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Title: A high accuracy defect-correction multigrid method for the steady incompressible navier-stokes equations

Abstract

The solution of large sets of equations is required when discrete methods are used to solve fluid flow and heat transfer problems. Although the cost of the solution is often a drawback when the number of equations in the set becomes large, higher order numerical methods can be employed in the discretization of differential equations to decrease the number of equations without losing accuracy. For example, using a fourth-order difference scheme instead of a second-order one would reduce the number of equations by approximately half while preserving the same accuracy. In a recent paper, Gupta has developed a fourth-order compact method for the numerical solution of Navier-Stokes equations. In this paper we propose a defect-correction form of the high order approximations using multigrid techniques. We also derive a fourth-order approximation to the boundary conditions to be consistent with the fourth-order discretization of the underlying differential equations. The convergence analysis will be discussed for the parameterized form of a general second-order correction difference scheme which includes a fourth-order scheme as a special case. 9 refs., 1 fig., 5 tabs.

Authors:
 [1];  [2]
  1. Charles Sturt Univ., Wagga Wagga, (Australia)
  2. University of Queensland, (Australia)
Publication Date:
OSTI Identifier:
99053
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 114; Journal Issue: 2; Other Information: PBD: Oct 1994
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING NOT INCLUDED IN OTHER CATEGORIES; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; NAVIER-STOKES EQUATIONS; CALCULATION METHODS; VISCOUS FLOW; NUMERICAL SOLUTION; NATURAL CONVECTION; INCOMPRESSIBLE FLOW; TWO-DIMENSIONAL CALCULATIONS; CONVERGENCE; ACCURACY

Citation Formats

Altas, I, and Burrage, K. A high accuracy defect-correction multigrid method for the steady incompressible navier-stokes equations. United States: N. p., 1994. Web. doi:10.1006/jcph.1994.1162.
Altas, I, & Burrage, K. A high accuracy defect-correction multigrid method for the steady incompressible navier-stokes equations. United States. https://doi.org/10.1006/jcph.1994.1162
Altas, I, and Burrage, K. 1994. "A high accuracy defect-correction multigrid method for the steady incompressible navier-stokes equations". United States. https://doi.org/10.1006/jcph.1994.1162.
@article{osti_99053,
title = {A high accuracy defect-correction multigrid method for the steady incompressible navier-stokes equations},
author = {Altas, I and Burrage, K},
abstractNote = {The solution of large sets of equations is required when discrete methods are used to solve fluid flow and heat transfer problems. Although the cost of the solution is often a drawback when the number of equations in the set becomes large, higher order numerical methods can be employed in the discretization of differential equations to decrease the number of equations without losing accuracy. For example, using a fourth-order difference scheme instead of a second-order one would reduce the number of equations by approximately half while preserving the same accuracy. In a recent paper, Gupta has developed a fourth-order compact method for the numerical solution of Navier-Stokes equations. In this paper we propose a defect-correction form of the high order approximations using multigrid techniques. We also derive a fourth-order approximation to the boundary conditions to be consistent with the fourth-order discretization of the underlying differential equations. The convergence analysis will be discussed for the parameterized form of a general second-order correction difference scheme which includes a fourth-order scheme as a special case. 9 refs., 1 fig., 5 tabs.},
doi = {10.1006/jcph.1994.1162},
url = {https://www.osti.gov/biblio/99053}, journal = {Journal of Computational Physics},
number = 2,
volume = 114,
place = {United States},
year = {Sat Oct 01 00:00:00 EDT 1994},
month = {Sat Oct 01 00:00:00 EDT 1994}
}