G. B. Jacobs

B. W. Wissink, G. B. Jacobs, J. K. Ryan et al.

A smoothness-increasing accuracy conserving filtering approach to the regularization of discontinuities is presented for single domain spectral collocation approximations of hyperbolic conservation laws. The filter is based on convolution of a polynomial kernel that approximates a delta-sequence. The kernel combines a $k^{th}$ order smoothness with an arbitrary number of ${m}$ zero moments. The zero moments ensure a $m^{th}$ order accurate approximation of the delta-sequence to the delta function. Through exact quadrature the projection error of the polynomial kernel on the spectral basis is ensured to be less than the moment error. A number of test cases on the advection equation, Burger's equation and Euler equations in 1D and 2D shown that the filter regularizes discontinuities while preserving high-order resolution

T. B. Keesom, P. P. Popov, P. Dhyani et al.

A method to infer and synthetically extrapolate roughness fields from electron microscope scans of additively manufactured surfaces using an adaptation of Rogallo's synthetic turbulence method [R. S. Rogallo, NASA Technical Memorandum 81315, 1981] based on Fourier modes is presented. The resulting synthetic roughness fields are smooth and are compatible with grid generators in computational fluid dynamics or other numerical simulations. Unlike machine learning methods, which can require over twenty scans of surface roughness for training, the Fourier mode based method can extrapolate homogeneous synthetic roughness fields using a single physical roughness scan to any desired size and range. Five types of synthetic roughness fields are generated using an electron microscope roughness image from literature. A comparison of their spectral energy and two-point correlation spectra show that the synthetic fields closely approximate the roughness structures and spectral energy of the scan.