In
scientific visualization
Scientific visualization ( also spelled scientific visualisation) is an interdisciplinary branch of science concerned with the visualization of scientific phenomena. Michael Friendly (2008)"Milestones in the history of thematic cartography, st ...
, Lagrangian–Eulerian advection is a technique mainly used for the visualization of
unsteady flows. The
computer graphics
Computer graphics deals with generating images and art with the aid of computers. Computer graphics is a core technology in digital photography, film, video games, digital art, cell phone and computer displays, and many specialized applications. ...
generated by the technique can help scientists visualize changes in
velocity field
In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the f ...
s. This technique uses a hybrid
Lagrangian and Eulerian specification of the flow field
Lagrangian may refer to:
Mathematics
* Lagrangian function, used to solve constrained minimization problems in optimization theory; see Lagrange multiplier
** Lagrangian relaxation, the method of approximating a difficult constrained problem wit ...
. It is a special case of a
line integral convolution
In scientific visualization, line integral convolution (LIC) is a method to visualize a vector field (such as fluid motion) at high spatial resolutions. The LIC technique was first proposed by Brian Cabral and Leith Casey Leedom in 1993.
In LIC, ...
.
The method consists of using
nearest-neighbour interpolation followed by an error correction mechanism. The Lagrangian specification is used during the integration
to update the particle positions. The property of interest is
advected in the Eulerian frame of reference. It was originally designed by Bruno Jobard and others for steady flows but was extended to unsteady flows.
The main idea is to create a white noise texture of the desired resolution, which is used as a base, on top of which the vector field can be applied. That means for every particle looking backward in the vector field to find out the new value for the cell it is contained in. Then looking forward – to calculate the new position of the particle in the cell.
In its application, the Lagrangian–Eulerian method can be accelerated using the
GPUs
A graphics processing unit (GPU) is a specialized electronic circuit designed for digital image processing and to accelerate computer graphics, being present either as a discrete video card or embedded on motherboards, mobile phones, personal ...
used in common chipsets present in
Nvidia
Nvidia Corporation ( ) is an American multinational corporation and technology company headquartered in Santa Clara, California, and incorporated in Delaware. Founded in 1993 by Jensen Huang (president and CEO), Chris Malachowsky, and Curti ...
and
ATI Radeon
Radeon () is a brand of computer products, including List of AMD graphics processing units, graphics processing units, random-access memory, RAM disk software, and solid-state drives, produced by Radeon Technologies Group, a division of AMD. The ...
graphics cards.
Ensuring that the moving texture always follows the velocity field of the fluid, while maintaining properties of the original texture, is key to avoid visual artifacts. A new method developed in 2009 improves the results of the previous one, running real-time.
[ Paper on Research Gate]
/ref>
See also
* Lagrangian analysis Lagrangian analysis is the use of Lagrangian coordinates to analyze various problems in continuum mechanics.
Lagrangian analysis may be used to analyze currents and flows of various materials by analyzing data collected from gauges/sensors embed ...
* Lagrangian drifter
A drifter (not to be confused with a ''profiling float, float'') is an Oceanography, oceanographic device floating on the surface to investigate ocean currents by tracking location. They can also measure other parameters like sea surface temperatu ...
References
Numerical function drawing
{{computer-graphics-stub