The present study deals with development of a general model for close-contact melting (CCM), and its associated physical phenomena, namely, convection in the melt and solid bulk motion. An analysis of the literature reveals that although CCM is a well-known phenomenon, the existing numerical methods for solid-liquid phase change simulation, including the enthalpy-porosity approach, are not capable of modeling CCM processes properly. The proposed model is based on solution of all the relevant conservation equations and, in addition, on the force balance for the solid bulk. It allows full coupling between the solid body motion and the melt behavior, including natural convection. This fixed-grid model is based on the enthalpy method, and advanced numerical techniques from the literature are applied to simulate the solid bulk motion by using properly dispersed momentum sources. A special procedure, devised to move the solid across the grid, guarantees that the solid bulk moves as a rigid body and cannot be stretched or deformed like a highly viscous fluid. The new model is verified against benchmark results from the literature. Then, a test case that involves CCM is studied, namely, melting in a rectangular isothermal cavity, heated from all its sides. For this configuration, the new model is compared with a conduction-based CCM model and validated against experimental results from the literature. By using dimensional analysis, both the experimental and numerical results are generalized. It is also demonstrated that the new model can solve complex melting problems, where the solid bulk inertia is not negligible. The proposed model may be extended to include other effects, such as solid bulk rotation and melting over a range of temperatures. (C) 2017 Elsevier Ltd. All rights reserved.