A Lagrangian-Eulerian numerical scheme for the investigation of bubble motion in turbulent flow is developed. The flow is analyzed in the Eulerian reference frame while the bubble motion is simulated in the Lagrangian one. Finite volume scheme is used, and SIMPLEC algorithm is utilized for the pressure and velocity linkage. The Reynolds stresses are modeled by the RSTM model of Launder. Upwind ...

Intermittency is a basic feature of fully developed turbulence, for both velocity and passive scalars. Intermittency is classically characterized by Eulerian scaling exponent of structure functions. The same approach can be used in a Lagrangian framework to characterize the temporal intermittency of the velocity and passive scalar concentration of a an element of fluid advected by a turbulent i...

In this work, the finite element simulation of dissimilar friction stir welding process is investigated. The welded materials are AA 6061-T6 and AA 7075-T6 aluminum alloys. For this purpose, a 3D coupled thermo-mechanical finite element model is developed according to the Coupled Eulerian-Lagrangian (CEL) method. The CEL method has the advantages of both Lagrangian and Eulerian approaches, whic...

Lagrangian isopycnal diffusivities quantify the along-isopycnal mixing of any tracer with mean gradients along isopycnal surfaces. They are studied in the Southern Ocean of the 1/108 Parallel Ocean Program (POP) model using more than 50 000 float trajectories. Concurrent Eulerian isopycnal diffusivities are estimated directly from the eddy fluxes and mean tracer gradients. Consistency, spatial ...

In this work, we deal with the 1D compressible fluid coupled with elastic solid in an Eulerian-Lagrangian system. To facilitate the analysis, the Naviers equation for elastic solid is cast into a 2×2 system similar to the Euler equation but in Lagrangian coordinate. The modified Ghost Fluid Method is employed to treat the fluid-elastic solid coupling, where an Eulerian-Lagrangian Riemann proble...

For a distribution advected by a simple chaotic map with diffusion, the "strange eigenmode" is investigated from the Lagrangian (material) viewpoint and compared to its Eulerian (spatial) counterpart. The eigenmode embodies the balance between diffusion and exponential stretching by a chaotic flow. It is not strictly an eigenmode in Lagrangian coordinates, because its spectrum is rescaled expon...

This review article aims to provide a comprehensive and understandable account of the theoretical foundation, modeling issues, and numerical implementation of the Lagrangian–Eulerian (LE) approach for multiphase flows. The LE approach is based on a statistical description of the dispersed phase in terms of a stochastic point process that is coupled with an Eulerian statistical representation of...

We show how the change from Eulerian to Lagrangian coordinates for the two-component Camassa–Holm system can be understood in terms of certain reparametrizations of the underlying isospectral problem. The respective coordinates correspond to different normalizations of an associated first order system. In particular, we will see that the two-component Camassa– Holm system in Lagrangian variable...

Laser plasma is modeled by Lagrangian hydrodynamical equations including heat conductivity and laser absorption. The hyperbolic part of the model is treated by Arbitrary Lagrangian Eulerian (ALE) method which avoids moving mesh distortion and parabolic heat conductivity part is treated by splitting and mimetic method. High velocity laser accelerated disc impact problems for which standard Lagra...

We note that there are essentially two methods of solving the hydrostatic primitive equations in general vertical coordinates: the quasi-Eulerian class of algorithms are typically used in quasi-stationary coordinates (e.g. height, pressure, or terrain following) coordinate systems; the quasi-Lagrangian class of algorithms are almost exclusively used in layered models and is the preferred paradi...