We synthesize and animate general texture patterns over arbitrary 3D mesh surfaces. The animation is controlled by flow fields over the target mesh, and the texture can be arbitrary user input as long it satisfies the Markov-Random-Field assumptions. We achieve this by extending the texture optimization framework over 3D mesh surfaces. We propose an efficient discrete solver inspired by k-coherence search, allowing interactive flow texture animation while avoiding the blurry blending problem for the least square solver in previous work. Our technique has potential applications ranging from simulation, visualization, and special effects.