A hardware-based approach for visualizing unsteady flow fields by means of Lagrangian-Eulerian advection is presented. Both noise-based and dyebased texture advection is supported. The implementation allows the advection of each texture to be performed completely on the graphics hardware in a single-pass rendering. We discuss experiences with the interactive visualization of unsteady flow field...

The present lecture notes address three columns on which the Lagrangian perturbation approach to cosmological dynamics is based: 1. the formulation of a Lagrangian theory of self–gravitating flows in which the dynamics is described in terms of a single field variable; 2. the procedure, how to obtain the dynamics of Eulerian fields from the Lagrangian picture, and 3. a precise definition of a Ne...

Variational principles for magnetohydrodynamics were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of barotropic magnetohydrodynamics can be derived. The variational principle is given in terms of six independent functions for non-stationary barotropic flows and three ...

We study the hp version of three families of Eulerian-Lagrangian mixed discontinuous finite element (MDFE) methods for the numerical solution of advectiondiffusion problems. These methods are based on a space-time mixed formulation of the advection-diffusion problems. In space, they use discontinuous finite elements, and in time they approximately follow the Lagrangian flow paths (i.e., the hyp...

We begin by placing the Generalized Lagrangian Mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincaré (EP) variational framework of fluid dynamics, for an averaged Lagrangian. We then state the EP Averaging Lemma – that GLM averaged equations arise from GLM averaged Lagrangians in the EP framework. Next, we derive a set of approximate small amplitude GLM equations (glm ...

The computational fluid dynamics (CFD) methods has been widely used in modeling particle transport and distribution in enclosed spaces. Generally, the particle models can be classified as either Eulerian or Lagrangian methods while each has its own pros and cons. This investigation is to compare the two modeling methods with an emphasis on their performance of predicting particle concentration ...

A spatially resolved stochastic weighted particle method for inception–coagulation– advection problems is presented. Convergence to a deterministic limit is briefly studied. Numerical experiments are carried out for two problems with very different coagulation kernels. These tests show the method to be robust and confirm the convergence properties. The robustness of the weighted particle method...