A radial basis function based ghost cell method with improved mass conservation for complex moving boundary flows

Abstract

A sharp interface immersed boundary method is presented for simulating flows around moving boundaries with arbitrary complex geometries. A time semi-implicit finite difference method is used to solve the incompressible Navier–Stokes equations on a fixed, staggered Cartesian grid. The boundary conditions at the immersed interface are enforced by a ghost cell method. Tracking complex moving boundaries and suppressing pressure oscillations are two major challenges in the sharp interface method. In this work, a polynomial radial basis function (PRBF) is introduced to the ghost cell method to implicitly represent and reconstruct the arbitrary immersed boundaries. In addition, a simple and robust signed identification strategy is used to determine the phase state of the grid cells. To suppress violent pressure oscillations on the moving boundaries, a fractional area representation (FAR) method, together with a mass force term, is introduced to the pressure Poisson equation. This FAR method not only retains the desirable property of consistent discretization in the ghost cell method but also takes advantage of the mass conservation property of the cut cell method. The proposed method is validated using five test cases, including the flow around a hydrofoil, in-line oscillation of a cylinder in a static fluid, uniform flows around a transversely oscillating cylinder, twin oscillating cylinders, and a pitching hydrofoil. The present results are in good agreement with the reference results, which validates the accuracy and capability of the proposed method.