the mesh near the capsule to increase the accuracy and efficiency of computation. A finite element model is incorporated to obtain the forces acting on the membrane nodes of the three-dimensional capsule which is discretized into flat triangular elements. The present method was validated by studying the transient deformation of initially spherical and oblate-spheroidal capsules with various membrane constitutive laws under shear flow; and there were good agreements with previous theory or numerical results. The versatility of the present method was demonstrated by studying the effects of inertia on the deformation of capsules in shear flow; and the inertia effects were found to be significant. The transient deformation of capsules with initially biconcave discoid shape in shear flow was also studied. The unsteady tank-treading motion was observed, in which the capsule undergoes periodic shape deformation and inclination oscillation while its membrane is rotating around the liquid inside. To our knowledge, this motion of three-dimensional biconcave discoid capsules has not been fully recovered by numerical simulation so far.

Application of multi-block approach in the immersed boundary-lattice Boltzmann method for viscous fluid flows

The immersed boundary-lattice Boltzmann method was presented recently to simulate the rigid particle motion. It combines the desirable features of the lattice Boltzmann and immersed boundary methods. It uses a regular Eulerian grid for the flow domain and a Lagrangian grid for the boundary. For the lattice Boltzmann method, as compared with the single-relaxation-time collision scheme, the multi-relaxation-time collision scheme has better computational stability due to separation of the relaxations of various kinetic models, especially near the geometric singularity. So the multi-relaxation-time collision scheme is used to replace the single-relaxation-time collision scheme in the original immersed boundary-lattice Boltzmann method. In order to obtain an accurate result, very fine lattice grid is needed near the solid boundary. To reduce the computational effort, local grid refinement is adopted to offer high resolution near a solid body and to place the outer boundary far away from the body. So the multi-block scheme with the multi-relaxation-time collision model is used in the immersed boundary-lattice Boltzmann method. In each block, uniform lattice spacing can still be used. In order to validate the multi-block approach for the immersed boundary-lattice Boltzmann method with multi-relaxation-time collision scheme, the numerical simulations of steady and unsteady flows past a circular cylinder and airfoil are carried out and good results are obtained.

A new flow regime in a Taylor–Couette flow

In this Brief Communication, we report a new finding on a Taylor–Couette flow in which the outer cylinder is stationary and the inner cylinder is accelerated linearly from rest to a desired speed. The results show that when the acceleration (dRe/dt) is higher than a critical value of about 2.2u2002s−1, there exists a new flow regime in which the flow pattern shows remarkable resemblance to regular Taylor vortex flow but is of shorter wavelength. However, when the acceleration is lower than 2.2u2002s−1, a wavy flow is found to occur for the same Reynolds number range. To our knowledge, this is probably the first time that such a phenomenon has been observed. For completeness, the case of a decelerating cylinder is also investigated, and the results are found to be almost the same.

A LATTICE BOLTZMANN STUDY ON THE LARGE DEFORMATION OF RED BLOOD CELLS IN SHEAR FLOW

The transient deformation of a liquid-filled elastic capsule, simulating a red blood cell, was studied in simple shear flow. The simulation is based on a hybrid method which introduces the immersed boundary concept in the framework of the multi-block lattice Boltzmann model. The method was validated by the study on deformation of an initially circular capsule with Hookes membrane. Also studied were capsules with Skalak membrane of initially elliptical and biconcave shapes, which are more representative of a red blood cell. Membrane tank treading motion is observed. As the ratio between membrane dilation modulus and shear modulus increases, the capsule shows asymptotic behavior. For an initially elliptical capsule, it is found that the steady shape is independent of initial inclination angle. For an initially biconcave capsule, the tank treading frequency from two-dimensional modeling is comparable to that of real cells. Another interesting finding is that the tank treading velocity has not attained steady state when the capsule shape becomes steady; and at this state there is the internal vortex pair. The treading velocity continues to decrease and reaches a steady value when the internal vortex pair has developed into a single vortex.

A HYBRID VORTEX METHOD FOR FLOWS OVER A BLUFF BODY

A hybrid vortex method was developed to simulate the two-dimensional viscous incompressible flows over a bluff body numerically. It is based on a combination of the diffusion–vortex method and the vortex-in-cell method by dividing the flow field into two regions. In the region near the body surface the diffusion–vortex method is used to solve the Navier–Stokes equations, while the vortex-in-cell method is used in the exterior domain. Comparison with results obtained by the finite difference method, other vortex methods and experiments shows that the present method is well adapted to calculate two-dimensional external flows at high Reynolds number. It is capable of calculating not only the global characteristics of the separated flow but also the evolution of the fine structure of the flow field with time precisely. The influence of the grid system and region decomposition on the results will also be discussed.

A New Differential Lattice Boltzmann Equation and Its Application to Simulate Incompressible Flows on Non-Uniform Grids

A new differential lattice Boltzmann equation (LBE) is presented in this work, which is derived from the standard LBE by using Taylor series expansion only in spatial direction with truncation to the second-order derivatives. The obtained differential equation is not a wave-like equation. When a uniform grid is used, the new differential LBE can be exactly reduced to the standard LBE. The new differential LBE can be applied to solve irregular problems with the help of coordinate transformation. The present scheme inherits the merits of the standard LBE. The 2-D driven cavity flow is chosen as a test case to validate the present method. Favorable results are obtained and indicate that the present scheme has good prospects in practical applications.

A fractional step lattice Boltzmann method for simulating high Reynolds number flows

A fractional step lattice Boltzmann scheme is presented to greatly improve the stability of the lattice Boltzmann method (LBM) in modelling incompressible flows at high Reynolds number. This method combines the good features of the conventional LBM and the fractional step technique. Through the fractional step, the flow at an extreme case of infinite Reynolds number (inviscid flow) can be effectively simulated. In addition, the non-slip boundary condition can be directly implemented.

An object-oriented and quadrilateral-mesh based solution adaptive algorithm for compressible multi-fluid flows

In this paper, an object-oriented and quadrilateral-mesh based solution adaptive algorithm for the simulation of compressible multi-fluid flows is presented. The HLLC scheme (Harten, Lax and van Leer approximate Riemann solver with the Contact wave restored) is extended to adaptively solve the compressible multi-fluid flows under complex geometry on unstructured mesh. It is also extended to the second-order of accuracy by using MUSCL extrapolation. The node, edge and cell are arranged in such an object-oriented manner that each of them inherits from a basic object. A home-made double link list is designed to manage these objects so that the inserting of new objects and removing of the existing objects (nodes, edges and cells) are independent of the number of objects and only of the complexity of O(1). In addition, the cells with different levels are further stored in different lists. This avoids the recursive calculation of solution of mother (non-leaf) cells. Thus, high efficiency is obtained due to these features. Besides, as compared to other cell-edge adaptive methods, the separation of nodes would reduce the memory requirement of redundant nodes, especially in the cases where the level number is large or the space dimension is three. Five two-dimensional examples are used to examine its performance. These examples include vortex evolution problem, interface only problem under structured mesh and unstructured mesh, bubble explosion under the water, bubble-shock interaction, and shock-interface interaction inside the cylindrical vessel. Numerical results indicate that there is no oscillation of pressure and velocity across the interface and it is feasible to apply it to solve compressible multi-fluid flows with large density ratio (1000) and strong shock wave (the pressure ratio is 10,000) interaction with the interface.