The solution of the parabolized Navier-Stokes equations by a fully implicit method

1982 ◽  
Keyword(s):  
Stokes Equations ◽  
Implicit Method ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fully Implicit

Studies on Aerodynamic Characteristics of Dump Diffusers for Modern Aircraft Engines

2012 ◽  
Vol 232 ◽  
pp. 246-251 ◽  
Author(s):  
P. Sathyan ◽  
S. Srikanth ◽  
I. Dheepan ◽  
M. Arun ◽  
C. Aswin ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Dynamic ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Finite Volume Scheme ◽  
Aircraft Engines ◽  
Navier Stokes Equations ◽  
Dynamic Constraints ◽  
Fully Implicit

The geometrical optimization of dump diffusers are extremely demanding as the flow fields and stress fields are very complex and must be well understood to achieve the required design efficiencies. In this paper parametric analytical studies have been carried out for examining the aerodynamics characteristics of different dump diffusers for modern aircraft engines. Numerical studies have been carried out using SST K- ω turbulence model. This code solves SST k- ω turbulence equations using the coupled second order implicit unsteady formulation. In the numerical study, a fully implicit finite volume scheme of the compressible, Reynolds-Averaged, Navier-Stokes equations is employed. We concluded that in addition to the dump gap ratio, the aerodynamic shape of the flame tube case and the other geometric variables are also need to be optimized judiciously after considering the fluid dynamic constraints for controlling the pressure recovery and the losses.

Application of a Navier–Stokes Analysis to Flows Through Plane Cascades

1986 ◽  
Vol 108 (1) ◽  
pp. 103-111 ◽  
Author(s):  
O. Scha¨fer ◽  
H.-H. Fru¨hauf ◽  
B. Bauer ◽  
M. Guggolz
Keyword(s):  
Thin Layer ◽  
Stokes Equations ◽  
Density Ratio ◽  
Separated Flows ◽  
Stability And Convergence ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fully Implicit ◽  
First Results ◽  
Viscous Solutions

A newly developed method is used to compute a variety of laminar/turbulent, attached/separated flows through plane turbine or compressor cascades. The thin-layer or full Navier–Stokes equations are solved in a 2-D or quasi-2-D/quasi-3-D form taking into account variable axial velocity density ratio/cascade aspect ratio. The turbulence is modeled by the Baldwin–Lomax algebraic two-layer eddy viscosity approach. Improved mesh generation and discretization techniques are introduced. A fully implicit formulation of the flow problem is developed which ensures high stability and convergence. Numerous quantitative comparisons of viscous solutions with experiments and other existing solutions are performed to validate the method. First results on the applicability of the thin-layer assumption are included.

A Novel High-Order Accurate Compact Stencil Poisson Solver: Application to Cavity Flows

2015 ◽  
Vol 07 (01) ◽  
pp. 1550006 ◽  
Author(s):  
Omer San
Keyword(s):  
Stokes Equations ◽  
Time Integration ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Poisson Solver ◽  
Fully Implicit ◽  
Stream Function Formulation ◽  
Compact Stencil ◽  
Discrete Formulation

In this paper, a fourth-order compact stencil finite difference scheme is developed for solving elliptic Poisson equation. The scheme presented here is based on a modular approach using a linear combination of compact difference algorithms that results in different discrete formulation than the well-known Mehrstellen scheme. An adjoint optimal V-cycle multigrid (MG) iterative solver are developed, implemented, and tested. The robustness of the adjoint Poisson solver is illustrated by solving incompressible Navier–Stokes equations in vorticity-stream function formulation. Using a fully implicit factorized delta-scheme algorithm for the time integration, benchmark quality results of the cavity flow problem are presented and compared to existing literature for various Reynolds numbers.

scholarly journals Strong $L^2$ convergence of time numerical schemes for the stochastic two-dimensional Navier–Stokes equations

2018 ◽  
Vol 39 (4) ◽  
pp. 2135-2167 ◽  
Author(s):  
Hakima Bessaih ◽  
Annie Millet
Keyword(s):  
Stokes Equations ◽  
Random Perturbation ◽  
Time Discretization ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Exponential Moment ◽  
Navier Stokes Equations ◽  
Fully Implicit ◽  
Moment Estimates ◽  
Discretization Schemes

Abstract We prove that some time discretization schemes for the two-dimensional Navier–Stokes equations on the torus subject to a random perturbation converge in $L^2(\varOmega )$. This refines previous results that established the convergence only in probability of these numerical approximations. Using exponential moment estimates of the solution of the stochastic Navier–Stokes equations and convergence of a localized scheme we can prove strong convergence of fully implicit and semiimplicit temporal Euler discretizations and of a splitting scheme. The speed of the $L^2(\varOmega )$ convergence depends on the diffusion coefficient and on the viscosity parameter.

Rotor-Stator Interaction Analysis Using the Navier-Stokes Equations and a Multigrid Method

1995 ◽  
Author(s):  
Andrea Arnone ◽  
Roberto Pacciani
Keyword(s):  
Stokes Equations ◽  
Interaction Analysis ◽  
Time Discretization ◽  
Navier Stokes ◽  
Implicit Time ◽  
Navier Stokes Equations ◽  
Time Stepping ◽  
Fully Implicit ◽  
Rotor Stator Interaction ◽  
Stage Analysis

A recently developed, time-accurate multigrid viscous solver has been extended to the analysis of unsteady rotor-stator interaction. In the proposed method, a fully-implicit time discretization is used to remove stability limitations. By means of a dual time-stepping approach, a four-stage Runge-Kutta scheme is used in conjunction with several accelerating techniques typical of steady-state solvers, instead of traditional time-expensive factorizations. The accelerating strategies include local time stepping, residual smoothing, and multigrid. Two-dimensional viscous calculations of unsteady rotor-stator interaction in the first stage of a modem gas turbine are presented. The stage analysis is based on the introduction of several blade passages to approximate the stator:rotor count ratio. Particular attention is dedicated to grid dependency in space and time as well as to the influence of the number of blades included in the calculations.

Multigrid Computations of Unsteady Rotor-Stator Interaction Using the Navier-Stokes Equations

1995 ◽  
Vol 117 (4) ◽  
pp. 647-652 ◽  
Author(s):  
A. Arnone ◽  
R. Pacciani ◽  
A. Sestini
Keyword(s):  
Stokes Equations ◽  
Time Discretization ◽  
Navier Stokes ◽  
Implicit Time ◽  
Navier Stokes Equations ◽  
Time Stepping ◽  
Fully Implicit ◽  
Local Time Stepping ◽  
Rotor Stator Interaction ◽  
Residual Smoothing

A Navier-Stokes time-accurate solver has been extended to the analysis of unsteady rotor-stator interaction. In the proposed method, a fully-implicit time discretization is used to remove stability limitations. A four-stage Runge-Kutta scheme is used in conjunction with several accelerating techniques typical of steady-state solvers, instead of traditional time-expensive factorizations. Those accelerating strategies include local time stepping, residual smoothing, and multigrid. Direct interpolation of the conservative variables is used to handle the interfaces between blade rows. Two-dimensional viscous calculations of unsteady rotor-stator interaction in a modern gas turbine stage are presented to check for the capability of the procedure.

Sign in / Sign up

Export Citation Format

Share Document