Conservation properties for the Galerkin and stabilised forms of the advection–diffusion and incompressible Navier–Stokes equations

2005 ◽  
Vol 194 (9-11) ◽  
pp. 1141-1159 ◽  
Author(s):  
Thomas J.R. Hughes ◽  
Garth N. Wells
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Advection Diffusion

scholarly journals Scalable Block Preconditioners for Linearized Navier-Stokes Equations at High Reynolds Number

Algorithms ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 199
Author(s):  
Filippo Zanetti ◽  
Luca Bergamaschi
Keyword(s):  
Stokes Equations ◽  
Schur Complement ◽  
Iterative Solution ◽  
Viscosity Coefficient ◽  
Building Blocks ◽  
Low Rank ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Diffusion Operator ◽  
Advection Diffusion

We review a number of preconditioners for the advection-diffusion operator and for the Schur complement matrix, which, in turn, constitute the building blocks for Constraint and Triangular Preconditioners to accelerate the iterative solution of the discretized and linearized Navier-Stokes equations. An intensive numerical testing is performed onto the driven cavity problem with low values of the viscosity coefficient. We devise an efficient multigrid preconditioner for the advection-diffusion matrix, which, combined with the commuted BFBt Schur complement approximation, and inserted in a 2×2 block preconditioner, provides convergence of the Generalized Minimal Residual (GMRES) method in a number of iteration independent of the meshsize for the lowest values of the viscosity parameter. The low-rank acceleration of such preconditioner is also investigated, showing its great potential.

A HYBRID FINITE-ANALYTIC ALGORITHM FOR SOLVING THREE-DIMENSIONAL ADVECTION-DIFFUSION EQUATIONS

2004 ◽  
Vol 01 (03) ◽  
pp. 407-430 ◽  
Author(s):  
H. M. HU ◽  
K.-H. WANG
Keyword(s):  
Convergence Rates ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Diffusion Equations ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
The Stability

The hybrid finite-analytic (HFA) method for discretization of a three-dimensional advection-diffusion equation is developed using the superposition of the HFA solutions of locally linearized one-dimensional advection-diffusion equations. An example calculation of a system of three-dimensional nonlinear equations is conducted to test the convergence and accuracy of the 7-point numerical scheme. Good agreements between calculated and analytical solutions are obtained. An algorithm based on the HFA method with multigrid technique and Gauss-Seidel iteration is also developed to solve the three-dimensional Navier-Stokes equations in a staggered grid system. The stability and efficiency of the method are demonstrated by performing calculations of the fluid flow in a three-dimensional cubic cavity with a moving top wall. The proposed procedure is observed to exhibit good rates of smoothing and almost grid-independent convergence rates in comparison with a single-grid iteration method. The results are in excellent agreement with other published computational results.

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.

Sign in / Sign up

Export Citation Format

Share Document