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The rheology of a material especially related to mechanical behavior is an important characteristic to understand for product design. Rheology has wide applications for example in nanomaterials, engineering design, biology, and in a large scale case in geodynamics study. Rheology relies on several physical equations such as continuity equation, momentum equation, gravity potential, state equation, heat transfer, and advection equation. The equations seem to be simple, however the application of those equations to a real case is not easy and cause many numerical problems. Marker-in-Cell (MIC) is a technique to solve a numerical rheology modeling problem especially diffusion of sharp gradients during the advection process. The technique successfully simulates the advection process for thermomechanical viscous material for a 2-dimensional case study. The model was initially set up two parts with laterally contrast difference of material characteristics. The lateral density difference of material induced gravitational force and generated circular movement of material. After the simulation was ran the for the 20-time step, the whole material moved more clockwise circulation. The model started to be stable when all denser material at the lower layer and lower density material at the upper part. The model was fully stable and become at stationary state at a time more than 100 time steps. The final simulation result showed that the MIC algorithm successfully simulated the conversion process involving the thermomechanical mechanism with diffusion error control and without breaking the contrast density of the material.