### Abstract

A strongly implicit solution technique for the incompressible, steady, two dimensional Navier-Stokes equations in general curvilinear orthogonal and non-orthogonal coordinate systems has been developed. The governing equations, written in primitive variables, are discretized using finite difference approximations. The formulation is fully second order accurate and the well known staggered grid of Harlow and Welch is used. The solution algorithm is based on an iterative marching technique in which the algebraic equations are linearized by evaluating the coefficients at the previous iteration level. The resulting system of linear equations is solved in a marching fashion by employing a block tridiagonal solution algorithm to obtain the solution along lines transverse to the main flow direction. The strong pressure-velocity coupling inherent in the present formulation results in high convergence rates. Flows in channels of different geometries have been computed and the results have been compared to available data in the literature. In all cases the method has demonstrated to be both accurate and computationally efficient. (A)

Original language | English (US) |
---|---|

Title of host publication | Unknown Host Publication Title |

State | Published - Jan 1 1991 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Unknown Host Publication Title*

**Strongly implicit solutions of the incompressible steady Navier- Stokes equations in general curvilinear coordinate systems.** / Vradis, George; Zalak, V.; Bentson, J.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Unknown Host Publication Title.*

}

TY - CHAP

T1 - Strongly implicit solutions of the incompressible steady Navier- Stokes equations in general curvilinear coordinate systems

AU - Vradis, George

AU - Zalak, V.

AU - Bentson, J.

PY - 1991/1/1

Y1 - 1991/1/1

N2 - A strongly implicit solution technique for the incompressible, steady, two dimensional Navier-Stokes equations in general curvilinear orthogonal and non-orthogonal coordinate systems has been developed. The governing equations, written in primitive variables, are discretized using finite difference approximations. The formulation is fully second order accurate and the well known staggered grid of Harlow and Welch is used. The solution algorithm is based on an iterative marching technique in which the algebraic equations are linearized by evaluating the coefficients at the previous iteration level. The resulting system of linear equations is solved in a marching fashion by employing a block tridiagonal solution algorithm to obtain the solution along lines transverse to the main flow direction. The strong pressure-velocity coupling inherent in the present formulation results in high convergence rates. Flows in channels of different geometries have been computed and the results have been compared to available data in the literature. In all cases the method has demonstrated to be both accurate and computationally efficient. (A)

AB - A strongly implicit solution technique for the incompressible, steady, two dimensional Navier-Stokes equations in general curvilinear orthogonal and non-orthogonal coordinate systems has been developed. The governing equations, written in primitive variables, are discretized using finite difference approximations. The formulation is fully second order accurate and the well known staggered grid of Harlow and Welch is used. The solution algorithm is based on an iterative marching technique in which the algebraic equations are linearized by evaluating the coefficients at the previous iteration level. The resulting system of linear equations is solved in a marching fashion by employing a block tridiagonal solution algorithm to obtain the solution along lines transverse to the main flow direction. The strong pressure-velocity coupling inherent in the present formulation results in high convergence rates. Flows in channels of different geometries have been computed and the results have been compared to available data in the literature. In all cases the method has demonstrated to be both accurate and computationally efficient. (A)

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M3 - Chapter

AN - SCOPUS:85041141013

SN - 0791807010

SN - 9780791807019

BT - Unknown Host Publication Title

ER -