Large time-step explicit integration method for solving problems with dominant convection

Idelsohn, Sergio; Nigro, Norberto M.; Limache, Alejandro Cesar; Oñate, Eugenio

doi:10.1016/j.cma.2011.12.008

Cited by 57 publications

(83 citation statements)

References 16 publications

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“…The Particle Finite Element Method, second generation (PFEM-2) has been described in [28,29]. Only a summary will be presented here for completeness.…”

Section: The Particle Finite Element Method Second Generation (Pfem-2)mentioning

confidence: 99%

“…The possibility to use the PFEM to solve non-linear problems with large time-steps in order to obtain an accurate and fast solution was successfully explored by the authors for the solution of the homogeneous incompressible Navier-Stokes equations [28] and multi-fluid problems [29]. This new strategy was named PFEM-2.…”

Section: Introductionmentioning

confidence: 99%

“…

AbstractThe 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]

…”

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confidence: 99%

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Lagrangian versus Eulerian integration errors

Idelsohn

Oñate

Nigro

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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“…The Particle Finite Element Method, second generation (PFEM-2) has been described in [28,29]. Only a summary will be presented here for completeness.…”

Section: The Particle Finite Element Method Second Generation (Pfem-2)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Lagrangian versus Eulerian integration errors

Idelsohn

Oñate

Nigro

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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“…free-surface/multi-fluid flows with violent interface motions, polymer melting and burning simulations, multi-fluid mixing and buoyancy driven segregation problems, etc. A recent development within the framework of the PFEM is the X-IVAS (eXplicit Integration along the Velocity and Acceleration Streamlines) scheme [9]. Its development was motivated in the need for a faster and more accurate time integrator for incompressible flows.…”

Section: Introductionmentioning

confidence: 99%

“…The X-IVAS hypothesis has been tested [9,8] by successfully simulating some benchmark CFD and FSI examples using very large time steps, e.g. 10-15 times the standard Courant-Friedrichs-Lewy stability limit.…”

Section: Introductionmentioning

confidence: 99%

Numerically stable formulas for a particle-based explicit exponential integrator

Nadukandi

2015

Comput Mech

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Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the Particle Finite Element Method. Algebraically, this scheme involves two steps: 1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and 2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourthorder divided differences of the exponential function.

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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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Large time-step explicit integration method for solving problems with dominant convection

Cited by 57 publications

References 16 publications

Lagrangian versus Eulerian integration errors

Lagrangian versus Eulerian integration errors

Numerically stable formulas for a particle-based explicit exponential integrator

Particle Methods in Computational Fluid Dynamics

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