# Euler method

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## Euler method

[′oi·lər ‚meth·əd]
(mathematics)
A method of obtaining an approximate solution of an ordinary differential equation of the form dy / dx = f (x, y), where f is a specified function of x and y. Also known as Eulerian description.
(mechanics)
A method of studying fluid motion and the mechanics of deformable bodies in which one considers volume elements at fixed locations in space, across which material flows; the Euler method is in contrast to the Lagrangian method.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Shen, "An Eulerian method for water droplet impingement prediction and its implementations," in Proceedings of the 1st International Symposium on Aircraft Airworthiness, pp.
A CEL method that attempts to capture the advantages of both the Lagrangian and the Eulerian method is implemented in Abaqus .
The discretization applied to a fluid computation widely is Eulerian method with a calculation grid.
The deformation of AAA wall altered the volume of fluid domain, which was handled by inducing a moving coordinate system using the Arbitrary Lagrangian Eulerian method .
A Lagrangian based particle tracking method, versus a Eulerian method, has the advantage of realistic subgrid scale motion and best approximates the movement of particles .
One merit of the LSM is that the model can execute numerical calculations and meanwhile avoid the processing of parameterizing these targets called the Eulerian method , with the curves and surfaces on a stabilized Cartesian grid.
However, our Eulerian method does not have much in common with these methods.
Therefore, Eulerian method is suitable for simulation of large deformation and fluid movement (Dorosevas 2007).
Eulerian method typically used in simulating fluid, in which the material flows through a stationary domain represented by grids).
One may also divide these methods into three groups: the Lagrangian method, the Eulerian method and the arbitrary Lagrangian --Eulerian method.
The advantage of the Eulerian method is the possibility to obtain the distributions of all dynamic parameters of the flow, including the particle mass concentration.
In the so-called Eulerian method, the phases are handled as two interpenetrating continua and are governed by a set of differential equations representing conservation laws.

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