Water Waves in a Rectangular Pool
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Water motion is a complex phenomenon which
has yet to be fully captured in interactive computer simulation. Our
study focuses on developing and analyzing an efficient and stable algorithm
for animating waves based upon a set of two-dimensional
shallow water equations. By taking advantage of the considerable effort
already invested in analyzing
water motion in areas such as physics and fluid dynamics, a physically-based
fluid model is capable of producing realistic wave motions.
Wave Animation with Non-trivial Boundary Conditions
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Our formulation captures gentle ocean waves and falls in the middle of the
complexity spectrum of fluid models, which range from the most
comprehensive Navier-Stokes equations, to the simple wave equation.
In our model, the shallow water equations are integrated by the implicit
semi-Lagrangian integration scheme, which allows large timesteps while
maintaining stability.
We have shown how the model can be used to animate water waves and
objects drifting on the water, and how to incorporate obstacles and
boundaries of various shapes.
Boundary conditions are handled by setting the perpendicular components
of the velocity to zero.
By comparing our algorithm with a method previously-developed
by Kass and Miller (1990), we have
demonstrated that our algorithm is both stable and
computationally efficient with a complexity of O(N^2),
where N is the number of grid subintervals in one dimension.
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