Second Order Bounce Back Boundary Condition for the Latice Boltzmann Fluid Simulation

Kim, In-Chan The Korean Society of Mechanical Engineers 2000 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.14 No.1

A new bounce back boundary method of the second order in error is proposed for the lattice Boltzmann fluid simulation. This new method can be used for the arbitrarily irregular lattice geometry of a non-slip boundary. The traditional bounce back boundary condition for the lattice Boltzmann simulation is of the first order in error. Since the lattice Boltzmann method is the second order scheme by itself, a boundary technique of the second order has been desired to replace the first order bounce back method. This study shows that, contrary to the common belief that the bounce back boundary condition is unilaterally of the first order, the second order bounce back boundary condition can be realized. This study also shows that there exists a generalized bounce back technique that can be characterized by a single interpolation parameter. The second order bounce back method can be obtained by proper selection of this parameter in accordance with the detailed lattice geometry of the boundary. For an illustrative purpose, the transient Couette and the plane Poiseuille flows are solved by the lattice Boltzmann simulation with various boundary conditions. The results show that the generalized bounce back method yields the second order behavior in the error of the solution, provided that the interpolation parameter is properly selected. Coupled with its intuitive nature and the ease of implementation, the bounce back method can be as good as any second order boundary method.

Lattice Boltzmann 방법을 사용한 층류 및 난류 해석

최석기(Seok-Ki Choi),김성오(Seong-O Kim) 한국전산유체공학회 2010 한국전산유체공학회 학술대회논문집 Vol.2010 No.11

A finite volume formulation commonly employed in the well-known SIMPLE family algorithms is used to discretize the lattice Boltzmann euqations on a cell-centered, non-uniform grid. The convection terms are treated by a higher-order bounded scheme to ensure accuracy and stability of solutions, especially in the simulation of turbulent flows. The source terms are linearized by a convetional method, and the resulted algebraic equations are solved by a strongly implicit procedure. The method is applied to the a laminar flow and atubulent flow. The predicted solutions are compared with the experimental data, benchmark solution and the solutions by the conventional finite volume method. The results of these numerical experiments for laminar flow show that the present formulation of the lattice Bolzmann method is slightly more diffusive than finite volume method when the same numerical grid and convection scheme are used. For a turbulent flow the finite volume lattice Boltzmann method slightly under-predicts the reattachment length in a separated flow. In general the finite volume lattice Boltzmann method is as acurate as the conventional finite volume method in predicting the mean velocity and the pressure at the wall. These observations show that the present method is stable and accurate enough to be used in the practical simulations of laminar and tubulent flows.

Lattice Boltzmann 방법을 사용한 자연대류 해석에서 열모델의 선택에 관한 연구

최석기(Seok-Ki Choi),김성오(Seong-O Kim) 한국전산유체공학회 2011 한국전산유체공학회지 Vol.16 No.4

A comparative analysis of thermal models in the lattice Boltzmann method(LBM) for the simulation of laminar natural convection in a square cavity is presented. A HYBRID method, in which the thermal equation is solved by the Navier-Stokes equation method while the mass and momentum conservation are resolved by the lattice Boltzmann method, is introduced and its merits are explained. All the governing equations are discretized on a cell-centered, non-uniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with a deferred correction method to ensure stability of the solutions. The HYBRID method and the double ?population method are applied to the simulation of natural convection in a square cavity and the predicted results are compared with the benchmark solutions given in the literatures. The predicted results are also compared with those by the conventional Navier-Stokes equation method. In general, the present HYBRID method is as accurate as the Navier-Stokes equation method and the double-population method. The HYBRID method shows better convergence and stability than the double-population method. These observations indicate that this HYBRID method is an efficient and economic method for the simulation of incompressible fluid flow and heat transfer problem with the LBM.

Lattice Boltzmann 방법을 사용한 층류 및 난류 자연대류 해석

최석기(Seok-Ki Choi),김성오(Seong-O Kim) 한국전산유체공학회 2011 한국전산유체공학회 학술대회논문집 Vol.2011 No.11

A study on the computation of laminar and turbulent natural convection with the lattice Boltzmann method(LBM) is presented. First, a comparative analysis of thermal models in the LBM for the simulation of natural convection in enclosures is presented. A HYBRID method, in which the thermal equation is solved by the Navier-Stokes equation method while the mass and momentum conservation are resolved by the LBM, is introduced and its merits are explained. All the governing equations are discretized on a cell-centered, non-uniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with a deferred correction method to ensure stability of the solutions. The HYBRID and double-population LBM are applied to the simulation of laminar natural convection in square cavity and the predicted results are compared with the benchmark solutions given in the literatures. The predicted results are also compared with those by the Navier-Stokes equation method. In general, the present HYBRID method is as accurate as the Navier-Stokes equation method and the double-population LBM. The HYBRID method shows better convergence and stability than the double-population LBM. The present HYBRID LBM is also applied to the prediction of a turbulent natural convection in a rectangular cavity and the computed results are compared with the experimental data. The elliptic-relaxation model is employed for the turbulence model and the turbulent heat fluxes are treated by the algebraic flux model. It is shown that the LBM with the present HYBRID thermal model predicts the mean velocity components and turbulent quantities accurately which are as good as those by the conventional finite-volume method.

단순격자볼츠만법에서 거시적변수들을 기반으로 한 대류경계조건 적용

이현균(H. Lee),이용준(Y. Lee),이주희(J. Lee) 한국전산유체공학회 2021 한국전산유체공학회지 Vol.26 No.2

Recently, researchers have developed simple lattice Boltzmann method without evolution of distribution functions. The method has an advantage that physical boundary conditions can be implemented directly. Taking the advantage, we implement a convection boundary scheme to the simple lattice Boltzmann method. This boundary scheme is derived from an assumption that the convection heat flux is equal to the conduction heat flux. Then, the heat transfer coefficient can be expressed by the thermal conductivity. Using the coefficients, the wall temperature is set directly on the boundary condition of simple lattice Boltzmann method unlike convectional lattice Boltzmann method. For verifications and validations, we apply our scheme to three cases in a row. First of all, we compute a natural convection in a square cavity for validation of simple lattice Boltzmann method. Secondly, the convection boundary scheme is applied to steady one-dimension heat conduction on a solid. Lastly, we simulate a square cavity with the convection boundary scheme. In this case, we assume that the boundary is thin. Our result is compared with commercial solver, FLUENT. The results show that the convection boundary scheme used in this study can be applied to the simple lattice Boltzmann method.

유한체적법 기반의 격자 볼츠만 해석 기법을 이용한 이차원 압축성 점성 유동 해석

양태호(T.H. Yang),권오준(O.J. Kwon) 한국전산유체공학회 2018 한국전산유체공학회지 Vol.23 No.2

This paper presents a finite-volume based lattice Boltzmann method for simulation of full compressible flows with flexible Prandtl number. The equilibrium distribution function is replaced with circular function where all mass, momentum, and energy is equally distributed along a circle. Two different density distribution functions are newly introduced to develop lattice Boltzmann model for compressible viscous flows. The equilibrium distribution function for the evolution equations can be derived from the integration of the Lagrangian interpolation polynomial, which depends on the configurations of the lattice model in the velocity phase space. Two-dimensional compressible flows in a shock tube were investigated to verify the accuracy of the current lattice Boltzmann method. The lattice Boltzmann method based on circular function was successfully adopted to two-dimenstional unsteady simulations with strong contact discontinuities. The present lattice Boltzmann code is applied to the subsonic laminar flow over an NACA0012 airfoil, and the computed results show fair agreement with the Navier-Stokes solution. The hypersonic flow passing through a cylinder is selected as a test case to verify the performances of the current lattice Boltzmann approach. The present solver gives a reasonable agreement with the continuum-based simulation results for flows including detached normal shock wave near the leading edge. Our results imply that the replacement of the Maxwellian distribution function with circular function may be the suitable approach for the evaluation of compressible viscous flows.

격자 볼츠만 기법을 이용한 선체 부가물 유동소음해석

여상재,홍석윤,송지훈,권현웅 해양환경안전학회 2020 해양환경안전학회지 Vol.26 No.6

The flow noise generated by hull appendages is directly related to the performance of the sonar in terms of self-noise and induces a secondary noise source through interaction with the propeller and rudder. Thus, the noise in the near field should be analyzed accurately. However, the acoustic analogy method is an indirect method that is not used to simulate the propagation of an acoustic signal directly; therefore, diffraction, reflection, and scattering characteristics cannot be considered, and near-field analysis is limited. In this study, the propagation process of flow noise in water was directly simulated by using the lattice Boltzmann method. The lattice Boltzmann method could be used to analyze flow noise by simulating the collision and streaming processes of molecules, and it is suitable for noise analysis because of its compressibility, low dissipation rate, and low dispersion rate characteristics. The flow noise source was derived using Reynolds-averaged Navier-Stokes equations for the hull appendages, and the propagation process of the flow noise was directly simulated using the lattice Boltzmann method by applying the developed flow-acoustic boundary conditions. The derived results were compared with Ffowcs Williams-Hawkings results and hydrodynamic pressure results based on the receiver location to verify the usefulness of the lattice Boltzmann method within the near-field range in comparison with other techniques. 선체 부가물에서 발생하는 유동소음은 자체소음 관점에서 소나의 성능과 직결되고, 추진기 및 방향타와 상호작용을 통해 2차 소음원을 야기해 근접장 범위의 엄밀한 분석이 요구된다. 하지만 유동소음 해석에 적용되는 기존의 음향상사법은 음향 신호의 전파를 직접 모사하지 않는 간접법에 해당해 회절, 반사, 산란 특성을 고려할 수 없으며, 근접장 해석이 제한적이다. 본 연구에서는 격자 볼츠만 기법을 적용해 수중환경 유동소음의 전파과정을 직접 모사하였다. 격자 볼츠만 기법은 분자의 충돌과 흐름 과정을 통해 유동소음을 해석하는 기법으로, 압축성과 낮은 소산율, 낮은 분산율의 특성을 가지고 있어 소음해석에 적합하다. 선체 부가물 형상을 대상으로 RANS 해석을 통해 유동소음원을 도출하고, 유동-음향 경계면을 적용한 격자 볼츠만 기법으로 유동소음의 전파과정을 직접적으로 모사했다. 도출된 결과를 수음점의 위치에 따라 FW-H 결과 및 유체동압력 결과와 비교를 통해 근접장에서 타 기법 대비 격자 볼츠만 기법의 유용성을 확인했다.

가상 경계 유한 차분 격자 볼츠만 법을 이용한 2 차원 열유동에 관한 수치적 연구

양희주(Hui-Ju Yang),정해권(Hae-Kwon Jeong),김래성(Lae-Sung Kim),하만영(Man-Yeong Ha) 대한기계학회 2007 대한기계학회 춘추학술대회 Vol.2007 No.10

In this paper, we performed thermal applications to implementing Immersed boundary in the Finite difference lattice Boltzmann method. The immersed boundary method uses the Lagrangian grid which represents the particles in the flow, whereas the lattice Boltzmann method is based on Eulerian grid. For a consideration of the coupling the immersed boundary method and the finite difference lattice Boltzmann equation, we used an equilibrium velocity scheme. The coupling method which many researchers used is not easy to apply the thermal application using the finite difference lattice Boltzmann method. However when the equilibrium velocity scheme is adopted, the thermal problem can be easily treated using a double population method. The results of the numerical simulations of a flow around a circular cylinder agreed well with benchmark data.

Lattice Boltzmann Method과 Smoothed Profile Method을 이용한 동심원의 자연대류 시뮬레이션

Suresh Alapati 한국기계기술학회 2017 한국기계기술학회지 Vol.19 No.2

In this work, the natural convection in an annulus between two concentric cylinders is studied numerically. The fluid flow between the cylinders is solved by the lattice Boltzmann method (LBM) while a separate finite difference method (FDM) is used to solve the heat transfer. No-slip and constant boundary conditions at curved boundaries of the cylinders are treated with a smoothed profile method (SPM). At first, the velocity and temperature profiles obtained from the present LBM-SPM and FDM-SPM are validated with the corresponding theoretical results. Later, natural convection simulations inside the annulus are performed using coupled scheme of LBM-FDM-SPM by varying Ra in the range Ra=1000, Ra=10000, Ra=50000, and Ra=100000. From the temperature and fluid flow patterns obtained at different Ra, it is found that the heat transfer is mainly dominated by conduction process when Ra is low and by convection process when Ra is high.

Lattice Boltzmann Method과 Smoothed Profile Method을 이용한 동심원의 자연대류 시뮬레이션

수레쉬 알라파티 한국기계기술학회 2017 한국기계기술학회지 Vol.19 No.2

In this work, the natural convection in an annulus between two concentric cylinders is studied numerically. The fluid flow between the cylinders is solved by the lattice Boltzmann method (LBM) while a separate finite difference method (FDM) is used to solve the heat transfer. No-slip and constant boundary conditions at curved boundaries of the cylinders are treated with a smoothed profile method (SPM). At first, the velocity and temperature profiles obtained from the present LBM-SPM and FDM-SPM are validated with the corresponding theoretical results. Later, natural convection simulations inside the annulus are performed using coupled scheme of LBM-FDM-SPM by varying Ra in the range Ra=1000, Ra=10000, Ra=50000, and Ra=100000. From the temperature and fluid flow patterns obtained at different Ra, it is found that the heat transfer is mainly dominated by conduction process when Ra is low and by convection process when Ra is high.