Semi-implicit schemes for transient Navier-Stokes equations and eddy viscosity models

Lisa G. Davis, Faranak Pahlevani

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

This study presents two computational schemes for the numerical approximation of solutions to eddy viscosity models as well as transient Navier-Stokes equations. The eddy viscosity model is one example of a class of Large Eddy Simulation models, which are used to simulate turbulent flow. The first approximation scheme is a first order single step method that treats the nonlinear term using a semi-implicit discretization. The second scheme employs a two step approach that applies a Crank-Nicolson method for the nonlinear term while also retaining the semi-implicit treatment used in the first scheme. A finite element approximation is used in the spatial discretization of the partial differential equations. The convergence analysis for both schemes is discussed in detail, and numerical results are given for two test problems one of which is the two dimensional flow around a cylinder.

Original language English (US) 212-231 20 Numerical Methods for Partial Differential Equations 25 1 https://doi.org/10.1002/num.20339 Published - Jan 1 2009

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Semi-implicit Scheme
Eddy Viscosity
Navier Stokes equations
Navier-Stokes Equations
Viscosity
Semi-implicit
Discretization
Large eddy simulation
Crank-Nicolson Method
Turbulent flow
Partial differential equations
Large Eddy Simulation
Term
Approximation Scheme
Finite Element Approximation
Numerical Approximation
Convergence Analysis
Turbulent Flow
Model
Test Problems

All Science Journal Classification (ASJC) codes

• Analysis
• Numerical Analysis
• Computational Mathematics
• Applied Mathematics

Cite this

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In: Numerical Methods for Partial Differential Equations, Vol. 25, No. 1, 01.01.2009, p. 212-231.

Research output: Contribution to journalArticle

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