During an instructional flight, in a twin-engine advanced jet trainer, a visual, simulated no-flap approach and landing was planned. Audio data provided by the Federal Aviation Administration (FAA) indicated that the pilot requested a left closed traffic, simulated no-flap pattern, and stated that he needed to go out about 4-miles on upwind. By the time the controller in the Air Traffic Control Tower (ATCT) responded, the pilot had already started the crosswind turn and therefore the controller cleared him to the overhead pattern, left closed traffic. Subsequently, the controller initially instructed the pilot to make the base turn when able, but then instructed him to turn now, in order to be sequenced in front of slower traffic, on a 5-mile final approach. The controller further stated to the pilot that they would get him the 4-miles on the next pattern. The pilot accepted the turn clearance and reported back to the controller that he was in a turn. A review of radar data indicated that during the final turn, the airplane overshot the final approach by over 1,800 ft to the northwest. The filed company report further stated that flying a no-flap approach and landing required maintaining a higher airspeed during the final turn and when established on final approach, the airplane's airspeed had to be quickly bled off. The higher approach speed, difficulty of maintaining airspeed, combined with the early turn to final, increased the pilot's workload during the simulated no-flap pattern. While on final approach, the pilot extended the air brakes, which are typically extended just prior to lowering the landing gear, but inadvertently failed to extend the landing gear. The flight instructor failed to notice the omission. Subsequently, the airplane landed on its belly and sustained substantial damage to the bottom of the fuselage. A post landing fire ensued. The pilots reported no preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation.