Granular flow usually occurs with strong interaction to the boundary, deposition, or other flow events. In particular, granular flows can frequently interact with each other, resulting in different behaviors. This paper employs a mesh-free numerical method coupled with mu(I) rheology to investigate interaction of granular surface waves. The waves are induced by the collapse of two granular columns propagating towards to each other. Experimental measurements are performed for validating the numerical method in reproducing the dynamics for the surface wave interaction. Validation is made in terms of free surface and velocity profiles and they are in good agreement. In the interaction, there are three stages or phases: independent spreading (Phase I), wave interaction (Phase II), and integrated-column collapse (Phase III). These phases are able to be distinguished in the simulations. Furthermore, the three phases are characterized with different energy variation, particularly for the kinetic energy. It is found that there are two energy dissipation mechanisms to dissipate wave front energy, including wave front collision and shearing movement. The energy dissipation can be affected by two parameters in the initial configuration as the aspect ratios of the two columns (a(l) and a(r)) and the height-difference-and-distance ratio b. For b = 0.0, wave front energy dissipation is mainly by collision while the energy is dissipated mainly by the wave front shearing movement for b equal to infinity. The collision and wave front shearing movement both contribute to the energy dissipation when b is larger than zero and smaller than infinite during interaction. By increasing the difference between of a(l) and a(r), the importance of wave front shearing movement in the energy dissipation is exemplified. (C) 2019 Published by Elsevier B.V.