Physics-Based Spectral Collocation Methods for Large Eddy Simulation on Adaptive Grids
Abstract
The objective of the proposed research is to devise a new class of high-order, physics-based, nonlinearly stable spectral collocation (SC) methods for large eddy simulation (LES) of three-dimensional compressible turbulent flows on adaptive unstructured grids. In contrast to the existing shock-capturing methods that introduce dissipation based on smoothness of a discrete solution rather than on the physics of a problem, we propose to regularize the continuous Navier-Stokes equations by adding an artificial dissipation operator of special form, which is a function of a user-defined resolved grid scale. This regularization unifies the principles of statistical and continuum mechanics and is consistent with the first and second laws of thermodynamics. A physically relevant weak solution of the Navier-Stokes equations is obtained as the limit solution of the regularized equations as the resolved grid scale approaches zero. There are several remarkable features of the proposed methodology. 1 ) The regularized Navier-Stokes equations guarantee existence and uniqueness of a weak solution, satisfy a general class of entropy inequalities, and ensure positivity of the thermodynamic variables, thus providing the existence of the artificial viscosity limit. 2) Unlike the conventional high-order methods that only capture strong discontinuities (whose thickness is inversely proportional to the Reynolds number and cannot be resolved on any affordable grid), the proposed methodology fully resolves shocks and contact discontinuities of the regularized Navier-Stokes equations to the user-defined resolved grid scale, thus providing fully consistent LES solutions for both smooth and discontinuous turbulent flows. We propose to develop a new class of high-order nonlinearly stable SC schemes that mimic the above key properties of the regularized Navier-Stokes equations at the discrete level. A key aspect of this project is to construct new artificial dissipation spectral collocation operators that satisfy the summation-by-parts convention and discrete entropy inequality, preserve the superconvergence properties of the SC operators, and provide positivity of the density and temperature, thus facilitating a nonlinear L2- stability proof for the symmetric form of the regularized 3-D Navier-Stokes equations on unstructured grids. Further improvement in accuracy will be achieved by incorporating a local adaptive hpr-refinement strategy into the spectral collocation framework. This grid adaptation technique based on the finite element residual of the regularized Navier-Stokes equations preserves the stability and positivity properties of the SC operators and is capable of efficiently reducing the spurious entropy production at strong discontinuities and unresolved features. Expected outcomes of the proposed project include an unparalleled level of robustness of the new high-order physics-based methodology for solving the 3-D unsteady Navier-Stokes equations in complex geometries across all speed regimes. The unique stability properties of the proposed high-order SC schemes will facilitate the development and use of advance turbulence models (such as LES and hybrid LES-RANS models) that are nonlinearly stable and capable of dramatically improving the accuracy of prediction of complex unsteady, nonlinear, multiscale phenomena inherent in separated turbulent flows. The proposed methodology will open new avenues for high-fidelity analysis and optimization of turbulent flows arising in variousÉ
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Oct 11, 2018
- Source ID
- W911NF1710443
Entities
People
- Nail Yamaleev
Organizations
- Army Contracting Command
- Old Dominion University
- United States Army