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Due to under-resolution of vortical dominated structures typical for LES type setups, element based high order methods suffer from stability issues caused by aliasing errors of the non-linear flux terms.
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The effect on aliasing errors of different formulations describing the cubically nonlinear convective terms within the discretized Navier Stokes equations is examined in the presence of a non-trivial density spectrum.
We use (Delta t_{mathrm{soft}}=1/1024) at (T=0), and as the binary becomes harder, we decrease (Delta t_{mathrm{soft}}) to suppress the aliasing error of the binary.
This paper explores the option of reducing the effects of temporal aliasing errors by directly estimating low degree and order gravity fields at short time intervals, ultimately resulting in data products with improved spatial resolution.
It is shown that all the results obtained for nonlinear partial differential equations projected and advanced in time in spectral space are not straightforwardly applicable to physical space calculations due to the nonequivalence by Fourier transform of spectral aliasing errors and numerical errors on a set of grid points in physical space.
The consequences of spectral static aliasing errors on a set of grid points are analyzed in one dimension of space for quadratic products and their derivatives.
Some recent studies on the effects of truncation and aliasing errors on the large eddy simulation (LES) of turbulent flows via the concept of modified wave number are revisited.
For underresolved situations, the avoidance of aliasing errors is a strong demand for stability.
Third, the effect of aliasing errors due to the nonlinearity is analyzed.
Using the properties of Legendre polynomials, the mechanism for this special case is analytically explained, considering the cancellation of aliasing errors.
For skew-symmetric and rotational forms, both spectral and finite-difference methods are energy-conserving even in the presence of aliasing errors.
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