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author | Adrian Kummerlaender | 2019-04-28 12:53:27 +0200 |
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committer | Adrian Kummerlaender | 2019-04-28 14:22:15 +0200 |

commit | ecaf665a05bdfcd10937152c378cfaec7cdf1836 (patch) | |

tree | b161f5fa94a054b672b81ff1826fbf3ca388975e /shell.nix | |

parent | fa708e6ed52115026f5dd09d270445cfb1b9f26a (diff) | |

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Experimental visualization of the velocity curl

Calculating the curl of our simulated velocity field requires an additional
compute shader step. Handling of buffer and shader switching depending on
the display mode is implemented rudimentarily for now.
Most of this commit is scaffolding, the actual computation is more or less
trivial:
```
const float dxvy = (getFluidVelocity(x+1,y).y - getFluidVelocity(x-1,y).y)
/ (2*convLength);
const float dyvx = (getFluidVelocity(x,y+1).x - getFluidVelocity(x,y-1).x)
/ (2*convLength);
setFluidExtra(x, y, dxvy - dyvx);
```
This implements the following discretization of the 2d curl operator:
Let $V : \mathbb{N}^2 \to \mathbb{R}^2$ be the simulated velocity field at
discrete lattice points spaced by $\Delta x \in \mathbb{R}_{\gt 0}$.
We want to approximate the $z$-component of the curl for visualization:
$$\omega := \partial_x F_y - \partial_y F_x$$
As we do not possess the actual function $F$ but only its values at a
set of discrete points we approximate the two partial derivatives using
a second order central difference scheme:
$$\overline{\omega}(i,j) := \frac{F_y(i+1,j) - F_y(i-1,j)}{2 \Delta x} - \frac{F_x(i,j+1) - F_x(i,j-1)}{2 \Delta x}$$
Note that the scene shader does some further rescaling of the curl to better
fit the color palette. One issue that irks me is the emergence of some
artefacts near boundaries as well as isolated "single-cell-vortices".
This might be caused by running the simulation too close to divergence
but as I am currently mostly interested in building an interactive fluid
playground it could be worth it to try running an additional smoothening
shader pass to straighten things out.

Diffstat (limited to 'shell.nix')

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