Accuracy Assessment of the 2D Laminar Boundary Layer on a Flat Plate in an Immersed Boundary-Fourier Pseudospectral Simulations

Resumo

We investigate the accuracy of the laminar boundary layer over a flat plate in the simulation by an

immersed boundary – Fourier pseudospectral methods (IMERSPEC). In this study, we use the The Fourier pseu-
dospectral method (FPM) combined with the Multi-Direct Forcing Method, can enforce the boundary conditions

accurately by determining the body force iteratively. The IMERSPEC solves the continuity equation and linear
momentum equations numerically implementing the Pseudospectral Fourier Method (PFM) with the use of the

Discrete Fourier Transform (DFT), specifically the Fast Fourier Transform (FFT) algorithm. The reduced com-
putational 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 found in momentum linear equations. Furthermore, the mathematical
process of pressure projection replaces the solution of Poisson Equation simultaneously ensures mass balance and
decouples the pressure from the computational solution. The simulations of the laminar boundary layer on a flat
plate at the Reynolds number of 104

are performed by using IMERSPEC and modelling the behaviour of the flow
after the flat’s leading edge to eliminate any undesirable Gibbs phenomenon. 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 1024x256 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.