An analytical model for eigensolution analysis in the ghost-cell immersed boundary method

Abstract

This paper presents a novel model for the discrete forcing ghost-cell method to make it applicable for eigensolution analysis, utilizing the sinusoidal property of real solutions to determine the location of mirror points, the values of which are linearly represented by the surrounding grid. This scheme can serve as an a priori analysis tool for evaluating immersed boundary methods. The analytical solution for a harmonic wave with the initial condition u(x,0)=exp(ikx) under periodic boundary conditions is obtained. Ghost cells (GCs) are interpolated from the internal grid, and the method is shown to effectively analyze dispersion–dissipation across different GC numbers and interpolation types. Finally, the conclusions are validated by simulating the Burgers equation.