Lagrangian versus Eulerian integration errors

Idelsohn, Sergio; Oñate, Eugenio; Nigro, Norberto M.; Becker, Pablo; Giménez, Juan M.

doi:10.1016/j.cma.2015.04.003

Cited by 23 publications

(31 citation statements)

References 35 publications

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“…, a h,n = a h (x, t n ) and f h,n+1 = f h (x, t n+1 ). We refer to earlier papers [17,19,16] on the SL-PFEM for several alternate time integration strategies for the Stokes system to be solved on the background mesh.…”

Section: Semi-lagrangian Particle Finite Element Methodsmentioning

confidence: 99%

“…Therefore the updates in the particle position and its velocity within a time-step are decoupled in the X-IVAS scheme. When the velocity field has a significant temporal variation within a time step, the trajectory computed using equation (19) will have a significant error. In the Stokes wave propagation problem, transporting particles along the streamlines (see Figure 6) with large time steps will lead to significant errors in the configuration of the fluid domain.…”

Section: Trajectory Approximation For Stokes Wavesmentioning

confidence: 99%

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Seakeeping with the semi-Lagrangian particle finite element method

et al. 2016

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The application of the semi-Lagrangian Particle Finite Element Method (SL-PFEM) for the seakeeping simulation of the Wave Adaptive Modular Vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL-PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented. Keywords Particle Finite Element Method • semi-Lagrangian formulations • seakeeping 1 Introduction The Particle Finite Element Method (PFEM) [18] is a versatile framework for the analysis of fluid-structure interaction problems. The PFEM combines Lagrangian particle-based techniques with the advantage of the integral formulation of the Finite Element Method (FEM). It has been shown [14, 15,21, 28, 13, 27] to successfully simulate a wide variety of complex engineering problems, e.g., free-surface/multi-fluid flows with violent interface motions, multi-fluid mixing and

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Section: Semi-lagrangian Particle Finite Element Methodsmentioning

confidence: 99%

Section: Trajectory Approximation For Stokes Wavesmentioning

confidence: 99%

Seakeeping with the semi-Lagrangian particle finite element method

et al. 2016

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“…On the other hand, as expected when using pure Lagrangian formulations with mesh‐based algorithms, the mesh quickly deteriorates in time. To overcome this difficulty, when the mesh becomes too distorted a remeshing should be performed with a highly computationally effective technique, to be repeatedly used during the analysis.…”

Section: Introductionmentioning

confidence: 99%

“…This requires a reliable mesh generation strategy, capable to produce regular meshes and fast enough to be repeatedly used during the simulation. Delaunay mesh generators have proved to be robust and versatile and particularly suited for this kind of applications …”

Section: Introductionmentioning

confidence: 99%

“…Delaunay mesh generators 8 have proved to be robust and versatile and particularly suited for this kind of applications. 3,9,10 Delaunay tessellation creates the convex hull starting from a given set of points. In two dimensions, the Delaunay triangulation guarantees remarkable optimality properties, such as the minimization of the maximum radius of an element circumcircle and the maximization of the minimum angle among all the elements.…”

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An efficient runtime mesh smoothing technique for 3D explicit Lagrangian free‐surface fluid flow simulations

Meduri

Cremonesi

Perego

2018

Numerical Meth Engineering

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Summary A fast runtime mesh smoothing algorithm for explicit Lagrangian simulations of 3D weakly compressible viscous fluid flows, implemented in conjunction with the particle finite element method (PFEM), is proposed. The formulation for weakly compressible fluids allows for the use of an explicit time integration scheme. Explicit solvers are appealing for large‐scale engineering problems characterized by fast dynamics and/or a high degree of nonlinearity. However, the conditional stability of these schemes requires the use of small time increments, proportional to the size of the element in the mesh with the worst geometrical quality. The Lagrangian description of the PFEM requires an efficient and robust runtime mesh generator algorithm, such as the Delaunay tessellation, to create new meshes during the analysis, whenever the current ones get too distorted because of the motion of the mesh nodes. When 3D problems are considered, a computationally effective mesh‐improving algorithm is also required because, in 3D, the Delaunay tessellation loses some of its optimality properties holding in 2D so that badly shaped tetrahedra are frequently included in the triangulation, leading to unacceptably small stable time step sizes for the explicit solver. To this purpose, a novel and efficient mesh smoothing technique is here proposed, exploiting an elastic analogy that allows for the use of the same explicit and parallelizable architecture of the fluid solver. This smoothing algorithm has been specifically designed to ensure reasonably large critical time step sizes at an acceptable computational cost. This is particularly appealing for the application of explicit Lagrangian PFEM in large‐scale 3D engineering problems, but it could be conveniently applied also to regularize the mesh and improve the solution of implicit solvers.

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Particle Methods in Computational Fluid Dynamics

Idelsohn

Oñate

Becker

2017

Encyclopedia of Computational Mechanics Second Edition

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Particle methods in computational fluid dynamics (CFD) are numerical tools for the solution of the equations of fluid dynamics, obtained by replacing the fluid continuum with a finite set of particles. One of the key attributes of particle methods is that pure advection is treated exactly. The convection of properties eases the solution of multi‐material problems, simplifying the detection of interfaces. The use of particles also allows to bridge the gap between the continuum and fragmentation in a natural way, for example, in fracture or droplets problems. Particle methods can be roughly classified into two types: (i) those based on probabilistic models, which represent macroscopic properties as statistical behaviors of microscopic particles, and (ii) those based on deterministic models, implying that the state in every point at a given time is perfectly defined. This chapter covers the most common deterministic particle methods. The layout of this chapter is as follows. First we present the governing equations for the motion of fluids. Then, we describe the basic concepts of two methods that rely only on the particles to obtain the field of variables and their derivatives: smoothed particle hydrodynamics (SPH) and the moving particle semi‐implicit method (MPS). The next sections describe three methods that use the particles in combination with a finite element method (FEM) mesh to improve the accuracy. First the material point method (MPM) is described, followed by a more detailed evaluation of the particle finite element method (PFEM) and the finite element method second generation (PFEM‐2). For each of the particle methods, the advantages and disadvantages of the strategies are evaluated. The chapter concludes with an overview of the DEM and the coupling of the DEM with the FEM for the analysis of particulate flows and their interaction with structures.

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Lagrangian versus Eulerian integration errors

Abstract: The possibility to use a Lagrangian frame to solve problems with large time-steps was successfully explored previously by the authors for the solution of homogeneous incompressible fluids and also for solving multi-fluid problems [28][29][30]

Cited by 23 publications

References 35 publications

Seakeeping with the semi-Lagrangian particle finite element method

Seakeeping with the semi-Lagrangian particle finite element method

An efficient runtime mesh smoothing technique for 3D explicit Lagrangian free‐surface fluid flow simulations

Particle Methods in Computational Fluid Dynamics

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