This paper presents a novel approach to numerical smoke simulation for computer graphics applications. The method leverages the unique physics of smoke to design a fast and efficient numerical scheme suitable for the coarse grids commonly used in computer graphics, as opposed to the finer grids typically employed in computational fluid dynamics (CFD). The model uses the inviscid Euler equations, which are more appropriate for gas modeling and less computationally intensive than the viscous Navier-Stokes equations. A physically consistent vorticity confinement term is introduced to model the small-scale rolling features characteristic of smoke, which are often absent in coarse grid simulations. The model also correctly handles the interaction of smoke with moving objects. The authors derive the model from the equations of fluid flow, solve them using a semi-Lagrangian integration scheme, and enforce incompressibility through a pressure-Poisson equation. They introduce a forcing term to reduce numerical dissipation, ensuring that the small-scale details of smoke are accurately represented. The model is stable for any choice of time step and can handle boundaries within the computational domain, allowing for realistic simulations of smoke swirling around objects. The paper discusses the implementation details, including the use of finite volume spatial discretization, boundary handling, and the solution of the pressure equation. It also presents two rendering algorithms: a hardware-based renderer for rapid feedback and a high-quality global illumination renderer based on the photon map for production-quality animations. The results demonstrate the effectiveness of the proposed model in producing realistic and detailed smoke simulations, even on relatively coarse grids. The authors conclude by highlighting the benefits of vorticity confinement and the potential for further research in this area, particularly in the context of other phenomena like fire.This paper presents a novel approach to numerical smoke simulation for computer graphics applications. The method leverages the unique physics of smoke to design a fast and efficient numerical scheme suitable for the coarse grids commonly used in computer graphics, as opposed to the finer grids typically employed in computational fluid dynamics (CFD). The model uses the inviscid Euler equations, which are more appropriate for gas modeling and less computationally intensive than the viscous Navier-Stokes equations. A physically consistent vorticity confinement term is introduced to model the small-scale rolling features characteristic of smoke, which are often absent in coarse grid simulations. The model also correctly handles the interaction of smoke with moving objects. The authors derive the model from the equations of fluid flow, solve them using a semi-Lagrangian integration scheme, and enforce incompressibility through a pressure-Poisson equation. They introduce a forcing term to reduce numerical dissipation, ensuring that the small-scale details of smoke are accurately represented. The model is stable for any choice of time step and can handle boundaries within the computational domain, allowing for realistic simulations of smoke swirling around objects. The paper discusses the implementation details, including the use of finite volume spatial discretization, boundary handling, and the solution of the pressure equation. It also presents two rendering algorithms: a hardware-based renderer for rapid feedback and a high-quality global illumination renderer based on the photon map for production-quality animations. The results demonstrate the effectiveness of the proposed model in producing realistic and detailed smoke simulations, even on relatively coarse grids. The authors conclude by highlighting the benefits of vorticity confinement and the potential for further research in this area, particularly in the context of other phenomena like fire.