Abstract: We describe novel methods to simulate the smoke's physics-based free flows and shape-controlled flows. Free flows and shape-controlled flows can be easily switched to each other with a time-varying method. By adding two control forces, the shape-controlled method is introduced to control the smoke's shapes that can be changing and moving. The vertex-resampled and volume-based methods are employed to improve appearances in the thin parts of the shape. These methods can produce the simulations: the smoke flows out somewhere and move freely maintaining realistic effects, after the user-specified time, the smoke starts to form the user-specified shape sequence represented by a geometric model sequence, or form a shape-moving object. By preprocessing, the additional computation on the Navier-Stokes solver is negligible.