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## Main Question or Discussion Point

Hi everyone,

Its my first post and am not sure if my trivial question really deserves to be on this forum. But it is troubling me since few days and hence would really appreciate if someone help me out.

I am computing the buoyancy force on an irregular shaped object (tessellated 3D model of boat with triangular facets). Specifics of the computing scenario are as follows:

1. The model is floating and I am exactly (to numeric precision) computing the wetted region of the model. The wetted region is nothing but the set of triangles which is a subset of the triangles representing the model.

2. The water level is changing in time and in space (an ocean surface). It follows a law such as

z = A

Where, A, B, C are constants representing the amplitude, direction, and frequency respectively,

x,y is coordinate of the point on the ocean nominal plane,

z is water height, and

t is any given time

3. For each wet triangle, I compute the height of the water (at its centroid at that time) and compute the volume of water column above the wet triangle. Then I sum them to get the displaced volume of water and use it to compute the buoyancy force.

Now my question pertains to the step 3. Is it right to assume that the water height just above the wet triangles in the bottom of the model (boat) is same as the wave height had the boat not been there (i.e by using the equation given in the step 2)? Or I should rather ask, what could be the errors due to this assumption?

Although I am computing things this way and results looks okay visually, I think that it is not correct from physics point of view.

I think it could potentially be solved accurately in Navier-Stokes formalism, but is there some faster (computationally) way which doesn't require me to solve the movement of fluid due to the boat motion explicitly.

I am sure physics people must have solved this problem in numerous ways. If someone knows of a good reference or some formula (faster computation), please let me know. I am emphasizing fast computing as this computation needs to run in real time.

Thanks

-frs

Its my first post and am not sure if my trivial question really deserves to be on this forum. But it is troubling me since few days and hence would really appreciate if someone help me out.

I am computing the buoyancy force on an irregular shaped object (tessellated 3D model of boat with triangular facets). Specifics of the computing scenario are as follows:

1. The model is floating and I am exactly (to numeric precision) computing the wetted region of the model. The wetted region is nothing but the set of triangles which is a subset of the triangles representing the model.

2. The water level is changing in time and in space (an ocean surface). It follows a law such as

z = A

_{1}cos(B_{1}x + B_{2}y + B_{3}t)Where, A, B, C are constants representing the amplitude, direction, and frequency respectively,

x,y is coordinate of the point on the ocean nominal plane,

z is water height, and

t is any given time

3. For each wet triangle, I compute the height of the water (at its centroid at that time) and compute the volume of water column above the wet triangle. Then I sum them to get the displaced volume of water and use it to compute the buoyancy force.

Now my question pertains to the step 3. Is it right to assume that the water height just above the wet triangles in the bottom of the model (boat) is same as the wave height had the boat not been there (i.e by using the equation given in the step 2)? Or I should rather ask, what could be the errors due to this assumption?

Although I am computing things this way and results looks okay visually, I think that it is not correct from physics point of view.

I think it could potentially be solved accurately in Navier-Stokes formalism, but is there some faster (computationally) way which doesn't require me to solve the movement of fluid due to the boat motion explicitly.

I am sure physics people must have solved this problem in numerous ways. If someone knows of a good reference or some formula (faster computation), please let me know. I am emphasizing fast computing as this computation needs to run in real time.

Thanks

-frs