Improved methodology for mass conservation in sharp interface immersed boundary method for moving boundaries

Abstract

Spurious pressure fluctuation and poor mass conservation are considered as the limitations of immersed boundary method (IBM). Over last decade, various implementations are developed to overcome these issues, which are usually mathematically involved and computationally expensive. In this paper, a simple and robust methodology has been proposed with good mass conservation property that results in smooth pressure fluctuations over moving surfaces. A simple quadratic interpolation/extrapolation scheme is used for reconstruction of solution at immersed and ghost nodes in. The proposed scheme has been implemented for fixed and moving three-dimensional boundaries and validated with available literature data. Overall second-order accuracy has been maintained. The achieved results show a second order accurate mass conservation. Spurious pressure fluctuations are also observed to disappear with mesh refinement.