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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/50002

Title: An effective explicit pressure gradient scheme implemented in the two-level non-staggered grids for incompressible Navier-Stokes equations
Authors: P. H. Chiu
W. H. Sheu
R. K. Lin
Contributors: 國立臺灣海洋大學:輪機工程學系
Keywords: Two-level method
Navier–Stokes equations
Prolongation operator
Explicit pressure gradient discretization
Date: 2008
Issue Date: 2018-09-07T02:02:19Z
Publisher: Journal of Computational Physics
Abstract: Abstract: In this paper, an improved two-level method is presented for effectively solving the incompressible Navier–Stokes equations.
This proposed method solves a smaller system of nonlinear Navier–Stokes equations on the coarse mesh and needs
to solve the Oseen-type linearized equations of motion only once on the fine mesh level. Within the proposed two-level
framework, a prolongation operator, which is required to linearize the convective terms at the fine mesh level using the
convergent Navier–Stokes solutions computed at the coarse mesh level, is rigorously derived to increase the prediction
accuracy. This indispensable prolongation operator can properly communicate the flow velocities between the two mesh
levels because it is locally analytic. Solution convergence can therefore be accelerated. For the sake of numerical accuracy,
momentum equations are discretized by employing the general solution for the two-dimensional convection–diffusion–
reaction model equation. The convective instability problem can be simultaneously eliminated thanks to the proper treatment
of convective terms. The converged solution is, thus, very high in accuracy as well as in yielding a quadratic spatial
rate of convergence. For the sake of programming simplicity and computational efficiency, pressure gradient terms are rigorously
discretized within the explicit framework in the non-staggered grid system. The proposed analytical prolongation
operator for the mapping of solutions from the coarse to fine meshes and the explicit pressure gradient discretization
scheme, which accommodates the dispersion-relation-preserving property, have been both rigorously justified from the
predicted Navier–Stokes solutions.
Relation: 1(4) pp.4018–4037
URI: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/50002
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