A Multigrid Solver for the Steady Incompressible Navier-Stokes Equations on Curvilinear Coordinate Systems

1994 ◽  
Vol 113 (1) ◽  
pp. 26-34 ◽  
Author(s):  
Lin-Bo Zhang
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Coordinate Systems ◽  
Multigrid Solver ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate

scholarly journals The Regularity Criteria and the A Priori Estimate on the 3D Incompressible Navier-Stokes Equations in Orthogonal Curvilinear Coordinate Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Fan Geng ◽  
Shu Wang ◽  
Yongxin Wang
Keyword(s):  
Stokes Equations ◽  
A Priori ◽  
Three Dimensional ◽  
A Priori Estimate ◽  
Regularity Criteria ◽  
Navier Stokes ◽  
Coordinate Systems ◽  
Priori Estimate ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate

The paper considers the regularity problem on three-dimensional incompressible Navier-Stokes equations in general orthogonal curvilinear coordinate systems. We establish one regularity criteria of the weak solutions involving only in a vorticity component ω 3 and one a priori estimate on the solution that H 3 u 3 L ∞ 0 , T ; L p ℝ 3 is bounded for 1 ≤ p ≤ ∞ to three-dimensional incompressible Navier-Stokes equations in orthogonal curvilinear coordinate systems. These extent greatly the corresponding results on axisymmetric cylindrical flow.

A Quasi-Generalized-Coordinate Approach for Numerical Simulation of Complex Flows

2006 ◽  
Vol 128 (6) ◽  
pp. 1394-1399 ◽  
Author(s):  
Donghyun You ◽  
Meng Wang ◽  
Rajat Mittal ◽  
Parviz Moin
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Effective ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate ◽  
Generalized Coordinate

A novel structured grid approach which provides an efficient way of treating a class of complex geometries is proposed. The incompressible Navier-Stokes equations are formulated in a two-dimensional, generalized curvilinear coordinate system complemented by a third quasi-curvilinear coordinate. By keeping all two-dimensional planes defined by constant third coordinate values parallel to one another, the proposed approach significantly reduces the memory requirement in fully three-dimensional geometries, and makes the computation more cost effective. The formulation can be easily adapted to an existing flow solver based on a two-dimensional generalized coordinate system coupled with a Cartesian third direction, with only a small increase in computational cost. The feasibility and efficiency of the present method have been assessed in a simulation of flow over a tapered cylinder.

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