# Lagrangian method

## Lagrangian method

[lə′grän·jē·ən ‚meth·əd]
(fluid mechanics)
A method of studying fluid motion and the mechanics of deformable bodies in which one considers volume elements which are carried along with the fluid or body, and across whose boundaries material does not flow; in contrast to Euler method. Also known as Lagrangian description.
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In the particle method, which is a complete Lagrangian method free from a computational grid, interface-neighboring particles are given interfacial boundary condition.
The multiscale approach consists of: 1) fully resolved simulations to obtain closures for translational and rotational gas drag tensors in crowded environments and near external and internal walls, 2) Discrete Particle Model simulations to validate the drag closures with matching experiments and to obtain statistics of angular and linear velocity changes due to inter-particle collisions between groups of particles, 3) a novel Lagrangian method based on stochastic multi-particle collisions.
Several rapid numerical algorithms can solve the numerical difficulties, which are, for example, alternating direction method of multipliers (ADMM) [26], augmented Lagrangian method (ALM) [27], splitting Bregman algorithm (SBA) [28], splitting Barzilai-Borwein (SBB) [24], and Bregman operator splitting (BOS) [29].
Brazilian mathematicians explain the augmented Lagrangian method for solving constrained optimization problems for engineers, chemists, physicists, economists, and others who use constrained optimization for solving real-life problems.
3) This study applied the three-dimensional fast Lagrangian method to the oil shale borehole hydraulic mining project design, and the research results provided a reference basis for shale borehole hydraulic mining.
A practical Lagrangian method for relating scalar concentrations to source distributions in vegetation canopies.
Unlike other commonly used discretization methods, SPH represents space with points that can move with materials, such as polymers or liquids, a process called the Lagrangian method (vs.
TAI, Augmented Lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial TV, and high order models, SIAM J.
One may also divide these methods into three groups: the Lagrangian method, the Eulerian method and the arbitrary Lagrangian --Eulerian method.
In the so-called Lagrangian method, the discrete elements are tracked through a turbulent-flow field by solving their equations of motion.
Shape is perceived by means of the normal contact force computed using the constrained Lagrangian method.
The LaGrangian method may be formulated using different minimands.

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