Development of an immersed boundary-phase field-lattice Boltzmann method for Neumann boundary condition to study contact line dynamics

2013 ◽  
Vol 234 ◽  
pp. 8-32 ◽  
Author(s):  
J.Y. Shao ◽  
C. Shu ◽  
Y.T. Chew
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Contact Line ◽  
Phase Field ◽  
Lattice Boltzmann ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Boundary Phase ◽  
Immersed Boundary ◽  
Boltzmann Method

A phase-field-based lattice Boltzmann method for moving contact line problems on curved stationary boundaries in two dimensions

2019 ◽  
Vol 30 (06) ◽  
pp. 1950044
Author(s):  
Weifeng Zhao
Keyword(s):  
Boundary Conditions ◽  
Lattice Boltzmann Method ◽  
Contact Line ◽  
Phase Field ◽  
Lattice Boltzmann ◽  
Two Dimensions ◽  
Curved Boundaries ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Boltzmann Method

In this work, we propose a phase-field-based lattice Boltzmann method to simulate moving contact line (MCL) problems on curved boundaries. The key point of this method is to implement the boundary conditions on curved solid boundaries. Specifically, we use our recently proposed single-node scheme for the no-slip boundary condition and a new scheme is constructed to deal with the wetting boundary conditions (WBCs). In particular, three kinds of WBCs are implemented: two wetting conditions derived from the wall free energy and a characteristic MCL model based on geometry considerations. The method is validated with several MCL problems and numerical results show that the proposed method has utility for all the three WBCs on both straight and curved boundaries.

Contact Line Dynamics in Liquid-Vapor Flows Using Lattice Boltzmann Method

2006 ◽  
Author(s):  
Shi-Ming Li ◽  
Danesh K. Tafti
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Contact Line ◽  
Lattice Boltzmann ◽  
Solid Wall ◽  
Hydrodynamic Theory ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Boltzmann Method ◽  
Contact Line Dynamics

A mean-field free-energy lattice Boltzmann method (LBM) is applied to simulate moving contact line dynamics. It is found that the common bounceback boundary condition leads to an unphysical velocity at the solid wall in the presence of surface forces. The magnitude of the unphysical velocity is shown proportional to the local force term. The velocity-pressure boundary condition is generalized to solve the problem of the unphysical velocity. The simulation results are compared with three different theories for moving contact lines, including a hydrodynamic theory, a molecular kinetic theory, and a linear cosine law of moving contact angle versus capillary number. It is shown that the current LBM can be used to replace the three theories in handling moving contact line problems.

A HYBRID PHASE-FIELD BASED LATTICE BOLTZMANN METHOD FOR CONTACT LINE DYNAMICS

2012 ◽  
Vol 19 ◽  
pp. 50-61
Author(s):  
JIANG YAN SHAO ◽  
CHANG SHU ◽  
YONG TIAN CHEW
Keyword(s):  
Lattice Boltzmann Method ◽  
Contact Line ◽  
Phase Field ◽  
Lattice Boltzmann ◽  
Solution Process ◽  
Droplet Spreading ◽  
Interface Evolution ◽  
Cahn Hilliard Equation ◽  
Boltzmann Method ◽  
Contact Line Dynamics

A hybrid phase-field based lattice Boltzmann method (LBM) is proposed in this paper to simulate the contact line dynamics. The flow field is obtained through the lattice Boltzmann equation (LBE). Concurrently, the interface capturing is accomplished by directly solving Cahn-Hilliard equation, which is the governing equation of interface evolution. A symmetric spatial discretization scheme is adopted to enhance the stability. Compared with the conventional algorithms which solve two sets of LBEs, the present method has several advantages such as reduction of the number of variables in the solution process, decoupling the mobility with relaxation time and enabling a more direct manner to implement wetting boundary conditions. The proposed algorithm is first validated through recovering the analytical profile of a surface layer. It is then applied to simulate droplet spreading on surfaces with different wettability.

A Boundary Condition-Implemented Immersed Boundary-Lattice Boltzmann Method and Its Application for Simulation of Flows Around a Circular Cylinder

2014 ◽  
Vol 6 (06) ◽  
pp. 811-829 ◽  
Author(s):  
X. Wang ◽  
C. Shu ◽  
J. Wu ◽  
L. M. Yang
Keyword(s):  
Boundary Condition ◽  
Circular Cylinder ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Delta Function ◽  
Slip Boundary Condition ◽  
Immersed Boundary ◽  
First Order ◽  
Slip Boundary ◽  
Boltzmann Method

AbstractA boundary condition-implemented immersed boundary-lattice Boltzmann method (IB-LBM) is presented in this work. The present approach is an improvement to the conventional IB-LBM. In the conventional IB-LBM, the no-slip boundary condition is only approximately satisfied. As a result, there is flow penetration to the solid boundary. Another drawback of conventional IB-LBM is the use of Dirac delta function interpolation, which only has the first order of accuracy. In this work, the no-slip boundary condition is directly implemented, and used to correct the velocity at two adjacent mesh points from both sides of the boundary point. The velocity correction is made through the second-order polynomial interpolation rather than the first-order delta function interpolation. Obviously, the two drawbacks of conventional IB-LBM are removed in the present study. Another important contribution of this paper is to present a simple way to compute the hydrodynamic forces on the boundary from Newton’s second law. To validate the proposed method, the two-dimensional vortex decaying problem and incompressible flow over a circular cylinder are simulated. As shown in the present results, the flow penetration problem is eliminated, and the obtained results compare very well with available data in the literature.

scholarly journals Simulation of Thermal Flow Problems via a Hybrid Immersed Boundary-Lattice Boltzmann Method

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
J. Wu ◽  
C. Shu ◽  
N. Zhao
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Heat Source ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Source Term ◽  
Immersed Boundary ◽  
Thermal Flow ◽  
Flow Problems ◽  
Boltzmann Method

A hybrid immersed boundary-lattice Boltzmann method (IB-LBM) is presented in this work to simulate the thermal flow problems. In current approach, the flow field is resolved by using our recently developed boundary condition-enforced IB-LBM (Wu and Shu, (2009)). The nonslip boundary condition on the solid boundary is enforced in simulation. At the same time, to capture the temperature development, the conventional energy equation is resolved. To model the effect of immersed boundary on temperature field, the heat source term is introduced. Different from previous studies, the heat source term is set as unknown rather than predetermined. Inspired by the idea in (Wu and Shu, (2009)), the unknown is calculated in such a way that the temperature at the boundary interpolated from the corrected temperature field accurately satisfies the thermal boundary condition. In addition, based on the resolved temperature correction, an efficient way to compute the local and average Nusselt numbers is also proposed in this work. As compared with traditional implementation, no approximation for temperature gradients is required. To validate the present method, the numerical simulations of forced convection are carried out. The obtained results show good agreement with data in the literature.

A Unified Wall-Boundary Condition for the Lattice Boltzmann Method and its Application to Force Evaluation

2014 ◽  
Vol 31 (1) ◽  
pp. 55-68 ◽  
Author(s):  
S.-Y. Lin ◽  
Y.-H. Chin ◽  
F.-L. Yang ◽  
J.-F. Lin ◽  
J.-J. Hu ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Solid Wall ◽  
Immersed Boundary ◽  
Equilibrium Pressure ◽  
Good Convergence ◽  
Wall Boundary Condition ◽  
Wall Boundary ◽  
Boltzmann Method

AbstractA unified wall-boundary condition for the pressure-based lattice Boltzmann method (LBM) is proposed. The present approach is developed from the direct-forcing technique in the immersed boundary method and is derived from the equilibrium pressure distribution function. The proposed method can handle many kinds of wall boundaries, such as fixed wall and moving wall boundaries, in the same way. It is found that the new method has the following advantages: (1) simple in concept and easy to implement, (2) higher-order accuracy, (3) mass conservation, and (4) a stable and good convergence rate. Based on this wall-boundary condition, if a solid wall is immersed in a fluid, then by applying Gauss's theorem, the formulas for computing the force and torque acting on the solid wall from fluid flow are derived from the volume integrals over the solid volume instead of from the surface integrals over the solid surface. Based on the pressure-based LBM, inlet and outlet boundary conditions are also proposed. The order of accuracy of the proposed boundary condition is demonstrated with the errors of the velocity field, wall stress, and gradients of velocity and pressure. The steady flow past a circular cylinder is simulated to demonstrate the efficiency and capabilities of the proposed unified method.

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