The effect of filter width ratio on the dynamicmodel对动态模型的滤波宽度比的影响.pptVIP

Introduction to classical large eddy simulation (LES) of turbulent flows Andrés E. Tejada-Martínez Center for Coastal Physical Oceanography Old Dominion University Outline Part I: Theory Part II: Computations Steps in large-eddy simulation (LES) Filtering in real space A filtered function is defined as: Examples of homogeneous filter kernels, , are Filtering attenuates scales less than and splits the function as Sketch of filtered energy spectra LES and other approaches For a turbulent flow, the Navier-Stokes (N-S) equations contain a large number of scales. While solving these equations numerically, the grid must contain a great number of points in order to represent (resolve) all of the scales present. In LES we filter the equations, thereby suppressing the smaller scales. With fewer scales, the filtered equations need less grid points. In direct numerical simulation (DNS) no filtering is performed, as the simulation attempts to represent all scales down to the dissipative ones In Reynolds-averaged N-S simulation (RANSS), we solve the ensemble-averaged N-S. Averaging suppresses all of the scales except for the largest, thus RANSS requires much fewer grid points than LES and DNS. LES resolves many more scales than RANSS, but not as many as DNS. Unfiltered equations Unfiltered equations Filtered equations Filtered equations Filtered equations Sketch of energy spectrum in LES Sketch of energy spectrum in LES Sketch of energy spectrum in LES Role of discretization in LES Dynamic Smagorinsky model Dynamic Smagorinsky model Dynamic Smagorinsky model LES methodology used in computations Horizontal derivatives (in x and y) are treated spectrally Vertical (z-) derivatives are treated with 6th or 5th order implicit stencils To prevent spurious high wavenumber content not resolvable by the grid, advection terms are: The high order accuracy of this discretization allows for it to b