Arbitrary Lagrangian–Eulerian method for Navier–Stokes equations with moving boundaries

2004 ◽  
Vol 193 (45-47) ◽  
pp. 4819-4836 ◽  
Author(s):  
Fabián Duarte ◽  
Raúl Gormaz ◽  
Srinivasan Natesan
Keyword(s):  
Stokes Equations ◽  
Moving Boundaries ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Eulerian Method ◽  
Arbitrary Lagrangian Eulerian Method

Simulation-Based Analysis of 3D Flow Inside a Micropump With Passive Valves

2007 ◽  
Author(s):  
A. F. Tabak ◽  
A. Solak ◽  
E. Y. Erdem ◽  
C. Akcan ◽  
S. Yesilyurt
Keyword(s):  
Flow Rate ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Driving Frequency ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
New Developments ◽  
Arbitrary Lagrangian Eulerian Method ◽  
Simulation Based

It is expected that chemical, biological and environmental applications of microdevices will increase with new developments in micromachining techniques. In this work, a micropump design that utilizes passive valves and an actuated diaphragm is presented. The flow rate is controlled by the deflection and the frequency of the diaphragm’s displacement. Passive valves are used for directing the flow. Poiseuille flow analogy is used to generate the equivalent pressure drop and flow rate via modifying the viscosity in the valve-channel in order to replace the variation of the channel width due to valve movement. Overall flow in the micropump is governed by three-dimensional time-dependent Navier Stokes equations. Deformation of the domain due to moving boundaries that coincide with the diaphragm motion is handled with the arbitrary Lagrangian-Eulerian method. Flow rate, hydraulic power and the efficiency of the micropump are obtained with respect to driving frequency and displacement of the diaphragm.

scholarly journals NUMERICAL SOLUTION OF FLUID-STRUCTURE INTERACTION PROBLEMS WITH CONSIDERING OF CONTACTS

2021 ◽  
Vol 61 (SI) ◽  
pp. 155-162
Author(s):  
Petr Sváček
Keyword(s):  
Stokes Equations ◽  
Fluid Motion ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Computational Domain ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Computational Mesh ◽  
Arbitrary Lagrangian Eulerian Method ◽  
High Reynolds

This paper is interested in the mathematical modelling of the voice production process. The main attention is on the possible closure of the glottis, which is included in the model with the concept of a fictitious porous media and using the Hertz impact force The time dependent computational domain is treated with the aid of the Arbitrary Lagrangian-Eulerian method and the fluid motion is described by the incompressible Navier-Stokes equations coupled to structural dynamics. In order to overcome the instability caused by the dominating convection due to high Reynolds numbers, stabilization procedures are applied and numerically analyzed for a simplified problem. The possible distortion of the computational mesh is considered. Numerical results are shown.

scholarly journals Vibrations of Nonlinear Elastic Structure Excited by Compressible Flow

2021 ◽  
Vol 11 (11) ◽  
pp. 4748
Author(s):  
Monika Balázsová ◽  
Miloslav Feistauer ◽  
Jaromír Horáček ◽  
Adam Kosík
Keyword(s):  
Compressible Flow ◽  
Nonlinear Elasticity ◽  
Vocal Tract ◽  
Stokes Equations ◽  
Vocal Folds ◽  
Nonlinear Material ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Reliable Solution

This study deals with the development of an accurate, efficient and robust method for the numerical solution of the interaction of compressible flow and nonlinear dynamic elasticity. This problem requires the reliable solution of flow in time-dependent domains and the solution of deformations of elastic bodies formed by several materials with complicated geometry depending on time. In this paper, the fluid–structure interaction (FSI) problem is solved numerically by the space-time discontinuous Galerkin method (STDGM). In the case of compressible flow, we use the compressible Navier–Stokes equations formulated by the arbitrary Lagrangian–Eulerian (ALE) method. The elasticity problem uses the non-stationary formulation of the dynamic system using the St. Venant–Kirchhoff and neo-Hookean models. The STDGM for the nonlinear elasticity is tested on the Hron–Turek benchmark. The main novelty of the study is the numerical simulation of the nonlinear vocal fold vibrations excited by the compressible airflow coming from the trachea to the simplified model of the vocal tract. The computations show that the nonlinear elasticity model of the vocal folds is needed in order to obtain substantially higher accuracy of the computed vocal folds deformation than for the linear elasticity model. Moreover, the numerical simulations showed that the differences between the two considered nonlinear material models are very small.

Iterative method for solving fully-coupled fluid solid systems

2010 ◽  
pp. 653-670
Author(s):  
Elisabeth Longatte
Keyword(s):  
Stokes Equations ◽  
Cross Flow ◽  
Elastic Cylinder ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Ale Formulation ◽  
Volume Method ◽  
Fully Coupled ◽  
Solid System

This work is concerned with the modelling of the interaction of a fluid with a rigid or a flexible elastic cylinder in the presence of axial or cross-flow. A partitioned procedure is involved to perform the computation of the fully-coupled fluid solid system. The fluid flow is governed by the incompressible Navier-Stokes equations and modeled by using a fractional step scheme combined with a co-located finite volume method for space discretisation. The motion of the fluid domain is accounted for by a moving mesh strategy through an Arbitrary Lagrangian-Eulerian (ALE) formulation. Solid dyncamics is modeled by a finite element method in the linear elasticity framework and a fixed point method is used for the fluid solid system computation. In the present work two examples are presented to show the method robustness and efficiency.

Numerical Simulations of Nonlinear Post-Critical Vibrations of an Airfoil After Flutter Instability

2011 ◽  
Author(s):  
Jaromi´r Hora´cˇek ◽  
Miloslav Feistauer ◽  
Petr Sva´cˇek
Keyword(s):  
Numerical Simulations ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Mass Matrix ◽  
Vertical Direction ◽  
Navier Stokes ◽  
Computational Domain ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Classical Flutter

The contribution deals with the numerical simulation of the flutter of an airfoil with three degrees of freedom (3-DOF) for rotation around an elastic axis, oscillation in the vertical direction and rotation of a flap. The finite element (FE) solution of two-dimensional (2-D) incompressible Navier-Stokes equations is coupled with a system of nonlinear ordinary differential equations describing the airfoil vibrations with large amplitudes taking into account the nonlinear mass matrix. The time-dependent computational domain and a moving grid are treated by the Arbitrary Lagrangian-Eulerian (ALE) method and a suitable stabilization of the FE discretization is applied. The developed method was successfully tested by the classical flutter computation of the critical flutter velocity using NASTRAN program considering the linear model of vibrations and the double-lattice aerodynamic theory. The method was applied to the numerical simulations of the post flutter regime in time domain showing Limit Cycle Oscillations (LCO) due to nonlinearities of the flow model and vibrations with large amplitudes. Numerical experiments were performed for the airfoil NACA 0012 respecting the effect of the air space between the flap and the main airfoil.

Optimization of Propulsion Kinematics of a Flexible Foil Using Integrated CFD-CSD Simulations

2012 ◽  
Author(s):  
Jiho You ◽  
Jinmo Lee ◽  
Donghyun You
Keyword(s):  
Structural Dynamics ◽  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Computational Simulation ◽  
Moving Boundaries ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Navier Stokes Equations ◽  
Simulation Methodology ◽  
Computational Structural Dynamics

A computational simulation methodology, which combines a computational fluid dynamics technique and a computational structural dynamics technique, is employed to design a deformable foil of which kinematics is inspired by the propulsive motion of a fin or a tail of fish and cetacean. The unsteady incompressible Navier-Stokes equations are solved using a second-order accurate finite-difference method and an immersed-boundary method to effectively impose boundary conditions on complex moving boundaries. A finite-element-based structural dynamics solver is employed to compute the deformation of the foil due to interaction with fluid. A phase angle between pitching and heaving motions as well as the flexibility of the foil, which is represented by the Youngs modulus are varied to find out how these factors affect the propulsion efficiency.

Simulation-Based Analysis of a Biologically-Inspired Micropump With a Rotating Spiral Inside a Microchannel

2008 ◽  
Author(s):  
Mustafa Koz ◽  
Serhat Yesilyurt
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Asymptotic Results ◽  
Navier Stokes Equations ◽  
Rate Maximum ◽  
Finite Element Package ◽  
Resistive Force Theory

Microorganisms such as bacteria use their rotating helical flagella for propulsion speeds up to tens of tail lengths per second. The mechanism can be utilized for controlled pumping of liquids in microchannels. In this study, we aim to analyze the effects of control parameters such as axial span between helical rounds (wavelength), angular velocity of rotations (frequency), and the radius of the helix (amplitude) on the maximum time-averaged flow rate, maximum head, rate of energy transfer, and efficiency of the micropump. The analysis is based on simulations obtained from the three-dimensional time-dependent numerical model of the flow induced by the rotating spiral inside a rectangular-prism channel. The flow is governed by Navier-Stokes equations subject to continuity in time-varying domain due to moving boundaries of the spiral. Numerical solutions are obtained using a commercial finite-element package which uses arbitrary Lagrangian-Eulerian method for mesh deformations. Results are compared with asymptotic results obtained from the resistive-force-theory available in the literature.

Review on Fluid Structure Interaction Solution Method for Biomechanical Application

2014 ◽  
Vol 660 ◽  
pp. 927-931 ◽  
Author(s):  
Nazri Huzaimi bin Zakaria ◽  
Mohd Zamani Ngali ◽  
Ahmad Rivai
Keyword(s):  
Stokes Equations ◽  
Complex Geometry ◽  
Fluid Structure Interaction ◽  
Navier Stokes ◽  
Structural Parameter ◽  
Clear Understanding ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Fluid Structure ◽  
Structure Interaction

Fluid-Structure Interaction engages with complex geometry especially in biomechanical problem. In order to solve critical case studies such as cardiovascular diseases, we need the structure to be flexible and interact with the surrounding fluids. Thus, to simulate such systems, we have to consider both fluid and structure two-way interactions. An extra attention is needed to develop FSI algorithm in biomechanic problem, namely the algorithm to solve the governing equations, the coupling between the fluid and structural parameter and finally the algorithm for solving the grid connectivity. In this article, we will review essential works that have been done in FSI for biomechanic. Works on Navier–Stokes equations as the basis of the fluid solver and the equation of motion together with the finite element methods for the structure solver are thoroughly discussed. Important issues on the interface between structure and fluid solvers, discretised via Arbitrary Lagrangian–Eulerian grid are also pointed out. The aim is to provide a crystal clear understanding on how to develop an efficient algorithm to solve biomechanical Fluid-Structure Interaction problems in a matrix based programming platform.

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