arXiv subjects

Victor C. B. Sousa

Publications and source records attributed to Victor C. B. Sousa.

4 recordsLinked to original sources

arXiv2024

Block Spectral Stresses (BSS) estimation for shock-capturing and turbulent modeling

A new combined sub-filter scale turbulence and shock-capturing model is developed for high-order finite volume numerics, extending previous work to unstructured solvers. Block Spectral Stresses (BSS) method relies on the spectra of the velocity gradients to estimate the subfilter scale stresses, heat-flux, and pressure-work based on the resolved field. The method is able to capture shocks with numerical order up to 25 and in a shock-vortex interaction simulation is able to capture the shock and not interfere with the vortex structure. In turbulence calculations the new method is compared with Smagorinsky, dynamic Smagorinsky, and Vreman methods adapted to a block spectral code. In the simulations of homogeneous isotropic turbulence, the new model is worse than the others when on coarse meshes and better on finer ones. Instead, for supersonic and hypersonic channel flow the case is the opposite because as expected the sub-filter terms are mostly depend on the numerical order and not the mesh resolution.

physics.flu-dyn↗

arXiv2022

A Legendre spectral viscosity (LSV) method applied to shock capturing for high-order flux-reconstruction schemes

A novel approach to shock capturing for high-order flux reconstruction schemes is derived based on the mathematical formalism of the filtered governing equations. While the latter perspective is only typically used for turbulence modeling in the context of Large-Eddy Simulations (LES), the novel Legendre Spectral Viscosity (LSV) sub-filter scale (SFS) closure model is capable of performing simulations in the presence of shock-discontinuities. The LSV method exploits the set of hierarchical basis functions formed by the Legendre polynomials to extract the information on the energy content near the resolution limit and estimate the overall magnitude of the required SFS dissipative terms, resulting in a scheme that dynamically activates only in cells where nonlinear behavior is important. Additionally, the modulation of such terms in the Legendre spectral space allows for the concentration of the dissipative action at small scales. The proposed method is tested in canonical shock-dominated flow setups in both one and two dimensions. These include the 1D Burgers' problem, a 1D shock tube, a 1D shock-entropy wave interaction, a 2D inviscid shock-vortex interaction and a 2D double Mach reflection. Results showcase a high-degree of resolution power, achieving accurate results with a small number of degrees of freedom, and robustness, being able to capture shocks associated with the Burgers' equation and the 1D shock tube within a single cell with orders 120 and higher.

physics.flu-dyn↗

arXiv2022

A unified Quasi-Spectral Viscosity (QSV) approach to shock capturing and large-eddy simulation

The Quasi-Spectral Viscosity (QSV) method is a novel closure for a high-order finite-difference discretization of the filtered compressible Navier-Stokes equations capable of unifying dynamic sub-filter scale (SFS) modeling and shock capturing under a single mathematical framework. Its innovation lies in the introduction of a physical-space implementation of a spectral-like SFS dissipation term by leveraging residuals of filter operations, achieving two goals: (1) estimating the energy of the resolved solution near the grid cutoff; (2) imposing a plateau-cusp shape to the spectral distribution of the added dissipation. The QSV approach has been tested in a variety of flows to showcase its capability to act interchangeably as: a shock capturing method, in the Shu-Osher, shock/vortex or shock/wall interactions problems; or as a SFS closure, in subsonic Taylor Green Vortex (TGV), and supersonic/hypersonic turbulent channel flows. QSV performs well compared to previous eddy-viscosity closures and shock capturing methods in such test cases. In a supersonic TGV flow, a case which exhibits shock/turbulence interactions, QSV alone outperforms the simple superposition of separate numerical treatments for SFS turbulence and shocks. QSV's combined capability of simulating shocks and turbulence independently, as well as simultaneously, effectively achieves the unification of shock capturing and Large-Eddy Simulation.

physics.flu-dyn↗

arXiv2017

Numerical Investigation of Second Mode Attenuation over Carbon/Carbon Surfaces on a Sharp Slender Cone

We have carried out axisymmetric numerical simulations of a spatially developing hypersonic boundary layer over a sharp 7$^{\circ{}}$-half-angle cone at $M_\infty=7.5$ inspired by the experimental investigations by Wagner (2015). Simulations are first performed with impermeable (or solid) walls with a one-time broadband pulse excitation applied upstream to determine the most convectively-amplified frequencies resulting in the range 260kHz -- 400kHz, consistent with experimental observations of second-mode instability waves. Subsequently, we introduce harmonic disturbances via continuous periodic suction and blowing at 270kHz and 350kHz. For each of these forcing frequencies complex impedance boundary conditions (IBC), modeling the acoustic response of two different carbon/carbon (C/C) ultrasonically absorptive porous surfaces, are applied at the wall. The IBCs are derived as an output of a pore-scale aeroacoustic analysis -- the inverse Helmholtz Solver (iHS) -- which is able to return the broadband real and imaginary components of the surface-averaged impedance. The introduction of the IBCs in all cases leads to a significant attenuation of the harmonically-forced second-mode wave. In particular, we observe a higher attenuation rate of the introduced waves with frequency of 350kHz in comparison with 270kHz, and, along with the iHS impedance results, we establish that the C/C surfaces absorb acoustic energy more effectively at higher frequencies.

physics.flu-dyn↗