This paper presents a comprehensive cardiovascular modeling framework that integrates partial differential equations (PDEs), computational fluid dynamics (CFD), and advanced optimization techniques to simulate blood circulation with high accuracy. Unlike traditional models, which rely on simplified assumptions, this approach incorporates pulsatile flow dynamics, non-Newtonian blood viscosity effects, and patient-specific data to enhance predictive capabilities. The governing equations account for arterial compliance, shear stress variations, and complex boundary conditions, providing a more physiologically relevant representation of blood flow. Convergence analysis demonstrates that the numerical solutions approach the exact solution with an error function given by E h = ||u h − u|| L 2 + ||p h − p|| L 2 , confirming a significantly improved convergence rate over classical methods. Stability analysis ensures perturbation decay over time, satisfying d dt ||u ′ || 2 ≤ 0, which guarantees the dissipation of disturbances and validates numerical robustness. A major advancement of this work is the integration of patient-specific parameters, enabling tailored simulations for cardiovascular interventions. The model has clinical applications in optimizing ventricular assist devices (VADs), refining surgical techniques, and improving drug delivery strategies. Future work will focus on real-time validation using clinical data and further refinement of computational efficiency to enhance applicability in medical practice.