We believe that a better alternative is to use the physics of fluid flows which have been
developed since the time of Euler, Navier and Stokes (from the 1750’s to the 1850’s). These
developments have led to the so-called Navier-Stokes Equations, a precise mathematical
model for most fluid flows occurring in Nature. These equations, however, only admit analytical
solutions in very simple cases. No progress was therefore made until the 1950’s when
researchers started to use computers and develop numerical algorithms to solve the
equations. In general, these algorithms strive for accuracy and are fairly complex and time
consuming. This is because the applications that require these solvers have to be physically
accurate. It is obviously crucial that the stresses and drag on an airplane or a bridge are
calculated precisely.
In computer graphics and in games on the other hand what matters most is that the
simulations both look convincing and are fast. In addition it is important that the solvers aren’t
too complex so that they can be implemented on standard PCs, game consoles or PDAs. In
this paper we present a set of algorithms which meet these requirements. To achieve these
goals we depart from conventional wisdom in computational physics and develop algorithms
custom tailored for creating visual effects. Unlike physically accurate solvers which have strict
bounds on their time steps, our algorithms are stable, and never “blow up.”
Read this seminal paper for the details:
http://www.dgp.toronto.edu/people/stam/reality/Research/pdf/...
Sample quote:
We believe that a better alternative is to use the physics of fluid flows which have been developed since the time of Euler, Navier and Stokes (from the 1750’s to the 1850’s). These developments have led to the so-called Navier-Stokes Equations, a precise mathematical model for most fluid flows occurring in Nature. These equations, however, only admit analytical solutions in very simple cases. No progress was therefore made until the 1950’s when researchers started to use computers and develop numerical algorithms to solve the equations. In general, these algorithms strive for accuracy and are fairly complex and time consuming. This is because the applications that require these solvers have to be physically accurate. It is obviously crucial that the stresses and drag on an airplane or a bridge are calculated precisely.
In computer graphics and in games on the other hand what matters most is that the simulations both look convincing and are fast. In addition it is important that the solvers aren’t too complex so that they can be implemented on standard PCs, game consoles or PDAs. In this paper we present a set of algorithms which meet these requirements. To achieve these goals we depart from conventional wisdom in computational physics and develop algorithms custom tailored for creating visual effects. Unlike physically accurate solvers which have strict bounds on their time steps, our algorithms are stable, and never “blow up.”