The flight instructor reported that he assumed control of the tailwheel-equipped airplane near the conclusion of the local instructional flight. During the approach to land on runway 15, he observed the wind from 240° at 12 knots with occasional wind gusts of 18 knots. During the landing roll with a right crosswind, the airplane encountered a wind gust. The airplane veered left of the runway centerline and its nose rotated right. The pilot applied left rudder and full engine power but was unable to regain directional control. The airplane exited the right side of the runway, traversed through a swale, impacted a culvert, and its left wing impacted the ground as it crossed a taxiway. The airplane came to rest in a grassy area adjacent to the taxiway. The airplane’s fuselage and left wing were substantially damaged during the accident sequence. The flight instructor reported that there were no preaccident mechanical malfunctions or failure with the airplane that would have precluded normal operation.