Accuracy assessment of the 2D laminar boundary layer on a flat plate in an immersed boundary-Fourier pseudospectral simulations

Abstract

We investigate the accuracy of the laminar boundary layer on a flat plate by an immersed boundary — Fourier pseudospectral methods denominated as (IMERSPEC). The IMERSPEC solves the continuity equation and linear momentum equations numerically implementing the Pseudospectral Fourier Method (PFM) with the Fast Fourier Transform (FFT) algorithm. The reduced computational cost is achieved by the use of FFT as well as the pseudospectral approach which does not solve the convolution product of the advective term. Furthermore, the mathematical process of pressure projection replaces the solution of Poisson Equation while simultaneously ensures mass balance and decouples the pressure from the computational solution. The simulations of the laminar boundary layer at the Reynolds number of $10^4$ are performed using IMERSPEC and modelling the behaviour of the flow after the flat plate’s leading edge. To obtain reasonably accurate results such that the maximum error from the friction coefficient distribution obtained is less than 4% over the useful domain we use at least a uniform mesh with 1024 × 256 collocation points. The rightness showed in these results indicates far improvement from the usual finite volume method’s modelling which needs a local refinement mesh with far more volumes to present comparable results.