Numerical solutions of the Navier-Stokes equations using the Imerspec methodology coupled with the Fourier-Gegenbauer method and spectral filtering technique - Vilela, Breno; Villela, Mariana; Mariano, Felipe; Albuquerque, Laura (Brazilian Journal of Production Engineering, 2025)
When modeling oil-rich rocks, it is of great interest to use numerical tools such as the IMERSPEC methodology: capable of simulating two-phase flows in complex and porous geometries. It is known that the Pseudospectral Fourier method presents uncured solutions in problems with discontinuities and non-periodic boundary conditions due to Gibbs phenomenon. The spectral filtering technique and the Fourier-Gegenbauer method are post-processing procedures that minimize these oscillations. The present work evaluates the implementation of the IMERSPEC methodology coupled to spectral filtering and the Fourier-Gegenbauer method in three problems associated with the Navier-Stokes equations: the Inviscid Burgers innovation, the classical Burgers innovation in non-periodic boundary conditions and a flow in a flat channel in conjunction with the Sparlat-Allmaras (S-A) turbulence model. Therefore, quantitative analyzes of the error and convergence rate are presented.
Keywords: Spectral Methods; Spectral Filtering; IMERSPEC; Fourier-Gegenbauer