A Global Preconditioning Method for Low Mach Number Viscous Flows in Rotating Machinery

2006 ◽  
Author(s):  
Chunhua Sheng ◽  
Xiao Wang
Keyword(s):  
Mach Number ◽  
Rotational Speed ◽  
Stokes Equations ◽  
Viscous Flows ◽  
Rotating Machinery ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Mach Number ◽  
Low Speed ◽  
Preconditioning Method

A preconditioning scheme is applied to a compressible turbomachinery flow solver MSU-TURBO for simulating viscous flows at low Mach number and incompressible region. The Navier-Stokes equations are cast in a non-inertial rotating frame. A constant diagonal preconditioning matrix is applied to the conservative form of the governing equations, which contains a single parameter depending on the reference Mach number and rotational speed of the relative frame. The effect of the rotational speed on preconditioned scheme is numerically investigated for two low speed viscous flows in rotating machinery, a NASA low speed centrifugal compressor (LSCC) and a marine propeller (P5168). Computations are compared against the original MSU-TURBO solutions, and suggestions are provided for computing the low Mach number flows in rotating turbomachinery using the preconditioned TURBO solver.

Artificial Compressibility Method and Preconditioning Method for Solving Two Dimensional Incompressibile Flow

2011 ◽  
Author(s):  
Hyungro Lee ◽  
Einkeun Kwak ◽  
Seungsoo Lee
Keyword(s):  
Mach Number ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Low Mach Number ◽  
Artificial Compressibility ◽  
Artificial Compressibility Method ◽  
Preconditioning Method

In this study, two commonly used numerical methods for the analysis of incompressible flows (or low Mach number flows), Chorins’ artificial compressibility method and Wiess and Smith’s preconditioning method are compared. Also, the convergence characteristics of two methods are numerically investigated for two-dimensional laminar and turbulent flows. Although the two methods have similar governing equations, the eigensystems and other details are very different. The eigensystems of the artificial compressibility method and the preconditioning method are analytically examined. An artificial compressibility code that solves the incompressible RANS (Reynolds Averaged Navier-Stokes) equations is newly developed for the study. An artificial compressibility code and a well-verified existing low Mach number code uses Roe’s approximate Riemann solver in conjunction with a cell centered finite volume method. Using MUSCL extrapolation with nonlinear limiters, 2nd order spatial accuracy is achieved while maintaining TVD (total variation diminishing) property. AF-ADI (approximate factorization-alternate direction implicit) method is used to get the steady solution for both codes. Menter’s k–ω SST turbulence model is used for the analysis of turbulent flows. Navier-Stokes equations and the turbulence model equations are solved in a loosely coupled manner.

scholarly journals Implicit MAC scheme for compressible Navier–Stokes equations: low Mach asymptotic error estimates

2020 ◽  
Author(s):  
David Maltese ◽  
Antonín Novotný
Keyword(s):  
Mach Number ◽  
Initial Data ◽  
Error Estimate ◽  
Strong Solution ◽  
Stokes Equations ◽  
Main Tool ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Mach Number ◽  
Mac Scheme

Abstract We investigate the error between any discrete solution of the implicit marker-and-cell (MAC) numerical scheme for compressible Navier–Stokes equations in the low Mach number regime and an exact strong solution of the incompressible Navier–Stokes equations. The main tool is the relative energy method suggested on the continuous level in Feireisl et al. (2012, Relative entropies, suitable weak solutions, and weak–strong uniqueness for the compressible Navier–Stokes system. J. Math. Fluid Mech., 14, 717–730). Our approach highlights the fact that numerical and mathematical analyses are not two separate fields of mathematics. The result is achieved essentially by exploiting in detail the synergy of analytical and numerical methods. We get an unconditional error estimate in terms of explicitly determined positive powers of the space–time discretization parameters and Mach number in the case of well-prepared initial data and in terms of the boundedness of the error if the initial data are ill prepared. The multiplicative constant in the error estimate depends on a suitable norm of the strong solution but it is independent of the numerical solution itself (and of course, on the discretization parameters and the Mach number). This is the first proof that the MAC scheme is unconditionally and uniformly asymptotically stable in the low Mach number regime.

scholarly journals On the Low Mach Number Limit for Quantum Navier--Stokes Equations

2020 ◽  
Vol 52 (6) ◽  
pp. 6105-6139
Author(s):  
Paolo Antonelli ◽  
Lars Eric Hientzsch ◽  
Pierangelo Marcati
Keyword(s):  
Mach Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Mach Number ◽  
Low Mach Number Limit

Study Method for Low Speed Flow Basic on Precondition

2014 ◽  
Vol 1070-1072 ◽  
pp. 1972-1977
Author(s):  
Lang Li ◽  
Guo Ping Cheng ◽  
Guo Quan Zhu ◽  
Wei Zhang
Keyword(s):  
Iterative Method ◽  
Stokes Equations ◽  
Time Derivative ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Speed ◽  
Speed Flow ◽  
Preconditioning Method ◽  
Derivative Term ◽  
Implicit Iterative Method

Based on Navier-stokes equations, Weiss-Smith matrix preconditioning method is implemented within pseudo time derivative term. AUSM+-up family schemes and LU-SGS implicit iterative method were used to solve low speed flows and were compared with literature data and theoretical value. Through comparing calculation with the literature data and theoretical value, The Results showed the preconditioning algorithm can be applied efficiently to the low speeds flow field ,All these works built foundations for further application of chemical flows.

scholarly journals Splitting methods for low Mach number Euler and Navier-Stokes equations

1989 ◽  
Vol 17 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Saul Abarbanel ◽  
Pravir Duth ◽  
David Gottlieb
Keyword(s):  
Mach Number ◽  
Stokes Equations ◽  
Splitting Methods ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Mach Number

Preconditioned Density-Based Methods for All-Speed Flows

2007 ◽  
Author(s):  
Sijun Zhang
Keyword(s):  
Mach Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Test Cases ◽  
Unsteady State ◽  
Navier Stokes Equations ◽  
Speed Flow ◽  
Preconditioning Technique ◽  
Preconditioning Method ◽  
Flow Through

A low Mach number preconditioning method has been implemented in commercial computational fluid dynamics software, CFD-FASTRAN. The preconditioning technique offers a way to formulate the Euler and Navier-Stokes equations such that convergences can be made independent of Mach number. This enhancement is shown to provide accurate steady/unsteady state solutions for transonic and low-speed flow through several test cases.

Sign in / Sign up

Export Citation Format

Share Document