Our paper titled Spectral/hp element methods' linear mechanism of (apparent) energy transfer in Fourier space: insights into dispersion analysis for implicit LES was just accepted for publication in Journal of Computational Physics.

Plain-language description

Broadly speaking, physical systems can be described by partial differential equations (PDEs). These are equations that depend on more than one independent variable (e.g, they may depend on time and space). In addition, they contain changes (or derivatives) of the physical (or prognostic) variables with respect to the independent variables). PDEs frequently exhibit highly nonlinear and multiscale behaviour, and the usually do not have analytical solutions. Hence, to solve them it is common to rely on numerical approximations. These approximations may suffer from numerical errors, that might produce an unphysical solution. In this paper, we build on previous work on the topic, and furhter characterize some of these errors for spectral element numerical methods.


In recent years, different dispersion-diffusion (eigen)analyses have been developed and used to assess various spectral element methods (SEMs) with regards to accuracy and stability, both of which are very important aspects for under-resolved computations of transitional and turbulent flows. Not surprisingly, eigenanalysis has been used recurrently to probe the inner-workings of SEM-based implicit LES approaches, where numerical dissipation acts alone in lieu of a subgrid model. In this study we present and discuss an intriguing linear mechanism that causes energy transfer across Fourier modes as seen in the energy spectrum of SEM computations. Despite its linear nature, this mechanism has not been considered in eigenanalyses so far, possibly due to its connection to the often overlooked multiple eigencurves feature of periodic eigenanalysis. As we unveil the mechanism in the simplified context of linear advection, we point out how its effects might take place in actual turbulence simulations. In particular, we highlight how taking it into account in eigenanalysis can improve dissipation estimates in wavenumber space, potentially allowing for a superior correlation between dissipation estimates and energy spectra measured in SEM-based eddy-resolving turbulence computations.