A stabilization algorithm of the Navier-Stokes equations based on algebraic Bernoulli equation

2011 ◽  
Vol 19 (4) ◽  
pp. 700-727 ◽  
Author(s):  
L. Amodei ◽  
J.-M. Buchot
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Bernoulli Equation ◽  
Navier Stokes Equations

scholarly journals Non-Invasive Assessment of Intravascular Pressure Gradients: A Review of Current and Proposed Novel Methods

Diagnostics ◽  
2018 ◽  
Vol 9 (1) ◽  
pp. 5 ◽  
Author(s):  
Tin-Quoc Nguyen ◽  
Kristoffer Hansen ◽  
Thor Bechsgaard ◽  
Lars Lönn ◽  
Jørgen Jensen ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Imaging Techniques ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Bernoulli Equation ◽  
Strong Correlations ◽  
Navier Stokes Equations ◽  
Non Invasive ◽  
Invasive Techniques

Invasive catheterization is associated with a low risk of serious complications. However, although it is the gold standard for measuring pressure gradients, it induces changes to blood flow and requires significant resources. Therefore, non-invasive alternatives are urgently needed. Pressure gradients are routinely estimated non-invasively in clinical settings using ultrasound and calculated with the simplified Bernoulli equation, a method with several limitations. A PubMed literature search on validation of non-invasive techniques was conducted, and studies were included if non-invasively estimated pressure gradients were compared with invasively measured pressure gradients in vivo. Pressure gradients were mainly estimated from velocities obtained with Doppler ultrasound or magnetic resonance imaging. Most studies used the simplified Bernoulli equation, but more recent studies have employed the expanded Bernoulli and Navier–Stokes equations. Overall, the studies reported good correlation between non-invasive estimation of pressure gradients and catheterization. Despite having strong correlations, several studies reported the non-invasive techniques to either overestimate or underestimate the invasive measurements, thus questioning the accuracy of the non-invasive methods. In conclusion, more advanced imaging techniques may be needed to overcome the shortcomings of current methods.

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

Development of O(Nm2) preconditioned multigrid solvers for Euler and Navier-Stokes equations

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 717-720
Author(s):  
Jack R. Edwards ◽  
James L. Thomas
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Multigrid Solvers

Data-parallel line relaxation method for the Navier-Stokes equations

AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 1603-1609 ◽  
Author(s):  
Michael J. Wright ◽  
Graham V. Candler ◽  
Deepak Bose
Keyword(s):  
Stokes Equations ◽  
Relaxation Method ◽  
Parallel Line ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Data Parallel

Viscous-inviscid interaction using the Navier-Stokes equations

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 1464-1471
Author(s):  
A. Filippone ◽  
J. N. Sorensen
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations
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