The paper sets the variables “c”, “Δt”, and ρ0 to 1 for simplicity. ρ is the fluid density, ρ0 is the average fluid density, and “u” is the fluid velocity. ω is the weight for each of the directions to determine the output flow of each direction. This equation uses “c” as “Δx/Δt”, where “x” is the lattice spacing.

They then use the incompressible variant to derive the next equation, which is: The variable ω is the relaxation parameter, which is set to 1 for simplicity. Here, the variable “f” is the flow of the particles in each of the 8 directions, and f0 is the density at the node in question. From the original Lattice Boltzmann equation, they derive equations which perform better on hardware.

We decided to adopt the equations described in for our design. The node then determines it new density and velocity and uses the Lattice Boltzmann equations to determine the new density on each of its eight flow directions, as well as the local density. In each iteration of the algorithm, each node obtains flow information for the surrounding nodes which influence it. Each node keeps track of its density as well as the direction of flow in eight discrete directions, two of which are vertical, two horizontal, and four diagonal. This method simulates flow by generating a field of static nodes which do not move and are of uniform size. The system for the Lattice Boltzmann simulation are described in. We already had a custom VGA controller that we used in Lab 3 and we thought it would be an interesting project to try to implement from scratch. The simulations in class were not interactive and they were MatLab simulations that were sped up. We chose this project idea because Bruce showed us Lattice Boltzmann simulations in class. In addition to aesthetics, it was a good combination of all the different concepts we learned from implementing previous labs throughout the semester. Our motivation for the project was that we thought the graphics of other implementations were really mesmerizing. The software side controls a USB mouse which allows for user interaction. The FPGA performed the computations, decoded the values into colors and drew the values on the screen.

We created a hardware and software design that simulated fluid flow in real time using the Lattice Boltzmann equations. This goal of this project is to create an interactive fluid dynamics simulation using the Lattice Boltzmann equation in real-time displaying 60 frames per second.

Lattice fpga simulation