#navierstokes — Public Fediverse posts

Navier-Stokes fluid simulation explained with Godot game engine

https://myzopotamia.dev/navier-stokes-fluid-simulation-explained-with-godot

#HackerNews #NavierStokes #GodotGameEngine #FluidSimulation #GameDevelopment #TechExploration

Navier-Stokes fluid simulation explained with Godot game engine

https://myzopotamia.dev/navier-stokes-fluid-simulation-explained-with-godot

#HackerNews #NavierStokes #GodotGameEngine #FluidSimulation #GameDevelopment #TechExploration

Basics of Numerical Weather Prediction (NWP):

1. THE HORIZONTAL MOMENTUM EQUATION:
\[
\frac{d\mathbf{V}}{dt} + f\hat{k} \times \mathbf{V} = -\nabla \phi + \frac{\sigma}{p_s} \frac{\partial \phi}{\partial \sigma} \nabla p_s + \mathbf{F}
\]

2. THE CONTINUITY EQUATION:
\[
\frac{\partial p_s}{\partial t} + \nabla \cdot (p_s \mathbf{V}) + \frac{\partial}{\partial \sigma}(p_s \dot{\sigma}) = 0
\]

3. THE THERMODYNAMIC ENERGY EQUATION:
\[
\frac{1}{R} \frac{d}{dt} \left[ \sigma \frac{\partial \phi}{\partial \sigma} \right] + \frac{RT}{C_p p} \left[ p_s \dot{\sigma} + \sigma\dot{p_s} \right] = -Q
\]

4. HYDROSTATIC EQUATION:
\[
\frac{\partial \phi}{\partial \sigma} = -\frac{RT_v}{\sigma}
\]

5. SURFACE PRESSURE TENDENCY EQUATION:
\[\displaystyle
\frac{\partial p_s}{\partial t} = -\int_{0}^{1} \nabla\cdot (p_s \mathbf{V}) \, d\sigma
\]

6. MOISTURE EQUATION:
\[\displaystyle
\frac{\partial}{\partial t} (p_s q) + \nabla\cdot (p_s q \mathbf{V}) + \frac{\partial}{\partial \sigma} (p_s q \dot{\sigma}) = p_s S
\]

The six primary unknowns are: \(\mathbf{V}\) (horizontal wind velocity), \(p_s\) (surface pressure), \(T\) (temperature), \(q\) (specific humidity or moisture), \(\phi\) (geopotential), and \(\dot{\sigma}\) (sigma velocity or vertical velocity in \(\sigma\)-coordinates).

#NWP #Weather #NumericalWeatherPrediction #Meteorology #Climate #ClimateScience #Earth #EarthScience #ClimateChange #ClimateSciences #Science #WeatherPrediction #Humidity #Moisture #Pressure #Velocity #SurfacePressure #HydrostaticEquation #WeatherPrediction #Ocean #Atmosphere #AOS #ClimateDynamics #WeatherDynamics #Geopotential #SigmaVelocity #VerticalVelocity #MoistureEquation #Thermodynamics #Dynamics #NavierStokes

#ThisMonthInFluiddyn it is. Let's go 😎

🔹@PierreAugier and friends are finishing up an article, so as a side project they released #formattex and #formatbibtex based on #TexSoup and #BibtexParser

https://pypi.org/project/formattex/
https://pypi.org/project/formatbibtex/

> a simple and uncompromising #Latex code formatter

🔹Version 0.7.4 of #fluidsim and fluidsim-core were released containing a refactored energy spectra for #NavierStokes solvers and other bug fixes

https://pypi.org/project/fluidsim/

#fluiddyn

#ThisMonthInFluiddyn it is. Let's go 😎

🔹@PierreAugier and friends are finishing up an article, so as a side project they released #formattex and #formatbibtex based on #TexSoup and #BibtexParser

https://pypi.org/project/formattex/
https://pypi.org/project/formatbibtex/

> a simple and uncompromising #Latex code formatter

🔹Version 0.7.4 of #fluidsim and fluidsim-core were released containing a refactored energy spectra for #NavierStokes solvers and other bug fixes

https://pypi.org/project/fluidsim/

#fluiddyn

#ThisMonthInFluiddyn it is. Let's go 😎

🔹@PierreAugier and friends are finishing up an article, so as a side project they released #formattex and #formatbibtex based on #TexSoup and #BibtexParser

https://pypi.org/project/formattex/
https://pypi.org/project/formatbibtex/

> a simple and uncompromising #Latex code formatter

🔹Version 0.7.4 of #fluidsim and fluidsim-core were released containing a refactored energy spectra for #NavierStokes solvers and other bug fixes

https://pypi.org/project/fluidsim/

#fluiddyn

#ThisMonthInFluiddyn it is. Let's go 😎

🔹@PierreAugier and friends are finishing up an article, so as a side project they released #formattex and #formatbibtex based on #TexSoup and #BibtexParser

https://pypi.org/project/formattex/
https://pypi.org/project/formatbibtex/

> a simple and uncompromising #Latex code formatter

🔹Version 0.7.4 of #fluidsim and fluidsim-core were released containing a refactored energy spectra for #NavierStokes solvers and other bug fixes

https://pypi.org/project/fluidsim/

#fluiddyn

#ThisMonthInFluiddyn it is. Let's go 😎

🔹@PierreAugier and friends are finishing up an article, so as a side project they released #formattex and #formatbibtex based on #TexSoup and #BibtexParser

https://pypi.org/project/formattex/
https://pypi.org/project/formatbibtex/

> a simple and uncompromising #Latex code formatter

🔹Version 0.7.4 of #fluidsim and fluidsim-core were released containing a refactored energy spectra for #NavierStokes solvers and other bug fixes

https://pypi.org/project/fluidsim/

#fluiddyn