scholarly journals In search of a variational formulation of the relativistic Navier‐Stokes equations

PAMM ◽  
2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Markus Scholle ◽  
Marcel Mellmann
Keyword(s):  
Variational Formulation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

Aerodynamic and Aeroacoustic Analyses of a Regenerative Blower

2015 ◽  
Author(s):  
Man-Woong Heo ◽  
Tae-Wan Seo ◽  
Chung-Suk Lee ◽  
Kwang-Yong Kim
Keyword(s):  
Shear Stress ◽  
Variational Formulation ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Side Channel ◽  
Leakage Flow ◽  
Navier Stokes Equations ◽  
Unsteady Flow Analysis

This paper presents a parametric study to investigate the aerodynamic and aeroacoustic characteristics of a side channel regenerative blower. Flow analysis in the side channel blower was carried out by solving three-dimensional steady and unsteady Reynolds-averaged Navier-Stokes equations with the shear stress transport turbulence closure. Aeroacoustic analysis was conducted by solving the variational formulation of Lighthill’s analogy on the basis of the aerodynamic sources extracted from the unsteady flow analysis. The height and width of the blade and the angle between inlet and outlet ports were selected as three geometric parameters, and their effects on the aerodynamic and aeroacoustic performances of the blower have been investigated. The results showed that the aerodynamic and aeroacoustic performances were enhanced by decreasing height and width of blade. It was found that angle between inlet and outlet ports significantly influences the aerodynamic and aeroacoustic performances of the blower due to the stripper leakage flow.

scholarly journals A non-conventional discontinuous Lagrangian for viscous flow

2017 ◽  
Vol 4 (2) ◽  
pp. 160447 ◽  
Author(s):  
M. Scholle ◽  
F. Marner
Keyword(s):  
Variational Formulation ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Local Equilibrium ◽  
Navier Stokes ◽  
Mathematical Treatment ◽  
Navier Stokes Equations ◽  
New Formalism ◽  
Limiting Case ◽  
Physical Phenomena

Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier–Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier–Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided.

Uncoupled ω–ψ Formulation for Plane Flows in Multiply Connected Domains

1997 ◽  
Vol 07 (06) ◽  
pp. 731-767 ◽  
Author(s):  
J.-L. Guermond ◽  
L. Quartapelle
Keyword(s):  
Stream Function ◽  
Variational Formulation ◽  
Stokes Equations ◽  
Mixed Finite Element ◽  
Navier Stokes ◽  
Multiply Connected Domains ◽  
Navier Stokes Equations ◽  
Multiply Connected ◽  
Finite Element Implementation ◽  
Transient Problems

This work deals with the numerical solution of the unsteady Navier–Stokes equations in the vorticity and stream function representation for problems in multiply connected two-dimensional regions. A particular decomposition of the stream function space is proposed which leads to an uncoupled variational formulation of the equations linearized and discretized in time, thus extending to transient problems the celebrated method proposed by Glowinski and Pironneau for the biharmonic problem. Numerical results calculated by a mixed finite element implementation of the new uncoupled method are presented.

On the Finite Element Formulation of Navier–Stokes Equations

1973 ◽  
Vol 2 (4) ◽  
pp. 205-208
Author(s):  
E. Bilgen ◽  
J.J.M. Too
Keyword(s):  
Finite Element ◽  
Variational Formulation ◽  
Stokes Equations ◽  
Finite Element Formulation ◽  
Navier Stokes ◽  
Simple Problem ◽  
Element Formulation ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Pressure Fields

A variational formulation of the Navier-Stokes equation for steady flow of an incompressible fluid is presented and the limitations of the resulting equation are discussed. The finite element formulation based on the minimizing of functionals of the velocity and pressure fields is presented and a simple problem is treated to illustrate the method.

Nonlinear wave interactions in shear flows. Part 1. A variational formulation

1974 ◽  
Vol 66 (2) ◽  
pp. 209-221 ◽  
Author(s):  
J. R. Usher ◽  
A. D. D. Craik
Keyword(s):  
Variational Formulation ◽  
Stokes Equations ◽  
Direct Method ◽  
Substantial Reduction ◽  
Resonant Interaction ◽  
Navier Stokes ◽  
Algebraic Complexity ◽  
Wave Interactions ◽  
Navier Stokes Equations ◽  
Parallel Shear Flow

A modified version of Bateman's variational formulation of the incompressible Navier-Stokes equations and boundary conditions (see Dryden, Murnaghan & Bateman 1956) is introduced. This is employed to examine a particular nonlinear problem of hydrodynamic stability which was treated previously, using a ‘direct’ approach, by Craik (1971). This problem concerns the resonant interaction at second order of a triad of wave modes in a parallel shear flow.The present method is conceptually attractive; it also has the major advantage over the ‘direct’ method of a substantial reduction in algebraic complexity, which allows results to be derived far more readily. Also, some further improvements are made upon Craik's previous analysis. Such a variational approach may often be simpler than present conventional methods of tackling nonlinear viscous-flow problems. The present paper shows how other problems of nonlinear stability and wave interactions may be tackled in this way.

A FICTITIOUS DOMAIN / DOMAIN DECOMPOSITION METHOD AND ITS APPLICATIONS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1523-1526
Author(s):  
CHUNHUA ZHOU ◽  
YONGFENG YAO
Keyword(s):  
Domain Decomposition ◽  
Variational Formulation ◽  
Decomposition Method ◽  
Stokes Equations ◽  
Domain Decomposition Method ◽  
Operator Splitting ◽  
Time Discretization ◽  
Navier Stokes ◽  
Fictitious Domain ◽  
Navier Stokes Equations

In this article, the combination of fictitious domain and domain decomposition has been presented. First, we construct an equivalent variational formulation for the Dirichlet problem of linear elliptic operators and discuss the space approximation. Then the approach is applied to the incompressible Navier-Stokes equations, including construction of the variational formulation and time discretization by operator splitting. Finally, some numerical results are presented to validate our approach.

scholarly journals Spectral discretization of time-dependent vorticity–velocity–pressure formulation of the Navier–Stokes equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mohamed Abdelwahed ◽  
Nejmeddine Chorfi
Keyword(s):  
Variational Formulation ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Time Discretization ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Pressure Formulation ◽  
Velocity Pressure ◽  
Spectral Discretization

Abstract In this work, we propose a nonstationary Navier–Stokes problem equipped with an unusual boundary condition. The time discretization of such a problem is based on the backward Euler’s scheme. However, the variational formulation deduced from the nonstationary Navier–Stokes equations is discretized using the spectral method. We prove that the time semidiscrete problem and the full spectral discrete one admit at most one solution.

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