Numerical methods for complex geometries
Immersed boundary (IB) methods have become an established approach for modelling complex and moving geometries. The main advantage and the popularity of these methods are due to their simplicity and efficiency. Unlike body-conforming methods which require a body-fitted grid and remeshing in moving boundary problems, a structured Cartesian grid is adopted for the IB method. The effect of the body surface is included through the addition of boundary forces in the Navier–Stokes equations. Use of structured grids greatly simplifies the task of grid generation, particularly for moving bodies and leads to more efficient computational algorithms with better convergence and stability properties.
The accuracy and stability of IB methods depend on the computation of the forcing term and the treatment of mass conservation at the boundary. We have developed a robust IB method which reduces the errors at the boundary and enhances stability compared to explicit forcing methods in the literature. The approach also employs a new mass source term that accurately accounts for the movement of the boundary and reduces the spurious force oscillations which typically arise in IB simulations of moving body problems. In addition, the method has been developed for use on curvilinear grids, which lends itself to a wide range of complex flow problems, and is particularly useful for the complex airway geometries.