I wanted to implement buoyancy in order to get object floating on my ocean. The way I implemented this was through buoyancy spheres. This is what was used in Assassins creed to implement buoyancy in an efficient and accurate manner. Multiple buoyancy spheres are attached to objects in order to provide an approximation of the objects shape. Below I have attached some buoyancy spheres onto a cube. I can then check the height of the ocean at each point of each sphere and determine how much of it is submerged to determine the amount of upwards force.
I factoring in 3 forces into these physics, gravity, buoyancy, and drag. I was having a few issues initially with reaching an equilibrium that would have the objects settle and float normally on the ocean. In the video below you can a real propulsion of objects out of the water.
I added some debug arrows to my buoyancy spheres to represent how much of each force was being applied to each one. This helped me find where the issue was in my math and find the point of equilibrium in my buoyancy. The green arrows is the force of gravity, blue is buoyancy, and yellow is drag, and purple is the overall force.
In the end I got some good results, I was really happy with the approach of buoyancy spheres. They provide great results with a low cost and a flexible application.