A hybrid Lagrangian-Eulerian (hLE) scheme, combining a particle-based, mesh-free technique with a finitevolume flow solver, is developed for direct simulations of two-phase flows. The approach uses marker points around the interface and advects the signed distance to the interface in a Lagrangian frame. The kernel–based derivative calculations typical of particle methods are used to extract the...

ALEGRA is a multi-material, arbitrary-Lagrangian-Eulerian (ALE) code for solid dynamics being developed by the Computational Physics Research and Development Department at Sandia +tionat Laboratories. It combines the features of modem Eulerian shock codes, such as CTH, with modem Lagrangian structural analysis codes. With the ALE algorithm, the mesh can be stationary (Eulerian) with the materia...

We study the observability of one and two point vortex flow from one or two Eulerian or Lagrangian observations. By observability we mean the ability to determine the locations and strengths of the vortices from the time history of the observations. An Eulerian observation is a measurement of the velocity of the flow at a fixed point in the domain of the flow. A Lagrangian observation is the me...

We consider an arbitrary-Lagrangian-Eulerian evolving surface finite element method for the numerical approximation of advection and diffusion of a conserved scalar quantity on a moving surface. We describe the method, prove optimal order error bounds and present numerical simulations that agree with the theoretical results.

We present a hybrid numerical method for computing the propagation of a diffusing passive pollutant in shallow water. The flow is modeled by the SaintVenant system of shallow water equations and the pollutant propagation is described by a convection-diffusion equation. In this paper, we extend the hybrid finite-volume-particle (FVP) method, which was originally introduced in [CK04, CKP06] for t...

We present a new reconnection-based Arbitrary Lagrangian Eulerian (ALE) method. The main elements in a standard ALE simulation are an explicit Lagrangian phase in which the solution and grid are updated, a rezoning phase in which a new grid is defined, and a remapping phase in which the Lagrangian solution is transferred (conservatively interpolated) onto the new grid. In standard ALE methods t...

Marine robots are playing important roles in environmental sensing andocean observation applications. This tutorial introduces the overall sys-tems architecture and patterns for data streams that enable autonomyfor marine robots in environmental sensing applications. The articleproposes the concept of cyber-maritime cycle and surveys its use as arecent development in marine ...

The gradient-flow dynamics of an arbitrary geometric quantity is derived using a generalization of Darcy’s Law. We consider flows in both Lagrangian and Eulerian formulations. The Lagrangian formulation includes a dissipative modification of fluid mechanics. Eulerian equations for self-organization of scalars, 1-forms and 2-forms are shown to reduce to nonlocal characteristic equations. We iden...

A method for solving the saturation equation for two-phase ow is presented. The method may be viewed as an operator splitting method or as an Eulerian-Lagrangian backtracking procedure or as a modiied method of characteristics. For each time step, the method consists of an advection step and a diiusion step. The advection step requires the tracking of streamlines locally around certain integrat...