Arbitrary Lagrangian Eulerian approximation with remeshing for Navier–Stokes equations

Murea, Cornel Marius

doi:10.1002/cnm.1223

Cited by 9 publications

(6 citation statements)

References 12 publications

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“…This latter approach is defined as monolithic in contrast to the previous partitioned ones, but does not strictly solve system variables simultaneously, which will insure accuracy and stability of the interface coupling. The Arbitrary Lagrangian Eulerian (ALE) [5,7,14,[23][24][25][26][27][28] method which can be coupled to both monolithic and partitioned approaches has the advantage of discretizing strictly separated material. It can be used for viscous flow governed by Navier-Stokes equation as well as elastic solid equation.…”

Section: Introductionmentioning

confidence: 99%

A multi-physics and multi-time scale approach for modeling fluid–solid interaction and heat transfer

Bordère

Caltagirone

2016

Computers & Structures

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A novel non-conservative formulation for equations governing thermo-mechanical phenomena is developed to address multi-material and multi-physics issues. The first key point is that this formulation achieves a unifying equation for compressible viscous fluid flow and elastic solid deformation.The second is that the thermo-mechanical equations are both written with velocity and thermal flux variables to solve them simultaneously. With that formulation, interaction conditions at the fluid-structure interface become implicit and state equation is no longer necessary. Multi-time scale problems are solved, from the time scale of acoustic and thermoacoustic wave propagation, to longer time scale of fluid flow and thermal diffusion.

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Section: Introductionmentioning

confidence: 99%

A multi-physics and multi-time scale approach for modeling fluid–solid interaction and heat transfer

Bordère

Caltagirone

2016

Computers & Structures

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“…Consequently, they typically require fewer grid points relative to the fixed grid techniques to achieve the same level of resolution near the moving boundaries. Large boundary movements, however, in the boundary-conforming approaches create highly skewed grids that reduce the convergence and accuracy of the numerical scheme [12, 13]. To avoid highly skewed grids, computationally expensive remeshing of the grid may be required [12–15].…”

Section: Methodsmentioning

confidence: 99%

“…Large boundary movements, however, in the boundary-conforming approaches create highly skewed grids that reduce the convergence and accuracy of the numerical scheme [12, 13]. To avoid highly skewed grids, computationally expensive remeshing of the grid may be required [12–15]. In what follows we examine these two classes of methods in more detail.…”

Section: Methodsmentioning

confidence: 99%

Left Ventricular Flow Analysis: Recent Advances in Numerical Methods and Applications in Cardiac Ultrasound

Borazjani

Westerdale

McMahon

et al. 2013

Computational and Mathematical Methods in Medicine

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The left ventricle (LV) pumps oxygenated blood from the lungs to the rest of the body through systemic circulation. The efficiency of such a pumping function is dependent on blood flow within the LV chamber. It is therefore crucial to accurately characterize LV hemodynamics. Improved understanding of LV hemodynamics is expected to provide important clinical diagnostic and prognostic information. We review the recent advances in numerical and experimental methods for characterizing LV flows and focus on analysis of intraventricular flow fields by echocardiographic particle image velocimetry (echo-PIV), due to its potential for broad and practical utility. Future research directions to advance patient-specific LV simulations include development of methods capable of resolving heart valves, higher temporal resolution, automated generation of three-dimensional (3D) geometry, and incorporating actual flow measurements into the numerical solution of the 3D cardiovascular fluid dynamics.

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“…The reason is that for U = 2, in the zone of the right end of the structure, some triangles of the ALE mesh became flat. To avoid this, it is possible to use ALE framework with remeshing as in [15], but we shall treat this in a forcoming paper.…”

Section: A Numerical Testmentioning

confidence: 99%

Stable Semi-Implicit Monolithic Scheme for Interaction Between Incompressible Neo-hookean Structure and Navier-Stokes Fluid

sci¹

2019

JMS

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We present a monolithic algorithm for solving fluid-structure interaction. The Updated Lagrangian framework is used for the incompressible neo-hookean structure and Arbitrary Lagrangian Eulerian coordinate is employed for the Navier-Stokes equations. The algorithm uses a global mesh for the fluid-structure domain which is compatible with the fluid-structure interface. At each time step, a non-linear system is solved in a domain corresponding to the precedent time step. It is a semi-implicit algorithm in the sense that the velocity, the pressure are computed implicitly, but the domain is updated explicitly. Using one velocity field defined over the fluid-structure mesh, and globally continuous finite elements, the continuity of the velocity at the interface is automatically verified. The equation of the continuity of the stress at the interface does not appear in this formulation due to action and reaction principle. The stability in time is proved. A second algorithm is introduced where at each time step, only a linear system is solved in order to find the velocity and the pressure. Numerical experiments are presented.

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Arbitrary Lagrangian Eulerian approximation with remeshing for Navier–Stokes equations

Cited by 9 publications

References 12 publications

A multi-physics and multi-time scale approach for modeling fluid–solid interaction and heat transfer

A multi-physics and multi-time scale approach for modeling fluid–solid interaction and heat transfer

Left Ventricular Flow Analysis: Recent Advances in Numerical Methods and Applications in Cardiac Ultrasound

Stable Semi-Implicit Monolithic Scheme for Interaction Between Incompressible Neo-hookean Structure and Navier-Stokes Fluid

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