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An optimal combination of time stepping scheme together with the high-order DG spatial scheme is presented.
The numerical solution of the adjoint equation is conducted by a finite-difference method with the Jameson spatial scheme employing the first and the third order dissipative fluxes.
Non-uniform grids are implemented for multidimensional spatial scheme and the results are compared with the result of uniform grid showing agreement.
From the results of a recent wide investigation (Fattorini et al. 2015), the so-called one-per stratum stratified sampling (OPSS) seems to be a suitable spatial scheme, accomplishing simplicity and efficiency, compared to other schemes investigated.
The hybrid spatial scheme includes Fourier spectral accuracy in two directions and sixth-order compact finite differences for first and second-order wall-normal derivatives, while time marching can be up to fourth-order accurate.
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The truncation errors contained in the inverse metrics are generated by the spatial schemes.
The spatial schemes for gradient, Laplacian and divergence are Gauss linear, Gauss linear corrected and Gauss linear schemes, respectively.
Moreover, explicit expressions for the second-order inclusion probabilities might be lacking for the most common spatial schemes.
Fourier analysis shows that the dispersion errors, by spatial schemes, have similarities to the transfer function of spatial filters.
The accuracy of the real frequency and damping rate due to the discrete time and spatial schemes is also derived using a perturbative method.
Particularly, the following exploration focuses on the singling out, manipulation and storing of memories in form of concrete images but also of spatial schemes and patterns, acting as spatial references for drawing on a blank space.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com