Some numerical schemes using curvilinear coordinate grids for incompressible and compressible Navier-Stokes equations

Sadhana ◽  
1993 ◽  
Vol 18 (3-4) ◽  
pp. 431-476 ◽  
Author(s):  
H Daiguji ◽  
B R Shin
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Numerical Schemes ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate

Kinetic-based numerical schemes for incompressible Navier–Stokes equations

2006 ◽  
Vol 35 (8-9) ◽  
pp. 879-887
Author(s):  
M.K. Banda ◽  
M. Junk ◽  
A. Klar
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Numerical Schemes ◽  
Navier Stokes Equations

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.

scholarly journals Enhanced Physics-Based Numerical Schemes for Two Classes of Turbulence Models

2009 ◽  
Vol 2009 ◽  
pp. 1-13
Author(s):  
Leo G. Rebholz
Keyword(s):  
Finite Element ◽  
Differential Operator ◽  
Stokes Equations ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Numerical Schemes ◽  
Discrete Laplacian ◽  
Navier Stokes Equations ◽  
Approximate Deconvolution ◽  
Finite Element Schemes

We present enhanced physics-based finite element schemes for two families of turbulence models, the models and the Stolz-Adams approximate deconvolution models. These schemes are delicate extensions of a method created for the Navier-Stokes equations in Rebholz (2007), that achieve high physical fidelity by admitting balances of both energy and helicity that match the true physics. The schemes' development requires carefully chosen discrete curl, discrete Laplacian, and discrete filtering operators, in order to permit the necessary differential operator commutations.

scholarly journals Discrete Functional Analysis Tools for Some Evolution Equations

2018 ◽  
Vol 18 (3) ◽  
pp. 477-493 ◽  
Author(s):  
Thierry Gallouët
Keyword(s):  
Functional Analysis ◽  
Stefan Problem ◽  
Evolution Equations ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Numerical Schemes ◽  
Navier Stokes Equations ◽  
Analysis Tools ◽  
Proof Of Convergence

AbstractWe present some discrete functional analysis tools for the proof of convergence of numerical schemes, mainly for equations including diffusion terms such as the Stefan problem or the Navier–Stokes equations in the incompressible and compressible cases. Some of the results covered here have been proved in previous works, coauthored with several coworkers.

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