Lattice Boltzmann Flux Solver: An Efficient Approach for Numerical Simulation of Fluid Flows
Lattice Boltzmann Flux Solver: An Efficient Approach for Numerical Simulation of Fluid Flows
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发表时间：
2014-03
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通讯作者：
Shu Chang;Yang Wang;M. YangL;J. Wu
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作者：
Shu Chang;Yang Wang;M. YangL;J. Wu
提出了一种用于模拟流体流动的格子玻尔兹曼通量求解器（LBFS）。与传统的计算流体动力学（CFD）求解器一样，新型求解器也应用有限体积法对控制微分方程进行离散化，但单元界面处的数值通量不是通过光滑函数近似或黎曼求解器来评估，而是通过单元界面处的格子玻尔兹曼方程（LBE）的局部解来评估。本文提出了两种版本的LBFS。一种是沿单元界面法线方向局部应用一维可压缩格子玻尔兹曼(LB)模型来模拟具有冲击波的可压缩无粘流。另一种是在单元界面上局部应用多维LB模型来模拟不可压缩粘性和无粘流。该求解器克服了传统格子玻尔兹曼方法(LBM)的缺点，如均匀网格的限制、网格间距和时间间隔的束缚、粘性的限制等。数值算例表明，该求解器可以很好地应用于模拟非均匀网格和弯曲边界的流体流动。
A lattice Boltzmann flux solver(LBFS)is presented for simulation of fluid flows.Like the conventional computational fluid dynamics(CFD)solvers,the new solver also applies the finite volume method to discretize the governing differential equations,but the numerical flux at the cell interface is not evaluated by the smooth function approximation or Riemann solvers.Instead,it is evaluated from local solution of lattice Boltzmann equation(LBE)at cell interface.Two versions of LBFS are presented in this paper.One is to locally apply one-dimensional compressible lattice Boltzmann(LB)model along the normal direction to the cell interface for simulation of compressible inviscid flows with shock waves.The other is to locally apply multi-dimensional LB model at cell interface for simulation of incompressible viscous and inviscid flows.The present solver removes the drawbacks of conventional lattice Boltzmann method(LBM)such as limitation to uniform mesh,tie-up of mesh spacing and time interval,limitation to viscous flows.Numerical examples show that the present solver can be well applied to simulate fluid flows with non-uniform mesh and curved boundary.