Simulations of a falling sphere with concentration in an infinite long pipe using a new moving mesh system

The purpose of this paper is to simulate a flow around a falling sphere with concentration in an infinite long pipe using a new moving mesh system. New moving mesh system is called a Trans-mesh method and a Moving Computational Domain method. In the Trans-mesh method, the bodies can move freely in a main mesh that covers the entire flow field. On the other hand, in the Moving Computational Domain method, the whole of the computational domain including bodies inside moves in the physical space without the limit of region size. These methods are constructed based on the four-dimensional control volume in space-time unified domain such that the method satisfies both the physical and geometrical conservation laws simultaneously. As a result of simulations, physically-meaningful flows are obtained, and it is confirmed that the new moving mesh system is useful for this simulation.