# Simulation of circular wave propagation in water - equation

I am trying to develop a simulation of circular water waves with CUDA and OpenGL. Scenario: there is a center of propagation (e.g. when a stone is dropped into water) in a limited area filled with water. From this center I want to compute the propagation of the circular wave(s). So now I am searching for an adequate equation to calculate this propagation. It does not have to be physically exact, a "simple" propagation model would fulfill my needs totally.

I found a first idea in this NVIDA blog entry. According to this post I want to compute the height field for a wave with equation 8a:

$$W_i(x,y,t) = 2A_i \times \left(\frac{\sin(D_i\cdot(x,y) \times w_i + t \times \varphi_i) + 1}{2}\right)^k$$

1. The equation says $(x,y) \times w_i$ which is the cross product between the coordinate and the frequency of wave $w_i$. But I thought the cross product is not defined for a vector and a scalar value, or, like in $t \times \varphi_i$, between two scalar values. So how is this meant or calculated?

2. I have no experience with the parameters, so maybe someone can suggest adequate/realistic values for $A_i, w_i$ and $\varphi_i$ ? Regarding this I see that in equation 13 $w$ is defined as $\sqrt[][g \times \frac{2\pi}{L}]$.

3. Is this a "good" starting point or would you use another propagation model? I am no physicist, but I am missing some kind of constant which discribes a physical/chemical feature of the fluid (water).