In this paper, a diffuse-interface immersed boundary method (IBM) is proposed for simulation of compressible viscous flows with stationary and moving boundaries. In the method, the solution of flow field and the implementation of boundary conditions are decoupled into two steps by applying the fractional step technique, ie, the predictor step and the corrector step. Firstly, in the predictor step, the intermediate flow field is resolved by a recently developed gas kinetic flux solver (GKFS) without consideration of the solid boundary. The GKFS is a finite volume approach that solves the Navier-Stokes equations for the flow variables at cell centers. In GKFS, the inviscid and viscous fluxes are evaluated as a single entity by reconstructing the local solution of continuous Boltzmann equation. Secondly, in the corrector step, the intermediate flow field is corrected by the present diffuse-interface IBM. During this process, the velocity field is firstly corrected by the implicit boundary condition-enforced IBM so that the no-slip boundary condition can be accurately satisfied. After that, the density correction is made by an iterative approach with the help of the continuity equation. Finally, the correction of the temperature field is made in the same way as that of the velocity field. Good agreements between the present simulations and the reference data in literature demonstrate the reliability of the proposed method. KEYWORDS compressible viscous flows, diffuse interface, fractional step technique, gas kinetic flux solver, immersed boundary method, moving boundary problem Int J Numer Meth Fluids. 2020;92:149-168. wileyonlinelibrary.com/journal/fld 149 150 SUN ET AL.Recently, to improve the computational efficiency and reduce the complexity of gas kinetic BGK scheme, a GKFS was proposed by Sun et al. 9 Different from the conventional gas kinetic BGK scheme, a straightforward way to approximate the nonequilibrium distribution function was developed in GKFS. That is, the nonequilibrium term is calculated by the difference of equilibrium distribution functions at the cell interface and its surrounding points. It has been proven that the GKFS is quite attractive because it can give almost the same results compared with the gas kinetic BGK scheme, while it only takes about 60% of the computational time of the latter. This scheme can be well applied to simulate both incompressible and compressible flows, even up to hypersonic flows. However, like most of the body-fitted solvers, the GKFS encounters difficulties in simulating flows with complex and moving boundaries due to the tedious mesh generation and remesh process. As an alternative approach, the immersed boundary method (IBM) has been widely utilized to tackle the solid boundary condition of these kinds of problems due to its simplicity and flexibility.The IBM was first presented by Peskin 10,11 in 1970s to simulate the incompressible blood flow in heart valves. The basic concept of IBM is that the deformation or displacement of the solid boundary will generate ...