Eulerian on Lagrangian Cloth Simulation

This thesis introduces a novel Eulerian-on-Lagrangian (EoL) approach for simulating cloth. This approach allows for the simulation of traditionally difficult cloth scenarios, such as draping and sliding cloth over sharp features like the edge of a table. A traditional Lagrangian approach models a cloth as a series of connected nodes. These nodes are free to move in 3d space, but have difficulty with sliding over hard edges. The cloth cannot always bend smoothly around these edges, as motion can only occur at existing nodes. An EoL approach adds additional flexibility to a Lagrangian approach by constructing special Eulerian on Lagrangian nodes (EoL Nodes), where cloth material can pass through a fixed point. On contact with the edge of a box, EoL nodes are introduced directly on the edge. These nodes allow the cloth to bend exactly at the edge, and pass smoothly over the area while sliding. Using this ‘Eulerian-on-Lagrangian’ discretization, a set of rules for introducing and constraining EoL Nodes, and an adaptive remesher, This simulator allows cloth to move in a sliding motion over sharp edges. The current implementation is limited to cloth collision with static boxes, but the method presented can be expanded to include contact with more complicated meshes and dynamic rigid bodies

The ALE-method with triangular elements: direct convection of integration point values

The arbitrary Lagrangian-Eulerian (ALE) finite element method is applied to the simulation of forming processes where material is highly deformed. Here, the split formulation is used: a Lagrangian step is done with an implicit finite element formulation, followed by an explicit (purely convective) Eulerian step. The purpose of this study is to investigate the Eulerian step for quadratic triangular elements. To solve the convection equation for integration point values, a new method inspired by Van Leer is constructed. The new method is based on direct convection of integration point values without intervention of nodal point values.\ud The Molenkamp test and a so-called block test were executed to check the performance and stability of the convection scheme. From these tests it is concluded that the new convection scheme shows accurate results. The scheme is extended to an ALE-algorithm. An extrusion process was simulated to test the applicability of the scheme to engineering problems. It is concluded that direct convection of integration point values with the presented algorithm leads to accurate results and that it can be applied to ALE-simulation

Numerische Modellierung und Simulation von Kavitationsblasenwolken mit einer Lagrange-Euler-Methode

In this thesis, the Lagrangian-Eulerian coupling model is proposed to investigate dynamically the cavitation bubble cloud. Based on the Lagrangian-Eulerian one-way coupling model, the homogeneous cavitation nucleation inside microchannel is studied. Furthermore, we develop the Lagrangian-Eulerian two-way coupling for the numerical simulation of the bubble cluster with pressure wave interaction and the bubble cloud Rayleigh collapse.In dieser Doktorarbeit wird das Lagrange-Euler-Kopplungsmodell vorgeschlagen, um die Kavitationsblasenwolke dynamisch zu untersuchen. Basierend auf dem Lagrange-Euler-Einweg-Kopplungsmodell wird die homogene Kavitationskeimbildung im Mikrokanal untersucht. Darüber hinaus entwickeln wir die Lagrange-Euler-Zweiwege-Kopplung zur numerischen Simulation des Blasenclusters mit Druckwellenwechselwirkung und dem Rayleigh-Kollaps der Bubble Cloud

Statistical properties of supersonic turbulence in the Lagrangian and Eulerian frameworks

We present a systematic study of the influence of different forcing types on the statistical properties of supersonic, isothermal turbulence in both the Lagrangian and Eulerian frameworks. We analyse a series of high-resolution, hydrodynamical grid simulations with Lagrangian tracer particles and examine the effects of solenoidal (divergence-free) and compressive (curl-free) forcing on structure functions, their scaling exponents, and the probability density functions of the gas density and velocity increments. Compressively driven simulations show a significantly larger density contrast, a more intermittent behaviour, and larger fractal dimension of the most dissipative structures at the same root mean square Mach number. We show that the absolute values of Lagrangian and Eulerian structure functions of all orders in the integral range are only a function of the root mean square Mach number, but independent of the forcing. With the assumption of a Gaussian distribution for the probability density function of the velocity increments on large scales, we derive a model that describes this behaviour.Comment: 24 pages, 13 figures, Journal of Fluid Mechanics in pres

Lagrangian filtered density function for LES-based stochastic modelling of turbulent dispersed flows

The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study turbulent dispersed flows when the computational cost of Direct Numerical Simulation (DNS) becomes too expensive. The applicability of this approach is however limited if the effects of the Sub-Grid Scales (SGS) of the flow on particle dynamics are neglected. In this paper, we propose to take these effects into account by means of a Lagrangian stochastic SGS model for the equations of particle motion. The model extends to particle-laden flows the velocity-filtered density function method originally developed for reactive flows. The underlying filtered density function is simulated through a Lagrangian Monte Carlo procedure that solves for a set of Stochastic Differential Equations (SDEs) along individual particle trajectories. The resulting model is tested for the reference case of turbulent channel flow, using a hybrid algorithm in which the fluid velocity field is provided by LES and then used to advance the SDEs in time. The model consistency is assessed in the limit of particles with zero inertia, when "duplicate fields" are available from both the Eulerian LES and the Lagrangian tracking. Tests with inertial particles were performed to examine the capability of the model to capture particle preferential concentration and near-wall segregation. Upon comparison with DNS-based statistics, our results show improved accuracy and considerably reduced errors with respect to the case in which no SGS model is used in the equations of particle motion

A note on the consistency of Hybrid Eulerian/Lagrangian approach to multiphase flows

The aim of the present paper is to introduce and to discuss inconsistencies errors that may arise when Eulerian and Lagrangian models are coupled for the simulations of turbulent poly-dispersed two-phase flows. In these hydrid models, two turbulence models are in fact implicitely used at the same time and it is essential to check that they are consistent, in spite of their apparent different formulations. This issue appears in particular in the case of very-small particles, or tracer-limit particles, and it is shown that coupling inconsistent turbulence models (Eulerian and Lagrangian) can result in non-physical results, notably for second-order fluid velocity moments. This problem is illustrated by some computations for fluid particles in a turbulent channel flow using several coupling strategies.Comment: 14 pages, 3 figure