Background

We will be using smoothed particle hydrodynamics (SPH) for the fluid simulation. The die will be regarded as one particle, and we will consider all of the various influences on the die in parallel. We think that every single step of this problem benefits from parallelism.

Die is shared
Die has interactions array

Each block writes deltas from all interacting particles into interactions array
Die sums array and then gets change

Loop over physics steps:
  Bucket all particles
  Spatial binning
  Thread sync

  Run fluid kernel
    Thread = particle and roughly block = bucket
    Figure out all interactions
    Figure out what threads are touching die
    Add die interactions to shared array
    Figure out who’s touching outside boundary
    Fix all particles running outside boundary
  Thread sync

  Run die kernel
    Sum all forces on die
    Update die

Challenges

Efficient neighbor search. In order for water particles to interact with each other, it needs to be able to know all the other water particles that are close to it. A brute force approach will be \(O(N^2)\) with the number of particles, which is unacceptable. We will need to experiment with more efficient particle representations that allow for finding neighbors faster.

Accumulating particle effects on the die. Every timestep, some of the particles will be interacting with the die. In order to update the die for the next timestep, we need a way to efficiently reduce all the contributions from those particles into a net force to be applied to the die.

Load balancing. If a thread has to do extra work when its particle is interacting with the die, then those threads will take longer — contributing to poor load balancing. We will need to address this through smarter work assignment schemes, or by splitting the particle processing into multiple phases.

Additional questions we’ll need to answer:

• Each particle does different amounts of work depending on if it interacts with the die or not.
• How do you quickly determine what other particles you’re going to interact with?
• Who updates the die?
• When do we update particles vs die — two waves?

Design Tradeoffs

• Reduce buckets before, or reduce the whole interactions array at once.
• Barnes–Hut style approximations (if relevant for longer-range interactions).
• Work partitioning and synchronization strategy between particle updates and rigid-body updates.

Platform Choice

We hope to target GHC and focus on using CUDA. This makes sense for our workload because it’s immensely parallel and in theory each particle is “simple” and does very similar things to each other, with divergence primarily around die/boundary interactions.

Resources: we will run our simulation on the GHC machines, and we will also take into account implementations found in research papers or open source projects for inspiration.

Goals and Deliverables

Plan to achieve

A realistic simulation of a single die suspended in a sphere of uniform fluid (every particle is the same) that runs and renders in real time. A demo suitable for the poster session, prioritizing a reasonable framerate (>= 30fps) while keeping approximations to a minimum.

Hope to achieve

• Multi-Body Dynamics (The "North Star")

  While the primary goal is a single-die simulation, the ultimate vision involves multiple dice interacting simultaneously.

  The Challenge: This introduces two-way coupling complexities: die-to-fluid, fluid-to-die, and die-to-die collisions.

  Impact: Achieving this would represent a fully realized environment, though it remains likely out of scope.

• Geometric Complexity: Differentially Shaped Dice

  Transitioning from a standard cube to varied polyhedral shapes (D4, D12, D20), spheres, stellated forms, other non-convex geometries, and non-uniform dice with intentionally biased internal weighting to study the effects of discontinuities.

  The Challenge: Requires a more generalized rigid body framework. We would need to implement a "hotswappable" model system and account for how sharp vertices and irregular faces create localized turbulence.

  Impact: This tests the robustness of the solver's ability to handle non-uniform boundary conditions.

• Advanced Fluid Environments

  Moving beyond homogeneous fluids to explore non-uniform environments.

  The Challenge: Modeling fluids with varying densities (stratification) or temperature gradients.

  Impact: This allows us to observe how buoyancy and thermal convection influence the die's trajectory, providing a much deeper look into computational fluid dynamics.

Schedule