Discontinuous Galerkin solution of the Reynolds-averaged Navier–Stokes and k–ω turbulence model equations

2005 ◽  
Vol 34 (4-5) ◽  
pp. 507-540 ◽  
Author(s):  
Francesco Bassi ◽  
Andrea Crivellini ◽  
Stefano Rebay ◽  
Marco Savini
Keyword(s):  
Discontinuous Galerkin ◽  
Turbulence Model ◽  
Navier Stokes ◽  
Galerkin Solution ◽  
Reynolds Averaged Navier Stokes ◽  
Model Equations

Discontinuous Galerkin Solution of Three-Dimensional Reynolds-Averaged Navier-Stokes Equations With S-A Turbulence Model

2010 ◽  
Author(s):  
Fan Feng ◽  
Chunwei Gu ◽  
Xuesong Li
Keyword(s):  
Discontinuous Galerkin ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Mach Reflection ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Navier Stokes Equations ◽  
Reynolds Averaged Navier Stokes ◽  
Double Mach Reflection

In this paper Discontinuous Galerkin Method (DGM) is applied to solve the Reynolds-averaged Navier-Stokes equations and S-A turbulence model equation in curvilinear coordinate system. Different schemes, including Lax-Friedrichs (LF) flux, Harten, Lax and van Leer (HLL) flux and Roe flux are adopted as numerical flux of inviscid terms at the element interface. The gradients of conservative variables in viscous terms are constructed by mixed formulation, which solves the gradients as auxiliary unknowns to the same order of accuracy as conservative variables. The methodology is validated by simulations of double Mach reflection problem and three-dimensional turbulent flowfield within compressor cascade NACA64. The numerical results agree well with the experimental data.

Simulation of the Transitional Flow in a Low Pressure Gas Turbine Cascade With a High-Order Discontinuous Galerkin Method

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
A. Ghidoni ◽  
A. Colombo ◽  
S. Rebay ◽  
F. Bassi
Keyword(s):  
Discontinuous Galerkin ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Time Integration ◽  
High Order ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Implicit Time ◽  
Turbine Cascade ◽  
High Reynolds

In the last decade, discontinuous Galerkin (DG) methods have been the subject of extensive research efforts because of their excellent performance in the high-order accurate discretization of advection-diffusion problems on general unstructured grids, and are nowadays finding use in several different applications. In this paper, the potential offered by a high-order accurate DG space discretization method with implicit time integration for the solution of the Reynolds-averaged Navier–Stokes equations coupled with the k-ω turbulence model is investigated in the numerical simulation of the turbulent flow through the well-known T106A turbine cascade. The numerical results demonstrate that, by exploiting high order accurate DG schemes, it is possible to compute accurate simulations of this flow on very coarse grids, with both the high-Reynolds and low-Reynolds number versions of the k-ω turbulence model.

A high-order Discontinuous Galerkin solver for the incompressible RANS and k–ω turbulence model equations

2014 ◽  
Vol 98 ◽  
pp. 54-68 ◽  
Author(s):  
F. Bassi ◽  
A. Ghidoni ◽  
A. Perbellini ◽  
S. Rebay ◽  
A. Crivellini ◽  
...  
Keyword(s):  
Discontinuous Galerkin ◽  
Turbulence Model ◽  
High Order ◽  
Model Equations

A Reynolds-Averaged Navier-Stokes Solver in a Turbomachinery Design System

2007 ◽  
Author(s):  
Fahua Gu ◽  
Mark R. Anderson
Keyword(s):  
Turbulence Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Integrated Design ◽  
Navier Stokes ◽  
Design System ◽  
Navier Stokes Equations ◽  
Wall Functions ◽  
Machine Performance ◽  
Reynolds Averaged Navier Stokes

The design of turbomachinery has been focusing on the improvement of the machine efficiency and the reduction of the design cost. This paper presents an integrated design system to create the machine geometry and to predict the machine performance at different levels of approximation, including one-dimensional design and analysis, quasi-three-dimensional-(blade-to-blade, throughflow) and full-three-dimensional-steady-state CFD analysis. One of the most important components, the Reynolds-averaged Navier-Stokes solver, is described in detail. It originated from the Dawes solver with numerous enhancements. They include the use of the low speed pre-conditioned full Navier-Stokes equations, the addition of the Spalart-Allmaras turbulence model and an improvement of wall functions related with the turbulence model. The latest upwind scheme, AUSM, has been implemented too. The Dawes code has been rewritten into a multi-block solver for O, C, and H grids. This paper provides some examples to evaluate the effect of grid topology on the machine performance prediction.

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