Comparison of the convergence rates between Fourier pseudo-spectral and finite volume method using Taylor-Green vortex problem

Numerical methods are one of the ways to solve problems represented by differential equations; these methods are implemented through algorithms and must be submitted to a numerical verification process to obtain reliable values. The verification of two numerical methods is presented in this study: the Fourier pseudo-spectral method (FPSM) and the finite-volume method (FVM), with and without the immersed boundary method (IBM). Both methodologies are used for incompressible two-dimensional flows, where the use of the IBM allows the modeling of flows involving complex geometries. The present study evaluates the accuracy and convergence rate of the FPSM and FVM using the Taylor-Green decaying vortex problem. The results show that, with the use of the IBM, FPSM and FVM reach the fourth and second order of numerical convergence, respectively, with a longer processing time in simulations with the FPSM.