The purpose of this paper is twofold. First, we give a derivation of the Lagrangian averaged Euler (LAE-α) and Navier-Stokes (LANS-α) equations. This theory involves a spatial scale α and the equations are designed to accurately capture the dynamics of the Euler and Navier-Stokes equations at length scales larger than α, while averaging the motion at scales smaller than α. The derivation involv...

Simultaneous measurements of turbulent vertical velocity fluctuations at a height of 300 ft. measured by means of a fixed anemometer, small floating balloons, and airplane gust equipment at Brookhaven are presented. The resulting Eulerian (fixed anemometer) turbulence energy mectra are similar to the Lagrangian (balloon) spectra but "-with a displacement toward higher frequencies. The term Eule...

For problems of convection–diffusion type, Eulerian–Lagrangian localized adjoint methods provide a methodology that maintains the accuracy and efficiency of Eulerian–Lagrangian methods, while also conserving mass and systematically treating any type of boundary condition. In groundwater hydrology, this framework is useful for solute transport, as well as vadose-zone transport, multiphase transp...

Problems involving a transition between dense and dilute dispersed phase regimes often require hybridization of Eulerian-Eulerian (EE) Eulerian-Lagrangian (EL) methods for accurate efficient computational modeling. A hybrid EE-EL formulation is developed in this work from first principles, which asymptotes to well-established EE EL limiting conditions. smooth dynamic criterion corresponding alg...

Bubble cloud collapse is one of the most destructive forms of cavitation. However, numerical modeling of this phenomenon is challenging and involves strong bubble dynamics, bubble-bubble, and bubble-wall interactions. Here we consider an initially spherical cloud near a rigid wall and treat the cloud bubbly mixture as a continuum and the bubbles in the cloud as discrete singularities. These two...

This paper studies the convergence properties of an arbitrary Lagrangian–Eulerian (ALE) Riemann-based SPH algorithm in conjunction with a Weighted Essentially Non-Oscillatory (WENO) high-order spatial reconstruction, framework DualSPHysics open-source code. A analysis is carried out for Lagrangian and Eulerian simulations numerical results demonstrate that, absence particle disorder, overall sc...

We develop a new methodology for the numerical modeling of nonlinear free surface waves, caused by an advancing free surface disturbance, based on combining Lagrangian and Eulerian, or pseudoLagrangian, methods for the time updating of free surface geometry and motion. We solve potential flow equations with a threedimensional (3D) higher-order Boundary Element Method (BEM; Grilli et al., 2000, ...