A compact streamfunction-velocity scheme for the 2-D unsteady incompressible Navier-Stokes equations in arbitrary curvilinear coordinates

2018 ◽  
Vol 31 (4) ◽  
pp. 827-839
Author(s):  
Jian-xin Qiu ◽  
Bo Peng ◽  
Zhen-fu Tian
Keyword(s):  
Stokes Equations ◽  
Curvilinear Coordinates ◽  
Navier Stokes ◽  
Navier Stokes Equations

Simulation of Flow Around Circular Cylinder Using a Collocation Spectral Method

2005 ◽  
Author(s):  
Johnny J. M. Rizales ◽  
Paulo T. T. Esperanc¸a ◽  
Andre´ Belfort Bueno
Keyword(s):  
Velocity Field ◽  
Circular Cylinder ◽  
Spectral Method ◽  
Stokes Equations ◽  
Curvilinear Coordinates ◽  
Navier Stokes ◽  
Implicit Time ◽  
Integration Scheme ◽  
Navier Stokes Equations ◽  
Collocation Spectral Method

The purpose of this paper is to develop a Fourier-Chebyshev collocation spectral method for computing unsteady two-dimensional viscous incompressible flow past a circular cylinder for low Reynolds numbers. The incompressible Navier-Stokes equations (INSE) are formulated in terms of the primitive variables, velocity and pressure. The incompressible Navier-Stokes equations in curvilinear coordinates are spectrally discretized and time integrated by a second-order mixed explicit/implicit time integration scheme. This scheme is a combination of the Crank-Nicolson scheme operating on the diffusive term and Adams-Bashforth scheme acting on the convective term. The projection method is used to split the solution of the INSE to the solution of two decoupled problems: the diffusion-convection equation (Burgers equation) to predict an intermediate velocity field and the Poisson equation for the pressure, it is used to correct the velocity field and satisfy the continuity equation. Finally, the numerical results obtained for the drag and lift coefficients around the circular cylinder are compared with results previously published.

Numerical Analysis of Ventilated Cavitation Using Non-Condensable Gas Injection on Underwater Vehicle

2011 ◽  
Author(s):  
Dong-Hyun Kim ◽  
Cong-Tu Ha ◽  
Warn-Gyu Park ◽  
Chul-Min Jung
Keyword(s):  
Numerical Analysis ◽  
Stokes Equations ◽  
Gas Injection ◽  
Curvilinear Coordinates ◽  
Navier Stokes ◽  
Cavitation Model ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Ventilated Cavitation ◽  
Homogeneous Mixture Model

Supercavitating torpedo uses the supercavitation technology that can reduce dramatically the skin friction drag. The present work focuses on the numerical analysis of the condensable/non-condensable cavitating flow around the supercavitating torpedo. The governing equations are the Navier-Stokes equations based on the homogeneous mixture model. The cavitation model uses a new cavitation model which was developed by Merkle (2006). The multiphase flow solver uses an implicit preconditioning scheme in curvilinear coordinates. The ventilated cavitation is implemented by non-condensable gas injection on backward of cavitator cone and the base of the torpedo.

Navier–Stokes Solution for Steady Two-Dimensional Transonic Cascade Flows

1988 ◽  
Vol 110 (3) ◽  
pp. 339-346 ◽  
Author(s):  
O. K. Kwon
Keyword(s):  
Stokes Equations ◽  
Solution Procedure ◽  
Curvilinear Coordinates ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Turbine Cascade ◽  
Navier Stokes Equations ◽  
Time Marching ◽  
Transonic Turbine ◽  
Transonic Cascade

A robust, time-marching Navier–Stokes solution procedure based on the explicit hopscotch method is presented for solution of steady, two-dimensional, transonic turbine cascade flows. The method is applied to the strong conservation form of the unsteady Navier–Stokes equations written in arbitrary curvilinear coordinates. Cascade flow solutions are obtained on an orthogonal, body-conforming “O” grid with the standard k–ε turbulence model. Computed results are presented and compared with experimental data.

The Theory of Molecular Dispersion in Flowing Fluids: An Analytic Solution of the Navier-Stokes Equations

2008 ◽  
Author(s):  
William Todd
Keyword(s):  
Reynolds Number ◽  
Free Energy ◽  
Analytic Solution ◽  
Stokes Equations ◽  
Fluid Model ◽  
Curvilinear Coordinates ◽  
Navier Stokes ◽  
Energy Calculation ◽  
Navier Stokes Equations

This development is a description of the transport of mass, energy and momentum in flowing viscous fluids at the molecular level; and results in: • A thermostatistical link between Reynolds’ number and momentum and free energy, • A wave characterization of the behavior of flowing fluids using the forces of attraction between molecules as a basis, • Calculation of the velocity components in flowing fluids for all Reynolds’ numbers greater than 535; thus defining a mathematical theory of turbulence, • An analytic solution of the Navier-Stokes equations for incompressible fluids in 3-dimensions. The following steps lead to the solution: • Definition of the fluid Model, • A re-characterization of Reynolds’ number in terms of momentum and free energy, • Calculation of the shear and circulatory components of velocity, • Transformation of the Navier-Stokes equations into the curvilinear coordinates of the intermolecular force waves, • Using the transformed equations to calculate the velocity components and Pressure-wave front resulting from the current, • Corroboration of the theoretical results with: a) wave fronts as manifest in the behavior of sails in uniform flow, b) boundary layer definition/behavior compared to theoretical and empirical developments of Schlichting and others, and c) empirical results for forces measured in the OCEANIC/DeepStar high Re beam-tow tests.

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