A major challenge during autonomous navigation in endovascular interventions is the complexity of operating in a deformable but constrained workspace with an instrument. Simulation of deformations for it can provide a cost-effective training platform for path planning. Aim of this study is to develop a realistic, auto-adaptive, and visually plausible simulator to predict vessels’ global deformation induced by the robotic catheter's contact and cyclic heartbeat motion. Based on a Position-based Dynamics (PBD) approach for vessel modeling, Particle Swarm Optimization (PSO) algorithm is employed for an auto-adaptive calibration of PBD deformation parameters and of the vessels movement due to a heartbeat. In-vitro experiments were conducted and compared with in-silico results. The end-user evaluation results were reported through quantitative performance metrics and a 5-Point Likert Scale questionnaire. Compared with literature, this simulator has an error of 0.23±0.13% for deformation and 0.30±0.85mm for the aortic root displacement. In-vitro experiments show an error of 1.35±1.38mm for deformation prediction. The end-user evaluation results show that novices are more accustomed to using joystick controllers, and cardiologists are more satisfied with the visual authenticity. The real-time and accurate performance of the simulator make this framework suitable for creating a dynamic environment for autonomous navigation of robotic catheters.