A catheter curvature brace, catheter assembly and method for managing fluid in a patient, the brace being attachable to a distal portion of a shaft of a catheter and having an elongated frame with a distal end and a proximal end. The frame is formed with at least one curve in a relaxed curved configuration. At least two coupling elements are connected to the frame, each coupling element configured to engage an outer surface of the catheter. At least the frame is formed of an elastic, biocompatible material capable of being straightened by a force and then returning to the relaxed curved configuration after the force is removed, thereby bending the catheter to substantially conform to the relaxed curved configuration.