14 research outputs found
Implicit large-eddy simulation of compressible flows using the Interior Embedded Discontinuous Galerkin method
We present a high-order implicit large-eddy simulation (ILES) approach for
simulating transitional turbulent flows. The approach consists of an Interior
Embedded Discontinuous Galerkin (IEDG) method for the discretization of the
compressible Navier-Stokes equations and a parallel preconditioned Newton-GMRES
solver for the resulting nonlinear system of equations. The IEDG method arises
from the marriage of the Embedded Discontinuous Galerkin (EDG) method and the
Hybridizable Discontinuous Galerkin (HDG) method. As such, the IEDG method
inherits the advantages of both the EDG method and the HDG method to make
itself well-suited for turbulence simulations. We propose a minimal residual
Newton algorithm for solving the nonlinear system arising from the IEDG
discretization of the Navier-Stokes equations. The preconditioned GMRES
algorithm is based on a restricted additive Schwarz (RAS) preconditioner in
conjunction with a block incomplete LU factorization at the subdomain level.
The proposed approach is applied to the ILES of transitional turbulent flows
over a NACA 65-(18)10 compressor cascade at Reynolds number 250,000 in both
design and off-design conditions. The high-order ILES results show good
agreement with a subgrid-scale LES model discretized with a second-order finite
volume code while using significantly less degrees of freedom. This work shows
that high-order accuracy is key for predicting transitional turbulent flows
without a SGS model.Comment: 54th AIAA Aerospace Sciences Meeting, AIAA SciTech, 201
A physics-based shock capturing method for unsteady laminar and turbulent flows
We present a shock capturing method for unsteady laminar and turbulent flows. The proposed approach relies on physical principles to increase selected transport coefficients and resolve unstable sharp features, such as shock waves and strong thermal and shear gradients, over the smallest distance allowed by the discretization. In particular, we devise various sensors to detect when the shear viscosity, bulk viscosity and thermal conductivity of the fluid do not suffice to stabilize the numerical solution. In such cases, the transport coefficients are increased as necessary to optimally resolve these features with the available resolution. The performance of the method is illustrated through numerical simulation of external and internal flows in transonic, supersonic, and hypersonic regimes.United States. Air Force. Office of Scientific Research (FA9550-16-1-0214)Pratt & Whitney Aircraft CompanyFundación Obra Social de La CaixaMassachusetts Institute of Technology. Office of the Dean for Graduate Education (Zakhartchenko Fellowship
Non-modal analysis of spectral element methods: Towards accurate and robust large-eddy simulations
We introduce a \textit{non-modal} analysis technique that characterizes the
diffusion properties of spectral element methods for linear
convection-diffusion systems. While strictly speaking only valid for linear
problems, the analysis is devised so that it can give critical insights on two
questions: (i) Why do spectral element methods suffer from stability issues in
under-resolved computations of nonlinear problems? And, (ii) why do they
successfully predict under-resolved turbulent flows even without a
subgrid-scale model? The answer to these two questions can in turn provide
crucial guidelines to construct more robust and accurate schemes for complex
under-resolved flows, commonly found in industrial applications. For
illustration purposes, this analysis technique is applied to the hybridized
discontinuous Galerkin methods as representatives of spectral element methods.
The effect of the polynomial order, the upwinding parameter and the P\'eclet
number on the so-called \textit{short-term diffusion} of the scheme are
investigated. From a purely non-modal analysis point of view, polynomial orders
between and with standard upwinding are well suited for under-resolved
turbulence simulations. For lower polynomial orders, diffusion is introduced in
scales that are much larger than the grid resolution. For higher polynomial
orders, as well as for strong under/over-upwinding, robustness issues can be
expected. The non-modal analysis results are then tested against under-resolved
turbulence simulations of the Burgers, Euler and Navier-Stokes equations. While
devised in the linear setting, our non-modal analysis succeeds to predict the
behavior of the scheme in the nonlinear problems considered
An Optimal EDG Method for Distributed Control of Convection Diffusion PDEs
We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their uxes, and the control. Moreover, we prove the optimize-then-discretize (OD) and discrtize-then-optimize (DO) approaches coincide. Numerical results confirm our theoretical results
Subgrid-scale modeling and implicit numerical dissipation in DG-based Large-Eddy Simulation
Over the past few years, high-order discontinuous Galerkin (DG) methods for Large-Eddy Simulation (LES) have emerged as a promising approach to solve complex turbulent flows. However, despite the significant research investment, the relation between the discretization scheme, the subgrid-scale (SGS) model and the resulting LES solver remains unclear. This paper aims to shed some light on this matter. To that end, we investigate the role of the Riemann solver, the SGS model, the time resolution, and the accuracy order in the ability to predict a variety of flow regimes, including transition to turbulence, wall-free turbulence, wall-bounded turbulence, and turbulence decay. The transitional flow over the Eppler 387 wing, the TaylorGreen
vortex problem and the turbulent channel flow are considered to this end. The focus is placed on post-processing the LES results and providing with a rationale for the performance of the various approaches.United States. Air Force. Office of Scientific Research (FA9550-16-1-0214