By combining a long Josephson junction (LJJ) with single-flux-quantum (SFQ) circuits, new digital applications for long junctions can be explored. To fully investigate the dynamics of the hybrid LJJlSFQ circuits, a numerical model was developed for an unshunted long junction coupled to shunted SFQ Josephson transmission line (JTL) through superconducting strips.The model is based on a onedimensional array of Josephson junctions that is described by a set of discrete sine-Gordon equations. Simulations support our experimental observation that the first zero-field step can exist when the LJJ is terminated by SFQ elements. The influences on the first zero-field step by the self-inductance, the critical current, and the shunt resistance of JTL cells are studied in detail. Simulation also confirms that each 471 phase leap at the end of the long junction creates two separated SFQ pulses after several overdamped JTL cells.