scholarly journals Coordinates over Complex Terrain in Atmospheric Model

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Wen-yih Sun
Keyword(s):  
Complex Terrain ◽  
Stokes Equations ◽  
Atmospheric Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vertical Coordinate ◽  
Curvilinear Coordinate ◽  
Terrain Following ◽  
Cartesian Coordinate ◽  
Energy And Momentum

In the terrain following coordinate, Gal-Chen and Somerville (1975) and other proposed a vertical coordinate  z*=(z-zb)/(zt-zb) and constant spatial intervals of dx* and  dy*along the other directions.  Because the variation of  and  was ignored, their coordinate does not really follow the terrain.  It fails to reproduce the divergence and curl over a complex terrain.  Aligning the coordinate with real terrain, the divergence and curl we obtained from the curvilinear coordinate are consistent with the Cartesian coordinate.  With a modification, the simulated total mass, energy, and momentum from the Navier-Stokes equations are conserved and in agreement with those calculated from Cartesian coordinate.

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.

A New Approach to Implement Sigma Coordinate in a Numerical Model

2012 ◽  
Vol 12 (4) ◽  
pp. 1033-1050 ◽  
Author(s):  
Yiyuan Li ◽  
Donghai Wang ◽  
Bin Wang
Keyword(s):  
Numerical Model ◽  
Atmospheric Model ◽  
New Method ◽  
Gradient Force ◽  
Pressure Gradient Force ◽  
Curvilinear Coordinate ◽  
Terrain Following ◽  
Cartesian Coordinate ◽  
Scalar Equations ◽  
Σ Coordinate

AbstractThis study shows a new way to implement terrain-following σ-coordinate in a numerical model, which does not lead to the well-known “pressure gradient force (PGF)” problem. First, the causes of the PGF problem are analyzed with existing methods that are categorized into two different types based on the causes. Then, the new method that bypasses the PGF problem all together is proposed. By comparing these three methods and analyzing the expression of the scalar gradient in a curvilinear coordinate system, this study finds out that only when using the covariant scalar equations of σ-coordinate will the PGF computational form have one term in each momentum component equation, thereby avoiding the PGF problem completely. A convenient way of implementing the covariant scalar equations of σ-coordinate in a numerical atmospheric model is illustrated, which is to set corresponding parameters in the scalar equations of the Cartesian coordinate. Finally, two idealized experiments manifest that the PGF calculated with the new method is more accurate than using the classic one. This method can be used for oceanic models as well, and needs to be tested in both the atmospheric and oceanic models.

scholarly journals ANALYTIC SOLUTIONS OF A TWO-FLUID HYDRODYNAMIC MODEL

2021 ◽  
Vol 26 (4) ◽  
pp. 582-590
Author(s):  
Imre Ferenc Barna ◽  
László Mátyás
Keyword(s):  
Stokes Equations ◽  
Analytic Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Two Fluids ◽  
Void Fractions ◽  
Self Similar ◽  
Cartesian Coordinate ◽  
Two Fluid

We investigate a one dimensional flow described with the non-compressible coupled Euler and non-compressible Navier-Stokes equations in the Cartesian coordinate system. We couple the two fluids through the continuity equation where different void fractions can be considered. The well-known self-similar Ansatz was applied and analytic solutions were derived for both velocity and pressure field as well.

scholarly journals Viscous Analysis of Three-Dimensional Turbomachinery Flows on Body Conforming Grids Using an Implicit Solver

1991 ◽  
Author(s):  
K. F. Weber ◽  
R. A. Delaney
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Three Dimensional ◽  
The Body ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Turbulence Effects ◽  
Implicit Solver ◽  
Cartesian Coordinate ◽  
Solution Accuracy

A 3-D Navier-Stokes analysis for turbomachinery flows on C- or O-type grids is presented. The analysis is based on the Beam and Warming implicit algorithm for solution of the unsteady Navier-Stokes equations and is derived from an early version of the ARC3D flow code developed at NASA Ames Research Center. The Navier-Stokes equations are written in a Cartesian coordinate system rotating about the z-axis, and then mapped to a general body-fitted coordinate system. All viscous terms are calculated and the turbulence effects are modelled using the Baldwin-Lomax turbulence model. The equations are discretized using finite differences on stacked body-conforming grids. Modifications made to convert ARC3D from external flow to internal turbomachinery flows and to improve solution accuracy are given in detail. The body-conforming grid construction procedure is also presented. Calculations for several rotor flows have been made, and results of code experimental verification studies are presented. Comparisons of the solutions obtained on the C- and O-type grids are also presented, with particular attention to shock resolution.

Numerical Site Calibration Over Complex Terrain

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Philippe Brodeur ◽  
Christian Masson
Keyword(s):  
Experimental Data ◽  
Numerical Method ◽  
Complex Terrain ◽  
Stokes Equations ◽  
Similarity Theory ◽  
Data Uncertainty ◽  
Navier Stokes ◽  
Special Treatment ◽  
Navier Stokes Equations ◽  
Roughness Lengths

This paper presents the development and assessment of a numerical method for simulated site calibration. The wind flow over complex terrain is predicted with a small length scale resolution. The flow field is resolved with the Reynolds averaged Navier–Stokes equations, complemented by the k‐ϵ turbulence model, with special treatment of the ground boundary to account for very large roughness lengths such as forest. The computational model is solved using FLUENT. A complex site, Riviere au Renard, located in Gaspesie, QC, Canada, has been selected and data have been collected from five met masts installed on this site. An experimental data analysis has been undertaken with emphasis on uncertainty evaluation. Three sets of results are presented. First, the numerical method is validated over flat terrain by comparing the simulation results with Monin–Obukhov similarity theory. Second, the assessment of the numerical method over complex terrain is done by comparing the wind velocity profiles at three of the met masts for three different wind orientations. Finally, traditional and numerical site calibrations for Riviere au Renard are presented for two wind directions. The numerical results are within the experimental data uncertainty.

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