Exact Dual Variational Principles for Unsteady 3-D Navier-Stokes Equations

2007 ◽  
Author(s):  
Gao-Lian Liu
Keyword(s):  
Variational Principles ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

scholarly journals New variational principles for locating periodic orbits of differential equations

2011 ◽  
Vol 369 (1944) ◽  
pp. 2211-2218 ◽  
Author(s):  
Bruce M. Boghosian ◽  
Luis M. Fazendeiro ◽  
Jonas Lätt ◽  
Hui Tang ◽  
Peter V. Coveney
Keyword(s):  
Periodic Orbits ◽  
Variational Principles ◽  
Stokes Equations ◽  
Iterative Algorithms ◽  
Navier Stokes ◽  
Unstable Periodic Orbits ◽  
Navier Stokes Equations ◽  
New Methods ◽  
Discrete Representations

We present new methods for the determination of periodic orbits of general dynamical systems. Iterative algorithms for finding solutions by these methods, for both the exact continuum case, and for approximate discrete representations suitable for numerical implementation, are discussed. Finally, we describe our approach to the computation of unstable periodic orbits of the driven Navier–Stokes equations, simulated using the lattice Boltzmann equation.

scholarly journals Generation and solutions to the time-space fractional coupled Navier-Stokes equations

2020 ◽  
Vol 24 (6 Part B) ◽  
pp. 3899-3905
Author(s):  
Chang-Na Lu ◽  
Sheng-Xiang Chang ◽  
Luo-Yan Xie ◽  
Zong-Guo Zhang
Keyword(s):  
Exact Solutions ◽  
Inverse Method ◽  
Fractional Derivatives ◽  
Variational Principles ◽  
Stokes Equations ◽  
Lagrange Equation ◽  
Numerical Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Space

In this paper, a Lagrangian of the coupled Navier-Stokes equations is proposed based on the semi-inverse method. The fractional derivatives in the sense of Riemann-Liouville definition are used to replace the classical derivatives in the Lagrangian. Then the fractional Euler-Lagrange equation can be derived with the help of the fractional variational principles. The Agrawal?s method is devot?ed to lead to the time-space fractional coupled Navier-Stokes equations from the above Euler-Lagrange equation. The solution of the time-space fractional coupled Navier-Stokes equations is obtained by means of RPS algorithm. The numerical results are presented by using exact solutions.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

Sensitivity analysis for Navier-Stokes equations on unstructured meshes using complex variables

AIAA Journal ◽  
2001 ◽  
Vol 39 ◽  
pp. 56-63
Author(s):  
W. Kyle Anderson ◽  
James C. Newman ◽  
David L. Whitfield ◽  
Eric J. Nielsen
Keyword(s):  
Sensitivity Analysis ◽  
Stokes Equations ◽  
Unstructured Meshes ◽  
Complex Variables ◽  
Navier Stokes ◽  
Navier Stokes Equations

Numerical solution of the reduced Navier-Stokes equations for internal incompressible flows

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1603-1614
Author(s):  
Martin Scholtysik ◽  
Bernhard Mueller ◽  
Torstein K. Fannelop
Keyword(s):  
Numerical Solution ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations
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