scholarly journals Topology Optimization of Time Dependent Viscous Incompressible Flows

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed Abdelwahed ◽  
Maatoug Hassine
Keyword(s):  
Fluid Flow ◽  
Stokes System ◽  
Incompressible Flows ◽  
Navier Stokes ◽  
Dissipated Energy ◽  
Viscous Incompressible Flows ◽  
Topology And Shape Optimization ◽  
Design Function ◽  
Flow Domain ◽  
Small Obstacle

In this paper, we consider topology and shape optimization problem related to the nonstationary Navier-Stokes system. The minimization of dissipated energy in the fluid flow domain is discussed. The proposed approach is based on a sensitivity analysis of a design function with respect to the insertion of a small obstacle in the fluid flow domain. Some numerical results show the efficiency and accurate of the proposed approach.

A Semi-Implicit Scheme for Modeling the Interaction Between Biological Cells and Electric Fields

2007 ◽  
Author(s):  
John H. Pierse ◽  
Arturo Ferna´ndez
Keyword(s):  
Fluid Flow ◽  
Electric Field ◽  
Maxwell Equations ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Computational Time ◽  
Biological Cells ◽  
Field Equations ◽  
Flow Equations

A numerical method for computing the simultaneous solution to the fluid flow equations and the electrostatic field equations is described. The methodology focuses on the modeling of biological cells suspended in fluid plasma. The fluid flow is described using the Navier-Stokes equations for incompressible flows. The electric field is computed trough the Maxwell equations neglecting magnetic effects. The effect of the electric field on the fluid flow is accounted for through the Maxwell stresses. The systems are described by a set of partial differential equations where the solution requires the simultaneous computation of the velocity, pressure and electric potential fields. A semi-implicit numerical scheme is proposed. In order to decrease the computational time required, it is proposed to use a semi-implicit splitting scheme where the Navier-Stokes and Maxwell equations are solved sequentially. The method is used to reproduce the response of human leukocytes immersed in a rotating electric field. An agreement between the numerical results and the data from experiments is observed.

scholarly journals Existence and approximation for Navier–Stokes system with Tresca’s friction at the boundary and heat transfer governed by Cattaneo’s law

2017 ◽  
Vol 23 (3) ◽  
pp. 519-540
Author(s):  
Mahdi Boukrouche ◽  
Imane Boussetouan ◽  
Laetitia Paoli
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Stokes System ◽  
Transfer Problem ◽  
Propagation Speed ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Splitting Technique ◽  
Tresca’S Friction ◽  
Cattaneo’S Law

We consider an unsteady non-isothermal incompressible fluid flow. We model heat conduction with Cattaneo’s law instead of the commonly used Fourier’s law, in order to overcome the physical paradox of infinite propagation speed. We assume that the fluid viscosity depends on the temperature, while the thermal capacity depends on the velocity field. The problem is thus described by a Navier–Stokes system coupled with the hyperbolic heat equation. Furthermore, we consider non-standard boundary conditions with Tresca’s friction law on a part of the boundary. By using a time-splitting technique, we construct a sequence of decoupled approximate problems and we prove the convergence of the corresponding approximate solutions, leading to an existence theorem for the coupled fluid flow/heat transfer problem. Finally, we present some numerical results.

scholarly journals Topological asymptotic formula for the 3D non-stationary Stokes problem and application

2020 ◽  
Vol Volume 32 - 2019 - 2020 ◽  
Author(s):  
Maatoug Hassine ◽  
Rakia Malek
Keyword(s):  
Asymptotic Expansion ◽  
Stokes System ◽  
Stokes Problem ◽  
Three Dimensional ◽  
Detection Algorithm ◽  
International Audience ◽  
Flow Domain ◽  
Topological Asymptotic Expansion ◽  
Small Obstacle ◽  
Theoretical Results

International audience This paper is concerned with a topological asymptotic expansion for a parabolic operator. We consider the three dimensional non-stationary Stokes system as a model problem and we derive a sensitivity analysis with respect to the creation of a small Dirich-let geometric perturbation. The established asymptotic expansion valid for a large class of shape functions. The proposed analysis is based on a preliminary estimate describing the velocity field perturbation caused by the presence of a small obstacle in the fluid flow domain. The obtained theoretical results are used to built a fast and accurate detection algorithm. Some numerical examples issued from a lake oxygenation problem show the efficiency of the proposed approach. Ce papier porte sur l'analyse de sensibilité topologique pour un opérateur parabolique. On considère le problème de Stokes instationnaire comme un exemple de modèle et on donne une étude de sensibilité décrivant le comportement asymptotique de l'opérateur relativement à une petite perturbation géométrique du domaine. L'analyse présentée est basée sur une estimation du champ de vitesse calculée dans le domaine perturbé. Les résultats de cette étude ont servi de base pour développer un algorithme d'identification géométrique. Pour la validation de notre approche, on donne une étude numérique pour un problème d'optimisation d'emplacement des injecteurs dans un lac eutrophe. Des exemples numériques montrent l'efficacité de la méthode proposée

scholarly journals ON THE SENSITIVITY OF THE NONLINEAR TERM IN THE OUTFLOW BOUNDARY CONDITION

2021 ◽  
Vol 61 (SI) ◽  
pp. 117-121
Author(s):  
Tomáš Neustupa ◽  
Ondřej Winter
Keyword(s):  
Boundary Condition ◽  
Fluid Flow ◽  
Kinetic Energy ◽  
Stokes System ◽  
Nonlinear Term ◽  
Navier Stokes ◽  
Outflow Boundary Condition ◽  
Flow Through ◽  
Outflow Boundary

This paper studies the artificial outflow boundary condition for the Navier-Stokes system. This type of condition is widely used and it is therefore very important to study its influence on a numerical solution of the corresponding boundary-value problem. We particularly focus on the role of the coefficient in front of the nonlinear term in the boundary condition on the outflow. The influence of this term is examined numerically, comparing the obtained results in a close neighbourhood of the outflow. The numerical experiment is carried out for a fluid flow through the channel with so called sudden extension. Presented numerical results are obtained by means of the OpenFOAM toolbox. They confirm that the kinetic energy of the flow in the channel can be controlled by means of the proposed boundary condition.

scholarly journals On the Solvability of a Problem of Stationary Fluid Flow in a Helical Pipe

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Igor Pažanin
Keyword(s):  
Boundary Condition ◽  
Weak Solution ◽  
Fluid Flow ◽  
Existence And Uniqueness ◽  
Stokes System ◽  
Navier Stokes ◽  
Small Data ◽  
Helical Pipe ◽  
Pressure Boundary Condition ◽  
Incompressible Newtonian Fluid

We consider a flow of incompressible Newtonian fluid through a pipe with helical shape. We suppose that the flow is governed by the prescribed pressure drop between pipe's ends. Such model has relevance to some important engineering applications. Under small data assumption, we prove the existence and uniqueness of the weak solution to the corresponding Navier-Stokes system with pressure boundary condition. The proof is based on the contraction method.

Finite element solution of the Navier—Stokes equations

Acta Numerica ◽  
1993 ◽  
Vol 2 ◽  
pp. 239-284 ◽  
Author(s):  
Michel Fortin
Keyword(s):  
Compressible Flows ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Molten Metals ◽  
Complex Flows ◽  
Navier Stokes Equations ◽  
Viscous Incompressible Flows ◽  
High Reynolds

Viscous incompressible flows are of considerable interest for applications. Let us mention, for example, the design of hydraulic turbines or rheologically complex flows appearing in many processes involving plastics or molten metals. Their simulation raises a number of difficulties, some of which are likely to remain while others are now resolved. Among the latter are those related to incompressibility which are also present in the simulation of incompressible or nearly incompressible elastic materials. Among the still unresolved are those associated with high Reynolds numbers which are also met in compressible flows. They involve the formation of boundary layers and turbulence, an ever present phenomenon in fluid mechanics, implying that we have to simulate unsteady, highly unstable phenomena.

Semi-lagrangian integration schemes for viscous incompressible flows

2002 ◽  
Vol 2 (4) ◽  
pp. 392-409 ◽  
Author(s):  
Mohammed Seaïd
Keyword(s):  
Incompressible Flows ◽  
Stokes Equations ◽  
Two Dimensions ◽  
Second Order ◽  
Navier Stokes ◽  
Modified Method ◽  
Integration Schemes ◽  
Viscous Incompressible Flows ◽  
High Reynolds ◽  
Stream Function Formulation

AbstractA new second-order accurate scheme for the computation of unsteady viscous incompressible flows is proposed. The scheme is based on the vorticity-stream function formulation along the characteristics and consists of combining the modified method of characteristics with an explicit scheme with an extended real stability interval. A comparison of the new method with the semi-Lagrangian Cranck-Nicolson and classical semi-Lagrangian Runge-Kutta schemes is presented. Numerical results are carried out on Navier-Stokes equations and this efficient second-order scheme has also made it possible to compute the driven cavity ow at a high Reynolds number on a refined grid at a reasonable cost. The procedure can be generalized to more than two dimensions.

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