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# SPDX-License-Identifier: GPL-2.0
#
# clang-format configuration file. Intended for clang-format >= 11.
#
# For more information, see:
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#   Documentation/process/clang-format.rst
#   https://clang.llvm.org/docs/ClangFormat.html
#   https://clang.llvm.org/docs/ClangFormatStyleOptions.html
#

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Realtime Fluid Simulation: Projection

The core of most real-time fluid simulators, like the one in EmberGen, are based on the "Stable Fluids" algorithm by Jos Stam, which to my knowledge was first presented at SIGGRAPH '99. This is a post about one part of this algorithm that's often underestimated: Projection

MG4_F32.mp4

Stable Fluids

The Stable Fluids algorithm solves a subset of the famous "Navier Stokes equations", which describe how fluids interact and move. In particular, it typically solves what's called the "incompressible Euler equations", where viscous forces are often ignored.

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[Browser Demo](https://sfc.vuejs.org/#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Noise Processing

[Browser Demo](https://sfc.vuejs.org/#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Randomly sampled square/circle

[Online Demo](https://sfc.vuejs.org/#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Computational Fluid Dynamics (in graphics mostly)

Disclaimer: I have no professional education in Compulational Fluid Dynamics, these are various notes on what I found/learned when trying to learn a bit on the topic. Some of the notes lack sources as I wrote them up later often just remembering some StackExchange answer. Some things I might have misinterpreted.

• Computational Fluid Dynamics (in graphics mostly)
• General / Overview
  • Overarching resources
• General Concepts & Keywords