Chapter 7 introduces the basic algorithms used to solve the governing equations of multiphase flows. The algorithms for incompressible, isothermal single-phase Newtonian fluid flow form the basis for more complex multiphase flow algorithms. Numerical techniques for the microscopic descriptions of fluid–particle interactions are focused on the discrete particle phase with rigid or nonrigid surfaces. Such methods are associated with the direct numerical simulation and can be categorized into the conformal mesh technique and the nonconformal mesh technique. Numerical techniques for the macroscopic descriptions of multiphase flow include the Eulerian–Lagrangian algorithm for continuum-discrete modeling, and the Eulerian–Eulerian algorithm for continuum modeling.The lattice Boltzmann method is a unique numerical technique for flow simulation. It is based on the discrete Boltzmann equation, rather than the typical Navier–Stokes equation in other CFD techniques. Its computational efficiency and some special treatment for multiphase models make it a suitable tool for flows with complex phase interactions.