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.

An Efficient Immersed Boundary-Lattice Boltzmann Method for the Simulation of Thermal Flow Problems

2016 ◽  
Vol 20 (5) ◽  
pp. 1210-1257 ◽  
Author(s):  
Yang Hu ◽  
Decai Li ◽  
Shi Shu ◽  
Xiaodong Niu
Keyword(s):  
Natural Convection ◽  
Boundary Conditions ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Immersed Boundary Method ◽  
Immersed Boundary ◽  
Thermal Flow ◽  
Flow Problems ◽  
Thermal Boundary Conditions ◽  
Boltzmann Method

AbstractIn this paper, a diffuse-interface immersed boundary method (IBM) is proposed to treat three different thermal boundary conditions (Dirichlet, Neumann, Robin) in thermal flow problems. The novel IBM is implemented combining with the lattice Boltzmann method (LBM). The present algorithm enforces the three types of thermal boundary conditions at the boundary points. Concretely speaking, the IBM for the Dirichlet boundary condition is implemented using an iterative method, and its main feature is to accurately satisfy the given temperature on the boundary. The Neumann and Robin boundary conditions are implemented in IBM by distributing the jump of the heat flux on the boundary to surrounding Eulerian points, and the jump is obtained by applying the jump interface conditions in the normal and tangential directions. A simple analysis of the computational accuracy of IBM is developed. The analysis indicates that the Taylor-Green vortices problem which was used in many previous studies is not an appropriate accuracy test example. The capacity of the present thermal immersed boundary method is validated using four numerical experiments: (1) Natural convection in a cavity with a circular cylinder in the center; (2) Flows over a heated cylinder; (3) Natural convection in a concentric horizontal cylindrical annulus; (4) Sedimentation of a single isothermal cold particle in a vertical channel. The numerical results show good agreements with the data in the previous literatures.

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.

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.

SIMPLIFIED FINITE DIFFERENCE THERMAL LATTICE BOLTZMANN METHOD

2008 ◽  
Vol 22 (22) ◽  
pp. 3865-3876 ◽  
Author(s):  
C. S. NOR AZWADI ◽  
T. TANAHASHI
Keyword(s):  
Temperature Field ◽  
Finite Difference ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Square Cavity ◽  
Flow Problems ◽  
Finite Difference Technique ◽  
Thermal Fluid Flow ◽  
Boltzmann Method ◽  
Thermal Lattice Boltzmann

In this paper, a well-known finite difference technique is combined with thermal lattice Boltzmann method to solve 2-dimensional incompressible thermal fluid flow problems. A small number of microvelocity components are applied for the calculation of temperature field. The combination of finite difference with lattice Boltzmann method is found to be an efficient and stable approach for the simulation at high Rayleigh number of natural convection in a square cavity.

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