A comparison of block preconditioners for isogeometric analysis discretizations of the incompressible Navier‐Stokes equations

2020 ◽  
Author(s):  
H. Horníková ◽  
C. Vuik ◽  
J. Egermaier
Keyword(s):  
Isogeometric Analysis ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Block Preconditioners

scholarly journals NUMERICAL SIMULATION OF LID-DRIVEN CAVITY FLOW BY ISOGEOMETRIC ANALYSIS

2021 ◽  
Vol 61 (SI) ◽  
pp. 33-48
Author(s):  
Bohumír Bastl ◽  
Marek Brandner ◽  
Jiří Egermaier ◽  
Hana Horníková ◽  
Kristýna Michálková ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Incompressible Fluid ◽  
Isogeometric Analysis ◽  
Stokes Equations ◽  
Cavity Flow ◽  
Navier Stokes ◽  
Incompressible Fluid Flow ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Driven Cavity

In this paper, we present numerical results obtained by an in-house incompressible fluid flow solver based on isogeometric analysis (IgA) for the standard benchmark problem for incompressible fluid flow simulation – lid-driven cavity flow. The steady Navier-Stokes equations are solved in their velocity-pressure formulation and we consider only inf-sup stable pairs of B-spline discretization spaces. The main aim of the paper is to compare the results from our IgA-based flow solver with the results obtained by a standard package based on finite element method with respect to degrees of freedom and stability of the solution. Further, the effectiveness of the recently introduced rIgA method for the steady Navier-Stokes equations is studied.The authors dedicate the paper to Professor K. Kozel on the occasion of his 80th birthday.

Block preconditioners for the discrete incompressible Navier-Stokes equations

2002 ◽  
Vol 40 (3-4) ◽  
pp. 333-344 ◽  
Author(s):  
Howard C. Elman ◽  
David J. Silvester ◽  
Andrew J. Wathen
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Block Preconditioners

Large-Eddy Simulation of Shallow Water Langmuir Turbulence Using Isogeometric Analysis and the Residual-Based Variational Multiscale Method

2011 ◽  
Vol 79 (1) ◽  
Author(s):  
Andrés E. Tejada-Martínez ◽  
Ido Akkerman ◽  
Yuri Bazilevs
Keyword(s):  
Large Eddy Simulation ◽  
Isogeometric Analysis ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Variational Multiscale ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Coastal Shelf ◽  
Current Interaction

We develop a residual-based variational multiscale (RBVMS) method based on isogeometric analysis for large-eddy simulation (LES) of wind-driven shear flow with Langmuir circulation (LC). Isogeometric analysis refers to our use of NURBS (Non-Uniform Rational B-splines) basis functions which have been proven to be highly accurate in LES of turbulent flows (Bazilevs, Y., et al. 2007, Comput. Methods Appl. Mech. Eng., 197, pp. 173–201). LC consists of stream-wise vortices in the direction of the wind acting as a secondary flow structure to the primary, mean component of the flow driven by the wind. LC results from surface wave-current interaction and often occurs within the upper ocean mixed layer over deep water and in coastal shelf regions under wind speeds greater than 3 m s−1. Our LES of wind-driven shallow water flow with LC is representative of a coastal shelf flow where LC extends to the bottom and interacts with the sea bed boundary layer. The governing LES equations are the Craik-Leivobich equations (Tejada-Martínez, A. E., and Grosch, C. E., 2007, J. Fluid Mech., 576, pp. 63–108; Gargett, A. E., 2004, Science, 306, pp. 1925–1928), consisting of the time-filtered Navier-Stokes equations. These equations possess the same structure as the Navier-Stokes equations with an extra vortex force term accounting for wave-current interaction giving rise to LC. The RBVMS method with quadratic NURBS is shown to possess good convergence characteristics in wind-driven flow with LC. Furthermore, the method yields LC structures in good agreement with those computed with the spectral method in (Thorpe, S. A., 2004, Annu. Rev. Fluids Mech., 36, pp. 584 55–79) and measured during field observations in (D’Alessio, S. J., et al., 1998, J. Phys. Oceanogr., 28, pp. 1624–1641; Kantha, L., and Clayson, C. A., 2004, Ocean Modelling, 6, pp. 101–124).

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.

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