Large Eddy Simulation for Turbulence Modeling
Research Title: LES for modeling and understanding the complex flow physics in turbulence.
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Supervisor: Dr. Omer San, Oklahoma State University.
Goal: Developing computationally more efficient and accurate LES algorithms to solve the system of Euler or Navier-Stokes equations for turbulent flow problems.
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Summary: In this work, we mostly worked on upwind-biased implicit LES schemes (improved WENO-Z reconstruction with Roe, Rusanov, AUSM, HLL, HLLC Riemann solvers), explicit LES schemes (approximate deconvolution, 6th order central schemes combined with relaxation filtering) and eddy viscosity models (Smagorinsky, dynamic Smagorinsky and scale similarity models). Based on their merits, we worked on various test filters for LES, for example, Gaussian filter, box filter, sharp cut-off filter, compact Padé filter, and so on. Following are some of the published works on our LES research:
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An optimized filtering kernel for LES: In general, filtering kernel, numerical approach, and specified grid resolution are free modeling parameters in any LES model. Since most of the state-of-the-art closure model requires specification of a low-pass filter, a consistent implementation of these filters becomes increasingly important for accurate LES computations in engineering applications. In this work, we propose an optimization framework to design a family of discrete filters with a consistent definition of modeling parameter and desired full attenuation property on the resolved grid. Later, we developed a localized form of the dynamic eddy viscosity model for computationally more efficient and accurate simulation of the turbulent flows governed by Euler equations. For details, please refer to Rahman and San, 2019.
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Figure: Transfer functions of the optimized low-pass spatial filter designed for proposed localized dynamic eddy viscosity models. Regular Gaussian filters (Left) and Optimized Gaussian filters (Right).
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A relaxation filtering approach for 2D Rayleigh-Taylor instability: In this work, we investigate the performance of a relaxation filtering approach for the Euler turbulence using a central seven-point stencil reconstruction scheme. High-resolution numerical experiments are performed for both multi-mode and single-mode inviscid Rayleigh–Taylor instability (RTI) problems in two-dimensional canonical settings. In our numerical assessments, we focus on the computational performance considering both the time evolution of the flow field and its spectral resolution up to three decades of inertial range. We show that the relaxation filtering approach equipped with a central seven-point stencil, sixth-order accurate discrete filter yields accurate results efficiently since there is no additional cost associated with the
computation of the smoothness indicators and interface Riemann solvers. Our a-posteriori spectral analysis also demonstrates that its resolution capacity is sufficiently high to capture the details of the flow behavior induced by the instability. Furthermore, its resolution capability can be effectively controlled by the filter shape and strength. For details, please refer to Rahman and San, 2019 (b).
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Figure: Time evolution of the density field for the RTI problem with multi-mode perturbation for t = 1.6, t = 2.4 and t = 4.0 respectively. Results are obtained by the ILES-Roe scheme at a resolution of 16384 X 24576.
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Figure: Density field at t = 4.7 for the RTI problem with single-mode perturbation for coarse grid resolutions using different ILES schemes.
