Physics based simulation of the dynamics of water spray - water droplets dispersed in air - is a means to increase the visual plausibility of computer graphics modeled phenomena such as waterfalls, water jets and stormy seas. Spray phenomena are frequently encountered by the visual effects industry and often challenge state of the art methods. Current spray simulation pipelines typically employ a combination of Lagrangian (particle) and Eulerian (volumetric) methods - the Eulerian methods being used for parts of the spray where individual droplets are not apparent. However, existing Eulerian methods in computer graphics are based on gas solvers that will for example exhibit hydrostatic equilibrium in certain scenarios where the air is expected to rise and the water droplets fall. To overcome this problem, we propose to simulate spray in the Eulerian domain as a two-way coupled two-continua of air and water phases co-existing at each point in space. The fundamental equations originate in applied physics and we present a number of contributions that make Eulerian two-continua spray simulation feasible for computer graphics applications. The contributions include a Poisson equation that fits into the operator splitting methodology as well as (semi-)implicit discretizations of droplet diffusion and the drag force with improved stability properties. As shown by several examples, our approach allows us to more faithfully capture the dynamics of spray than previous Eulerian methods.

Automatic codes for differential equations can be inadequate when the solutions have discontinuities.If the user provides an external mdicator for discontinuities (e.g., a switching function whose sign changes mdicate discontinuities), a code can be more efficient.A technique for detection and location of a discontinmty ts dtscussed which can be implemented when such indicators are not practical.It estimates the order and magmtude of the discontinuity and hence the stepsize which keeps the error under control while stepping over the discontinuity.