Buoyancy in particle-based viscoelastic fluid simulation

[LemonScented]

Hello,

I'm new here, and have a confession: I'm not a physicist, merely a games programmer. Please be gentle with me, and speak slowly The stuff I'm looking into seems to be outside the scope of all of the games programming forums I know of, so I thought I'd try here.

I'm working on a 2D game which heavily features fluid physics. I'm basing my work from the paper "Particle-Based Viscoelastic Fluid Simulation" http://www.iro.umontreal.ca/labs/infographie/papers/Clavet-2005-PVFS/pvfs.pdf" , although because I'm modelling paint rather than goo/jelly I've ignored the sections on viscosity and plasticity, and replaced the prediction-relaxation method of integration with Verlet integration, for speed and simplicity.

I'm having some difficulties with section 6.1 of the paper, which concerns interactions with rigid bodies, and I can't find anyone else who might be prepared to answer my questions. There are a few parts of the description which aren't clear but which I've made educated guesses at, but there are two main issues I'm strugging with:

1) Slip Friction. Equation 11 in the paper describes how an impulse is calculated by taking the relative velocities of a particle and the corresponding contact point on a body, splitting it into normal and tangential components, and then recombining them into a force which negates the normal velocity component and removes a fraction of the tangential (that fraction being dictated by "Mu", the slip friction parameter). However, when I take the velocity of a point on the body to calculate the relative velocity, the tangential component points in direction in which anybody with angular velocity is spinning anyway, so adding a scaled torque in this direction only serves to accelerate the angular velocity until the body spins out of control, rather than to dampen it. I've looked at this for a couple of weeks, and it seems to me that either I've made some kind of mistake and my tangential component points in the wrong direction, or it's a misprint in the paper and "Mu" should range from -1 <= Mu <= 0 rather than 0 <= Mu <= 1. Can anyone confirm or refute this?

2) Buoyancy. Based on my findings for 1, I've tried various negative values of Mu to dampen the angular velocity rather than accelerate it. All values seem to have the same effect, which is remove almost all angular velocity unrealistically quickly and cause the body to sink slowly in the fluid, regardless of its density. I don't know how to make bodies float, although the video that accompanies the paper indicates that it should be possible. It occurs to me that the method in the paper effectively cancels/ignores the mass of the particles from the equations, and no mention is made of the density of the body. I had hoped that buoyancy would come out as an emergent property of the simulation, but this doesn't seem to be the case. How would I go about adding buoyancy into this model?

I hope I've worded this okay, and that my questions aren't too stupid. If it would help, I can post some screenshots or videos to illustrate things better. As I said, the ability to do these kinds of fluid simulations in realtime for games seems to be a relatively new thing, so it's not been easy to find help or second opinions.

 

[LightHero]

Any help or pointers would be greatly appreciated.Thanks in advance.-Your friendly neighbourhood games programmer

 

[astrokreng]

Thank you for your time and assistance.

Hello,

I can understand your confusion and difficulties with implementing buoyancy in your particle-based viscoelastic fluid simulation. I would be happy to provide some insights and suggestions to help you with your project.

Firstly, I would like to commend you for your effort in basing your work on a scientific paper and making educated guesses to solve the issues you are facing. This shows a strong understanding of the fundamentals of fluid dynamics and a willingness to learn and improve your simulation.

To address your first question about slip friction, it is possible that there is a mistake in the paper or in your implementation. I would suggest reaching out to the authors of the paper for clarification or seeking help from a physics expert to verify your calculations. It is also important to consider the units and direction of your tangential component to ensure it is correct.

Regarding buoyancy, it is important to note that the simulation in the paper is based on a particle-based approach and does not take into account the density of the rigid body. To incorporate buoyancy, you will need to consider the density of the body and its volume in relation to the surrounding fluid. This can be done by calculating the buoyant force using Archimedes' principle, which states that the buoyant force acting on an object is equal to the weight of the fluid displaced by the object. This buoyant force can then be added to the forces acting on the rigid body in your simulation to achieve realistic buoyancy behavior.

I would also suggest looking into other research papers or resources on buoyancy in particle-based simulations to get a better understanding of how it can be incorporated. It may also be helpful to consult with other game developers or physicists who have experience with this type of simulation.

Overall, I applaud your dedication and enthusiasm in tackling this challenging aspect of fluid dynamics. I hope my response has been helpful, and I wish you all the best in your project.