CO \(_2\) flooding is a strategic measure to enhance oil recovery (EOR) while mitigating CO \(_2\) emissions. In recent years, dimethyl ether (DME) has emerged as a promising solvent used in EOR practices. Its potential application in CO \(_2\) flooding attracts considerable interest. However, accurate and robust modeling of the phase behavior of the DME-H \(_2\) O-CO \(_2\) -Hydrocarbon systems remains challenging, leading to the lack of a reliable reservoir simulation tool required by the industrial production simulation. This study proposes a robust and efficient multiphase equilibrium calculation framework for DME-H \(_2\) O-CO \(_2\) -Hydrocarbon systems. We have employed the Peng-Robinson Equation of State (PR EOS) paired with the Huron-Vidal (HV) mixing rule as our thermodynamic model. Novel strategies for the initialization of phase equilibrium constants, known as K-values, have been revealed, demonstrating their effectiveness in accurately detecting phase status during both single-phase and two-phase stability analysis. Furthermore, a combined successive substitution-Newton-trust region iterative algorithm has been implemented, ensuring convergence within the stability analysis and multiphase flash calculations. The performance of our model has been demonstrated using two characterized fluid systems sourced from the literature. The model has proven to be both accurate and robust, exhibiting no errors or convergence issues across tens of millions of tested data points. This work stands as the inaugural systematic study dedicated to multiphase equilibrium calculations for DME-H \(_2\) O-CO \(_2\) -Hydrocarbon systems. Our contributions are anticipated to underpin the development of compositional simulation for DME-enhanced CO \(_2\) flooding.