Immersed boundary/solid method for the numerical simulation of particle-laden flows

An outlook of computational fluid dynamics methods based on the fixed Cartesian grid, especially the immersed boundary (IB) method and related techniques, is provided. The basic idea of IB methods and the improvements to maintain consistency of boundary condition and mass conservation, that is the consistent projection method, are discussed. Then, recent examples for particle-laden flows are introduced. To deal with many particles, the immersed solid method is picked up as an efficient alternative to the IB method. In particular, we place focus on the flow and heat transfer of dense mixture of particles and liquid. In such a condition, the flow in narrow gap in between solid interfaces is considered by the lubrication equation. Finally, for further development of application in large-scale turbulent flows laden with particles, the importance of explicitly-defined volume averaging is pointed out based on our recent progress.