I have implemented an Eulerian Fluid Simulation where grid is represented by a staggered MAC Grid.
- Implementation is done with Taichi.
- Velocity field lies on the cell faces.
- Pressure and Quantity (dye in this case) fields lie in the cell centers.
- Pressure is currently computed using Jacobi Iterations.
- With left click user can add dye into the simulation.
- Space can be used to stop the simulation.
- With 'r' key the simulation can be reset.
It is hard to find people explaining the grid logic and index conversion they used in their code. I do not prefer converting indices in place in the code without explicitly stating in which grid the computation is done. The allocated fields are stored in row-major order whose origin is at the top-left. The cell centers are used as the cell indices. In other words, I use the classical multi-dimensional array convention. I did not want to do the math in this grid. Thus, I conceptualized a canonical grid which I call the world grid.
- The origin lies at the top-left. The cell centers are used as the cell indices.
- Fields are stored in this grid.
- Sampling is done in this field.
- The origin lies at the bottom-left. The cell centers are used as the cell indices.
- The math, like derivative computation and time integration, is done in this grid as it feels more natural to me.
- This grid serves as the canonical domain for all of the grids. As seen in the code, see advection functions, while converting indices from one field to the other; this grid is used as the intermediate domain. The idea resembles the similarity transformation from Linear Algebra.
- This grid is purely conceptual. It is not stored in the memory.
I implemented RK-1, RK-2 and RK-3 time integrators. Below, the comparison between them can be seen.
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RK_1.movRK-1 |
RK_2.movRK-2 |
RK_3.movRK-3 |
Free.Play.mov
- Implementing Conjugate Gradient Method for Pressure Computation.
- Making the timestep adaptable as described in the Bridson and Müller's notes.