Galilean invariance is one of the key requirements of many physical models adopted in theoretical and computational mechanics. Spurred by recent research developments in shock hydrodynamics computations [13], a detailed analysis on the principle of Galilean invariance in the context of SUPG operators is presented. It was observed in [13] that lack of Galilean invariance can yield catastrophic i...

In hierarchical models of gravitational clustering, virialized haloes are biased tracers of the matter distribution. As discussed by Mo & White (1996), this bias is nonlinear and stochastic. They developed a model which allows one to write down analytic expressions for the mean of the bias relation, in the initial Lagrangian, and the evolved, Eulerian, spaces. We provide analytic expressions fo...

The most common velocity measurement techniques, based on image analysis, calculate the velocity by cross-correlation of a portion of the digitized images, and give a Eulerian description of the investigated field. Particle tracking velocimetry (PTV), based on the recognition of trajectories of seeding particles, only furnishes a Eulerian description provided the trajectories are shorter than t...

This article presents a data assimilation method in a tidal system, where data from both Lagrangian drifters and Eulerian flow sensors were fused to estimate water velocity. The system is modeled by first-order, hyperbolic partial differential equations subject to periodic forcing. The estimation problem can then be formulated as the minimization of the difference between the observed variables...

We introduce a new computational method for embedding Lagrangian sink particles into an Eulerian calculation. Simulations of gravitational collapse or accretion generally produce regions whose density greatly exceeds the mean density in the simulation. These dense regions require extremely small time steps to maintain numerical stability. Smoothed particle hydrodynamics (SPH) codes approach thi...

We develop some new variations of the Randomized Spectral Method (RSM) and Fourier-Wavelet Method (FWM) for the simulation of homogeneous Gaussian random vector fields based on plane wave decompositions. Some general conditions on the spectral density tensor of the random field which guarantee the theoretical convergence of the numerical representations are given. We then compare the various ra...