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The Lagrangian and Eulerian specifications of the kinematics and dynamics of the flow field are related by the material derivative (also called the Lagrangian derivative, convective derivative, substantial derivative, or particle derivative). [1] Suppose we have a flow field u, and we are also given a generic field with Eulerian specification F ...
In continuum mechanics, the material derivative [1] [2] describes the time rate of change of some physical quantity (like heat or momentum) of a material element that is subjected to a space-and-time-dependent macroscopic velocity field. The material derivative can serve as a link between Eulerian and Lagrangian descriptions of continuum ...
Purely Lagrangian methods employ a framework in which a space is discretised into initial subvolumes, whose flowpaths are then charted over time. Purely Eulerian methods, on the other hand, employ a framework in which the motion of material is described relative to a mesh that remains fixed in space throughout the calculation. As the name ...
The Euler equations can be formulated in a "convective form" (also called the "Lagrangian form") or a "conservation form" (also called the "Eulerian form"). The convective form emphasizes changes to the state in a frame of reference moving with the fluid.
Methods have been developed for simulations of viscoelastic fluids, curved fluid interfaces, microscopic biophysical systems (proteins in lipid bilayer membranes, swimmers), and engineered devices, such as the Stochastic Immersed Boundary Methods of Atzberger, Kramer, and Peskin, [6] [7] Stochastic Eulerian Lagrangian Methods of Atzberger, [8 ...
Original file (WebM audio/video file, VP8, length 11 s, 1,280 × 480 pixels, 1.93 Mbps overall, ... Lagrangian and Eulerian specification of the flow field;
This category contains articles that relates to video game design. For articles on computer and video game creation in general, see Category:Video game development.
A Lagrangian density L (or, simply, a Lagrangian) of order r is defined as an n-form, n = dim X, on the r-order jet manifold J r Y of Y. A Lagrangian L can be introduced as an element of the variational bicomplex of the differential graded algebra O ∗ ∞ ( Y ) of exterior forms on jet manifolds of Y → X .