Extensive studies have been conducted to capture the acid stimulation process in calcite rocks. The related studies on the dolomite system are far more limited in number, and this work is motivated to improve the understanding of the acid stimulation process in dolomite carbonate rocks. The two-scale continuum model is improved to comprehensively consider the mass, momentum, and energy change within the acidizing system. Simulations are performed using the finite volume method. The reliability of the developed numerical model is confirmed and validated by commercial software and previously reported experimental results. Comparison results have shown good agreement. Based on this model, a general reaction and diffusion constitute model is used to conduct a parameter sensitivity study to examine the effect of acid solution physical parameters on the acid stimulation results. A comprehensive rheology model is also developed to describe the different viscosity constitutive relationships of acid fluids, including the Newtonian, non-Newtonian, and diversion mechanisms. The simulation results are further analyzed to reveal the working mechanisms for using different acid systems and to clarify the optimization principle for acid stimulation.