The aim of this project is to simulate the event of an oil spill as accurately as possible to use it for developing oill spill detection and thickness estimation algorithms.
The technical goal would be to extract information/parameters from waves equations, introduce them in a fluids simulation and extract radar reflectivities based on the oil distribution, environment factors (e.g. Surface roughness) and radar frequencies.
Mathematically, deep water waves are defined as those occurring in ocean depths greater than twice the wavelength of the wave. For example, if the wavelength of a particular wave is 10 meters, then the wave is considered a deep water wave if the depth of the ocean is greater than 5 meters where the wave is occurring.
- Philips Spectrum:
- The Phillips spectrum is widely used in the real-time scene simulation of ocean waves. Structural analysis has shown the Phillips spectrum to be an instantaneous spatial spectrum. Its frequency spectrum agrees with the spectrum form raised by Neumann, and is close to the P-M spectrum. (Based on Tessendorf's paper on simulating ocean water)
- Fast Fourier transform:
- Get frequency of height field of waves → Perform inverse FT to get a time representation of the waves (Height map at time t)
- DFT vs FFT: DFT O(n^2) and FFT O(n log2 (n))
- FFT algo → Cooley-Turkey (or Butterfly) algorithm
There are three steps for the movement of a basic fluids simulation:
- Add forces from velocities or external factors
- Diffuse
- Move
This is inspired by the paper written by Jos Stam: Real-Time Fluid Dynamics for Games
To keep it simple:
- Diffusion means that each cell exchanges density with its direct neighbors
- Advection means that the density moves through a static velocity field (We could have some fixed velocity for example to simulate wind)
The ultimate goal is to solve the main physical equations of fluid flow (Such as the Navier-Stokes equation which gives us a description of the evolution of a velocity field over time).
The first equation represents the velocity equation (How the velocities change with time) and the second equation refers to the density function (How density moves through time).
Here is the start of the simulation where we introduced an oil spill ranging from 1 -> 10 mm.
After introducing velocity vectors from the south-west directed to the north-east, we get the following result after a couple of seconds of simulation.
You can take a look the velocity field that was introduced.
Two parameters are mainly responsible for the diffusion of the density of the liquid and its velocity vectors:
- Diffusion Coefficient: It is directly proportional to how fast the liquid density will diffuse (If no velocity vectors are acting on it, the liquid will start dispersing on its own)
| Low diffusion coefficient (~0.1) | High diffusion coefficient (~0.42) |
|---|---|
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- Viscosity Coefficient: It is directly proportional to how fast the velocity vectors will diffuse (Viscous liquids are less affected by velocity vectors that non-viscous liquids)
| Low viscosity coefficient (~0.1) | High viscosity coefficient (~1) |
|---|---|
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The simulation's performance is acceptable, though the grid size should not exceed 250x250 in general. Here is a full view of the oil spill simulation:
- Set the parameters in the fluids window file
- Run
cmake . - After having all the cmake files ready, run the
makecommand - Launch the
Oil_Spill_Simulationexecutable