scholarly journals Numerical integration of the contravariant integral form of the Navier–Stokes equations in time-dependent curvilinear coordinate systems for three-dimensional free surface flows

2018 ◽  
Vol 31 (2) ◽  
pp. 491-519 ◽  
Author(s):  
G. Cannata ◽  
C. Petrelli ◽  
L. Barsi ◽  
F. Gallerano
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Integral Form ◽  
Free Surface Flows ◽  
Time Dependent ◽  
Navier Stokes ◽  
Coordinate Systems ◽  
Navier Stokes Equations ◽  
Surface Flows ◽  
Curvilinear Coordinate

Modélisation tridimensionnelle de l'écoulement au voisinage d'un aménagement portuaire

1989 ◽  
Vol 16 (6) ◽  
pp. 829-844
Author(s):  
A. Soulaïmani ◽  
Y. Ouellet ◽  
G. Dhatt ◽  
R. Blanchet
Keyword(s):  
Free Surface ◽  
Computational Analysis ◽  
Stokes Equations ◽  
A Priori ◽  
Three Dimensional ◽  
Free Surface Flows ◽  
Solution Algorithm ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Surface Flows

This paper is devoted to the computational analysis of three-dimensional free surface flows. The model solves the Navier-Stokes equations without any a priori restriction on the pressure distribution. The variational formulation along with the solution algorithm are presented. Finally, the model is used to study the hydrodynamic regime in the vicinity of a projected harbor installation. Key words: free surface flows, three-dimensional flows, finite element method.

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.

scholarly journals A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 756
Author(s):  
Federico Lluesma-Rodríguez ◽  
Francisco Álcantara-Ávila ◽  
María Jezabel Pérez-Quiles ◽  
Sergio Hoyas
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Direct Numerical Simulations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Thermal Flow ◽  
Navier Stokes Equations

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

scholarly journals Hydrodynamic Effects Produced by Submerged Breakwaters in a Coastal Area with a Curvilinear Shoreline

2019 ◽  
Vol 7 (10) ◽  
pp. 337 ◽  
Author(s):  
Francesco Gallerano ◽  
Giovanni Cannata ◽  
Federica Palleschi
Keyword(s):  
Coastal Area ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Integral Form ◽  
Navier Stokes ◽  
Hydrodynamic Effect ◽  
Riemann Solver ◽  
Three Dimensional Model ◽  
Navier Stokes Equations

A three-dimensional numerical study of the hydrodynamic effect produced by a system of submerged breakwaters in a coastal area with a curvilinear shoreline is proposed. The three-dimensional model is based on an integral contravariant formulation of the Navier-Stokes equations in a time-dependent curvilinear coordinate system. The integral form of the contravariant Navier-Stokes equations is numerically integrated by a finite-volume shock-capturing scheme which uses Monotonic Upwind Scheme for Conservation Laws Total Variation Diminishing (MUSCL-TVD) reconstructions and an Harten Lax van Leer Riemann solver (HLL Riemann solver). The numerical model is used to verify whether the presence of a submerged coastal defence structure, in the coastal area with a curvilinear shoreline, is able to modify the wave induced circulation pattern and the hydrodynamic conditions from erosive to accretive.

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 Numerical investigation of the three-dimensional velocity fields induced by wave-structure interaction

2019 ◽  
Vol 24 ◽  
pp. 02011
Author(s):  
Giovanni Cannata ◽  
Francesco Gallerano ◽  
Federica Palleschi ◽  
Chiara Petrelli ◽  
Luca Barsi
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Wave Structure ◽  
Integral Form ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Structure Interaction ◽  
Wave Trains ◽  
Hydrodynamic Effects ◽  
Wave Structure Interaction

Submerged shore-parallel breakwaters for coastal defence are a good compromise between the need to mitigate the effects of waves on the coast and the ambition to ensure the preservation of the landscape and water quality. In this work we simulate, in a fully three-dimensional form, the hydrodynamic effects induced by submerged breakwaters on incident wave trains with different wave height. The proposed three-dimensional non-hydrostatic finite-volume model is based on an integral form of the Navier-Stokes equations in σ-coordinates and is able to simulate the shocks in the numerical solution related to the wave breaking. The obtained numerical results show that the hydrodynamic phenomena produced by wave-structure interaction have features of three-dimensionality (undertow), that are locally important, and emphasize the need to use a non-hydrostatic fully-three-dimensional approach.

scholarly journals Numerical and Experimental Investigation of Wave Overtopping of Barriers

Water ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 451 ◽  
Author(s):  
Cannata ◽  
Tamburrino ◽  
Ferrari ◽  
Badas ◽  
Querzoli
Keyword(s):  
Free Surface ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Experimental Tests ◽  
Integral Form ◽  
Breaking Waves ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Wave Overtopping

We present a study of wave overtopping of barriers. The phenomenon of the wave overtopping over emerged structures is reproduced both numerically and experimentally. The numerical simulations are carried out by a numerical scheme for three-dimensional free-surface flows, which is based on the solution of the Navier–Stokes equations in a novel integral form on a time-dependent coordinate system. In the adopted numerical scheme, a novel wet–dry technique, based on the exact solution of the Riemann problem over the dry bed, is proposed. The experimental tests are carried out by adopting a nonintrusive and continuous-in-space image-analysis technique, which is able to properly identify the free surface even in very shallow waters or breaking waves. A comparison between numerical and experimental results, for several wave and water-depth conditions, is shown.

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