Ultrasound contrast agents have been used as vascular reporters for the past 40 years. The ability to enhance vascular features in ultrasound images with engineered lipid-shelled microbubbles has enabled break-throughs such as the detection of tissue perfusion or super-resolution imaging of the microvasculature. However, advances in the field of contrast-enhanced ultra-sound are hindered by experimental variables that are difficult to control in a laboratory setting, such as complex vascular geometries, the lack of ground truth, and tissue nonlinearities. In addition, the demand for large datasets to train deep learning-based computational ultrasound imaging methods calls for the development of a simulation tool that can reproduce the physics of ultrasound wave interactions with tissues and microbubbles. Here, we introduce a physically realistic contrast-enhanced ultrasound simulator (PROTEUS) consisting of four inter-connected modules that account for blood flow dynamics in segmented vascular geometries, intravascular microbubble trajectories, ultrasound wave propagation, and nonlinear microbubble scattering. The first part of this study describes numerical methods that enabled this development. We demonstrate that PROTEUS can generate contrast-enhanced radiofrequency data in various vascular architectures across the range of medical ultrasound frequencies. PROTEUS offers a customizable framework to explore novel ideas in the field of contrast-enhanced ultrasound imaging. It is released as an open-source tool for the scientific community.@en