0
$\begingroup$

I am trying to solve an equation used to calculate ocean wave refraction gotten from the irrotationality of the wave number k.

$$ \frac{\partial \, k\sin\theta}{\partial x}-\frac{\partial \, k\cos\theta}{\partial y}=0 $$

I am using a lax-wendroff explicit approach of taking a half step along both the x and y axis, where the equation has been reduced to $$ \frac{\partial A}{\partial x}-\frac{\partial B}{\partial y}=0 $$ where $A = k\sin\theta$ and $B = k\cos\theta$. In the equation, there exist two dependent variables $A$ and $B$. My question is since i have two dependent variables, will i have two computational grids for the solution or just one computational grid where at every grid point both variables exist.

$\endgroup$
  • $\begingroup$ Please use Mathjax. $\endgroup$ – Harry49 Sep 15 '17 at 20:47
0
$\begingroup$

This problem is not well-posed, since it has more unknows than equations. Therefore, it is useless to derive a numerical method to solve it. One more equation on $A$, $B$ would be sufficient.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.