Because of different behavior of reservoir water and dam material, the determination of hydrodynamic pressure during earthquake is very complicated. Thus, different formulations have been presented for modeling of the dam reservoir system under dynamic loading such as earthquake. These formulations can be categorized into two general groups, which are Lagrangian and Eulerian, each having advant...

Arbitrary Lagrangian Eulerian (ALE) methods have existed for several decades. However, three-dimensional multi-material arbitrary Lagrangian Eulerian (MMALE) methods for unstructured grids are relatively new. MMALE algorithms provide the framework to model sections of a simulation as either Lagrangian, ALE, or Eulerian. In addition, sections of a simulation can switch in time between mesh motio...

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and eve...

The immersed boundary (IB) method is a framework for modeling systems in which an elastic structure is immersed in a viscous incompressible fluid. The IB formulation of such problems describes the elasticity of the structure in Lagrangian form and describes the momentum, viscosity, and incompressibility of the fluid-structure system in Eulerian form. Interactions between Lagrangian and Eulerian...

This paper deals with the implementation of an efficient Arbitrary Lagrangian Eulerian (ALE) formulation for the three dimensional finite element modeling of mode I self-similar dynamic fracture process. Contrary to the remeshing technique, the presented algorithm can continuously advance the crack with the one mesh topology. The uncoupled approach is employed to treat the equations. So, each t...

This study reports the mutual transformations between the third-order Eulerian and Lagrangian solutions for the irrotational progressive gravity waves propagating on the uniform depth. Based on the fundamental principle of kinematics, the instantaneous Eulerian and Lagrangian velocities are identically equal, and using a successive Taylor series expansion to the path and the period of particle ...

Preferential concentration of inertial particles in turbulence is studied numerically by evaluating the Lagrangian compressibility of the particle velocity field using the "full Lagrangian method." This is compared with the "mesoscopic Eulerian particle velocity field" both in a direct numerical simulation of turbulence and in a synthetic flow field. We demonstrate that the Lagrangian method, i...

We propose a numerical method for modeling multimaterial flows where the domain is decomposed into separate Eulerian and Lagrangian subdomains. That is, the equations are written in Eulerian form in one subdomain and Lagrangian form in the other subdomain. This is of interest, for example, when considering the effect of underwater explosions on the hull of a ship or the impact of a low speed pr...

We develop an Eulerian-Lagrangian iterative solution technique for accurate and efficient numerical simulation of single-phase compositional flow through three-dimensional compressible porous media in the presence of multiple injection and production wells. In the numerical simulator, an Eulerian-Lagrangian method is used to solve the convectiondiffusion transport equations and a mixed finite e...