skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A practical discrete-adjoint method for high-fidelity compressible turbulence simulations

; ;
Publication Date:
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
Grant/Contract Number:
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 285; Journal Issue: C; Related Information: CHORUS Timestamp: 2016-09-04 17:43:25; Journal ID: ISSN 0021-9991
Country of Publication:
United States

Citation Formats

Vishnampet, Ramanathan, Bodony, Daniel J., and Freund, Jonathan B. A practical discrete-adjoint method for high-fidelity compressible turbulence simulations. United States: N. p., 2015. Web. doi:10.1016/
Vishnampet, Ramanathan, Bodony, Daniel J., & Freund, Jonathan B. A practical discrete-adjoint method for high-fidelity compressible turbulence simulations. United States. doi:10.1016/
Vishnampet, Ramanathan, Bodony, Daniel J., and Freund, Jonathan B. 2015. "A practical discrete-adjoint method for high-fidelity compressible turbulence simulations". United States. doi:10.1016/
title = {A practical discrete-adjoint method for high-fidelity compressible turbulence simulations},
author = {Vishnampet, Ramanathan and Bodony, Daniel J. and Freund, Jonathan B.},
abstractNote = {},
doi = {10.1016/},
journal = {Journal of Computational Physics},
number = C,
volume = 285,
place = {United States},
year = 2015,
month = 3

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/

Citation Metrics:
Cited by: 3works
Citation information provided by
Web of Science

Save / Share:
  • Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizationsmore » near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space–time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge–Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that its accuracy is limited by computing precision, and we demonstrate it on the aeroacoustic control of a mixing layer with a challengingly broad range of turbulence scales. For comparison, the error from a corresponding discretization of the continuous-adjoint equations is quantified to potentially explain its limited success in past efforts to control jet noise. The differences are illuminating: the continuous-adjoint is shown to suffer from exponential error growth in (reverse) time even for the best-resolved largest turbulence scales. Implications for jet noise reduction and turbulence control in general are discussed.« less
  • We analyze the potential performance benefits of estimating expected quantities in large eddy simulations of turbulent flows using true ensembles rather than ergodic time averaging. Multiple realizations of the same flow are simulated in parallel, using slightly perturbed initial conditions to create unique instantaneous evolutions of the flow field. Each realization is then used to calculate statistical quantities. Provided each instance is sufficiently de-correlated, this approach potentially allows considerable reduction in the time to solution beyond the strong scaling limit for a given accuracy. This study focuses on the theory and implementation of the methodology in Nek5000, a massively parallelmore » open-source spectral element code.« less
  • Flows in which shock waves and turbulence are present and interact dynamically occur in a wide range of applications, including inertial confinement fusion, supernovae explosion, and scramjet propulsion. Accurate simulations of such problems are challenging because of the contradictory requirements of numerical methods used to simulate turbulence, which must minimize any numerical dissipation that would otherwise overwhelm the small scales, and shock-capturing schemes, which introduce numerical dissipation to stabilize the solution. The objective of the present work is to evaluate the performance of several numerical methods capable of simultaneously handling turbulence and shock waves. A comprehensive range of high-resolution methodsmore » (WENO, hybrid WENO/central difference, artificial diffusivity, adaptive characteristic-based filter, and shock fitting) and suite of test cases (Taylor-Green vortex, Shu-Osher problem, shock-vorticity/entropy wave interaction, Noh problem, compressible isotropic turbulence) relevant to problems with shocks and turbulence are considered. The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation. The hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor. Artificial diffusivity methods in which the artificial bulk viscosity is based on the magnitude of the strain-rate tensor resolve vortical structures well but damp dilatational modes in compressible turbulence; dilatation-based artificial bulk viscosity methods significantly improve this behavior. For well-defined shocks, the shock fitting approach yields good results.« less
  • In this paper we present numerical modeling results for endcap and linear ion traps, used for experiments at the National Physical Laboratory in the U.K. and Innsbruck University respectively. The secular frequencies for {sup 88}Sr{sup +} and {sup 40}Ca{sup +} ions were calculated from ion trajectories, simulated using boundary-element and finite-difference numerical methods. The results were compared against experimental measurements. Both numerical methods showed high accuracy with boundary-element method being more accurate. Such simulations can be useful tools for designing new traps and trap arrays. They can also be used for obtaining precise trapping parameters for desired ion control whenmore » no analytical approach is possible as well as for investigating the ion heating rates due to thermal electronic noise.« less
  • An algorithm for solving the Poisson equation in separable coordinates is presented. (AIP) copyright 1987 Academic Press, Inc.