In this paper, a physically based approach for simulating tongue of fire is proposed. Realistic animation and real-time simulation are two objectives pursued in computer graphics applications. Traditional animation technique can obtain virtual movement, but it has difficulty for realistic movement. Compared with the traditional animation technique, physically based animation can represent realistic movement better. The incompressible Navier-Stokes equations are used in our model, and the operator splitting method including semi-Lagrangian scheme and fast Fourier transform is employed to split the model into external force term, advection term, diffusion term and projection term. Every step is stable, so the whole process is also stable. Thus, the big time step can be taken to ensure real-time simulation. Compared with the traditional technique, this method can be taken for realistic animation and real-time simulation of tongue of fire in computer graphics applications. A simple visualization approach is also proposed based on density field for rendering tongue of fire animations in real time.