<p>The Lattice Boltzmann Method (LBM), a weakly compressible approach, has attracted considerable attention for turbulent flow simulations but remains limited in high-Reynolds-number applications due to its reliance on uniform meshes. This study investigates the interpolation-based Lattice Boltzmann Method (IBLBM) for direct numerical simulation (DNS) of turbulent channel and duct flows using nonuniform grids. Simulations are conducted for turbulent Poiseuille channel flows at <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10494_2025_689_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="171" /> </InlineMediaObject> <EquationSource Format="TEX">\(\boldsymbol{Re_{\tau} = 180, 395, 640},\)</EquationSource> </InlineEquation> and <b>1000</b>, as well as for turbulent duct flow at <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10494_2025_689_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="90" /> </InlineMediaObject> <EquationSource Format="TEX">\(\boldsymbol{Re_{\tau} = 360}\)</EquationSource> </InlineEquation>. The predicted mean velocity profiles, Reynolds stresses, vorticity distributions, and turbulent kinetic energy budgets show excellent agreement with benchmark DNS data. The IBLBM scheme accurately resolves near-wall turbulence and secondary flow structures in ducts while maintaining similar computational overhead across different interpolation orders. For the 7- and 200-million-grid cases at <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10494_2025_689_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="90" /> </InlineMediaObject> <EquationSource Format="TEX">\(\boldsymbol{Re_{\tau} = 180}\)</EquationSource> </InlineEquation> and 640, LBM with <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10494_2025_689_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="65" /> </InlineMediaObject> <EquationSource Format="TEX">\(\boldsymbol{\Delta^+ \sim 3}\)</EquationSource> </InlineEquation> is approximately 1.9 and 3.7 times faster, respectively, than sixth-order IBLBM; however, to match IBLBMs wall resolution (<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10494_2025_689_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="80" /> </InlineMediaObject> <EquationSource Format="TEX">\(\boldsymbol{\Delta^+ \sim 0.3}\)</EquationSource> </InlineEquation>) using <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10494_2025_689_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="65" /> </InlineMediaObject> <EquationSource Format="TEX">\(\boldsymbol{\Delta^+ \sim 1}\)</EquationSource> </InlineEquation>, LBM becomes four to six times slower. These results demonstrate the robustness and accuracy of IBLBM for high-Reynolds-number wall-bounded turbulence, offering an optimal balance between computational efficiency and physical fidelity through the use of nonuniform grids.</p>

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Direct Numerical Simulations of Turbulent Channel and Duct Flows Using Interpolation-Based Lattice Boltzmann Method

  • Bo-Xiao Jin,
  • Sheng-Wei Feng,
  • Yi-Han Chiu,
  • Chao-An Lin

摘要

The Lattice Boltzmann Method (LBM), a weakly compressible approach, has attracted considerable attention for turbulent flow simulations but remains limited in high-Reynolds-number applications due to its reliance on uniform meshes. This study investigates the interpolation-based Lattice Boltzmann Method (IBLBM) for direct numerical simulation (DNS) of turbulent channel and duct flows using nonuniform grids. Simulations are conducted for turbulent Poiseuille channel flows at \(\boldsymbol{Re_{\tau} = 180, 395, 640},\) and 1000, as well as for turbulent duct flow at \(\boldsymbol{Re_{\tau} = 360}\) . The predicted mean velocity profiles, Reynolds stresses, vorticity distributions, and turbulent kinetic energy budgets show excellent agreement with benchmark DNS data. The IBLBM scheme accurately resolves near-wall turbulence and secondary flow structures in ducts while maintaining similar computational overhead across different interpolation orders. For the 7- and 200-million-grid cases at \(\boldsymbol{Re_{\tau} = 180}\) and 640, LBM with \(\boldsymbol{\Delta^+ \sim 3}\) is approximately 1.9 and 3.7 times faster, respectively, than sixth-order IBLBM; however, to match IBLBMs wall resolution ( \(\boldsymbol{\Delta^+ \sim 0.3}\) ) using \(\boldsymbol{\Delta^+ \sim 1}\) , LBM becomes four to six times slower. These results demonstrate the robustness and accuracy of IBLBM for high-Reynolds-number wall-bounded turbulence, offering an optimal balance between computational efficiency and physical fidelity through the use of nonuniform grids.