A consistent and conservative immersed boundary method for MHD flows and moving boundary problems

A consistent and conservative immersed boundary method has been developed to accurately and efficiently solve two topics: magnetohydrodynamics flows with a complex boundary and moving boundary problems. Based on a least square interpolation reconstruction method, a unified form of boundary condition is described to handle a single domain situation while a mixed boundary condition is used for coupled conditions of multi-domain. In order to achieve the consistency with a desired wall boundary condition, a so-called approximation-correction procedure is done, and an imposing Neumann boundary condition is discussed with two kinds of different schemes. Besides, a consistent and conservative scheme is implemented to satisfy both the charge and mass conservation laws on cells around the immersed surface. Then, a conservative interpolation is reconstructed for velocity in moving boundary problems. At last, the applied numerical method is validated by stationary and moving boundary cases and an excellent agreement is obtained with good accuracy, efficiency and conservation. Especially, the consistent and conservative immersed boundary method can obtain almost the same accurate results as those from the cut cell technique (Seo and Mittal, 2011) [14] for a moving boundary problem by reducing the spurious pressure.