### » Symbolically generate D3Q19 OpenCL kernel using SymPy

June 15, 2019 at 20:45 | opencl_playground | d71fae | Adrian KummerländerMy recent experiments in using the SymPy CAS library for automatically deriving optimized LBM codes have now evolved to the point where a single generator produces both D2Q9 and D3Q19 OpenCL kernels.

Automatically deriving kernel implementations from the symbolic formulation of e.g. the BGK relaxation operator presents itself as a very powerful concept. This could potentially be developed to the point where a LBM specific code generator could produce highly optimized GPU programs tailored to arbitrary simulation problems.

### » Experimental visualization of the velocity curl

April 28, 2019 at 12:53 | compustream | ecaf66 | Adrian KummerländerCalculating 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:

$\omega := \partial_x V_y - \partial_y V_x$

As we do not possess the actual function $V$ but only its values at a set of discrete points we approximate the two partial derivatives using a second order central difference scheme:

$\overline{\omega}(i,j) := \frac{V_y(i+1,j) - V_y(i-1,j)}{2 \Delta x} - \frac{V_x(i,j+1) - V_x(i,j-1)}{2 \Delta x}$

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.

### » Add basic physical scaling and Knudsen quality criterion

April 16, 2019 at 22:45 | compustream | fc02e4 | Adrian KummerländerThe paper Automatic grid refinement criterion for lattice Boltzmann method by Lagrava et al. describes a criterion for measuring the local simulation quality using a comparison of the theoretical Knudsen number and the quotient of the cells’s non-equilibrium and equilibrium function.

While this criterion was developed to enable automatic selection of areas to be refined, it also offers a interesting and unique perspective on the fluid structure.

As the criterion requires calculation of the modeled Reynolds-, Mach- and Knudsen-numbers I took the time to set up the basics for scaling the simulation to actually model a physical system. Or rather calculating which physical model is represented by the chosen resolution and relaxation time.

### » Published my BSc thesis on grid refined LBM in OpenLB

March 26, 2019 at 20:23 | grid_refinement_bsc_thesis | e4ba16 | Adrian KummerländerIn addition to the PDF (German, ~60 pages) all sources including any referenced simulation data are available on Github and cgit. The resulting actual implementation of the grid refinement method by Lagrava et al. in OpenLB is currently not available publicly and likely wont make it into the next release. Nevertheless – if you are interested in the code and I have not yet found the time to release a rebased patch for the latest OpenLB release don’t hesitate to contact me.

As a side note: The gnuplot-based setup for efficiently transforming Paraview CSV exports into plots such as the one above (i.e. plots that are neither misaligned Paraview screenshots nor overlarge PDF-reader-crashing PGFPlots figures) might be of interest even if one doesn’t care about grid refinement or Lattice Boltzmann Methods (which would be sad but to each their own :-)).

### » Compustream performance improvements and interactive wall drawing

February 25, 2019 at 22:08 | compustream | 846665 | Adrian KummerländerI found some time to further develop my GLSL compute shader based interactive LBM fluid simulation previously described in *Fun with compute shaders and fluid dynamics*. Not only is it now possible to interactively draw bounce back walls into the running simulation but performance was greatly improved by one tiny line:

glfwSwapInterval(0);

If this function is not called during GLFW window initialization the whole rendering loop is capped to 60 FPS – including compute shader dispatching. This embarrassing oversight on my part caused the simulation to run way slower than possible.

### » Describe custom gitolite and cgit setup

October 1, 2018 at 08:26 | nixos_system | 55daf8 | Adrian KummerländerReplaces short-term Gitea instance on `code.kummerlaender.eu`

.

The main reason for implementing this more complex setup is that Gitea both lacks in features in areas that I care about and provides distracting features in other areas that I do not use.

e.g. Gitea provides multi-user, discussion and organization support but doesn’t provide Atom feeds which are required for Overview.

This is why exposing gitolite-managed repositories via cgit is a better fit for my usecases.

Note that gitolite is further configured outside of Nix through its own admin repository.

As a side benefit `pkgs.kummerlaender.eu`

now provides further archive formats of its Nix expressions which simplifies Nix channel usage.