晶格波茲曼方法應用於雙相流問題之數值穩定性分析

NUMERICAL STABILITY ANALYSIS OF TWO-PHASE FLOW BASE ON LATTICE BOLTZMANN METHOD

本文基於晶格波茲曼方法(Lattice Boltzmann method，LBM)之Lee-Lin[1]模型，於方向導數上使用Lax-Wendroff與Beam-Warming的混合差分格式，並加入MUSCL格式做為自適應人工耗散(adaptive artificial dissipation)項求解具高密度差之雙相流不穩定性問題。於巨觀物理量計算上使用濾波因子，將密度與壓力做重新計算，以減少數值不穩定產生非物理性的假震盪。驗證演算法使用Kelvin-Helmholtz和Rayleigh-Taylor不穩定性問題為計算範例，測試在不同密度比與橫向、縱向擾動下，分析流場之不穩定性。計算結果顯示，加入混合差分格式與濾波因子法應用計算雙相流問題，可提升數值計算方法之穩定性。

This paper develops a Lattice Boltzmann Method (LBM) for multiphase flows based on the Lee-Lin [1] model using a hybrid scheme of Lax-Wendroff and Beam-Warming for the directional derivatives and adding the MUSCL format as the adaptive artificial dissipation term of Boltzmann method kinetic model. In calculating macroscopic physical quantities, a filtering factor method recalculates the density and pressure to reduce the false oscillations caused by the unstable values. The Kelvin-Helmholtz and Rayleigh-Taylor instability are used as examples to verify the stability of the calculated flow field under different density ratios and transverse and longitudinal perturbations. The results show that using the mixed difference format and the filter factor method can make the calculation more stable in flow conditions with strong shear.