An Analysis of the Numerical Stability of the Immersed Boundary Method

DOI10.1016/J.JCP.2022.111435arXiv2111.15065WikidataQ113871676 ScholiaQ113871676MaRDI QIDQ6384310

Publication date: 29 November 2021

Abstract: We present a numerical stability analysis of the immersed boundary(IB) method for a special case which is constructed so that Fourier analysis is applicable. We examine the stability of the immersed boundary method with the discrete Fourier transforms defined differently on the fluid grid and the boundary grid. This approach gives accurate theoretical results about the stability boundary since it takes the effects of the spreading kernel of the immersed boundary method on the numerical stability into account. In this paper, the spreading kernel is the standard 4-point IB delta function. A three-dimensional incompressible viscous flow and a no-slip planar boundary are considered. The case of a planar elastic membrane is also analyzed using the same analysis framework and it serves as an example of many possible generalizations of our theory. We present some numerical results and show that the observed stability behaviors are consistent with what are predicted by our theory.

Mathematics Subject Classification ID

Basic methods in fluid mechanics (76Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Incompressible viscous fluids (76Dxx)

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