scholarly journals A New Mass-Conservative, Two-Dimensional, Semi-Implicit Numerical Scheme for the Solution of the Navier-Stokes Equations in Gravel Bed Rivers with Erodible Fine Sediments

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 690
Author(s):  
Maurizio Tavelli ◽  
Sebastiano Piccolroaz ◽  
Giulia Stradiotti ◽  
Giuseppe Roberto Pisaturo ◽  
Maurizio Righetti
Keyword(s):  
Numerical Scheme ◽  
Stokes Equations ◽  
Transport Processes ◽  
Sediment Supply ◽  
Navier Stokes ◽  
Computational Domain ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Gravel Bed ◽  
Gravel Bed Rivers

The selective trapping and erosion of fine particles that occur in a gravel bed river have important consequences for its stream ecology, water quality, and overall sediment budgeting. This is particularly relevant in water bodies that experience periodic alternation between sediment supply-limited conditions and high sediment loads, such as downstream from a dam. While experimental efforts have been spent to investigate fine sediment erosion and transport in gravel bed rivers, a comprehensive overview of the leading processes is hampered by the difficulties in performing flow field measurements below the gravel crest level. In this work, a new two-dimensional, semi-implicit numerical scheme for the solution of the Navier-Stokes equations in the presence of deposited and erodible sediment is presented, and tested against analytical solutions and performing numerical tests. The scheme is mass-conservative, computationally efficient, and allows for a fine discretization of the computational domain. Overall, this makes the model suitable to appreciate small-scales phenomena such as inter-grain circulation cells, thus offering a valid alternative to evaluate the shear stress distribution, on which erosion and transport processes depend, compared to traditional experimental approaches. In this work, we present proof-of-concept of the proposed model, while future research will focus on its extension to a three-dimensional and parallelized version, and on its application to real case studies.

scholarly journals Numerical simulation of unsteady flow of a viscous incompressible liquid in flat channels of arbitrary shape of heat exchangers

2020 ◽  
Vol 34 ◽  
pp. 41-55
Author(s):  
Y. Chоvniuk ◽  
V. Kravchuk ◽  
A. Moskvitina ◽  
I. Pefteva
Keyword(s):  
Numerical Simulation ◽  
Fluid Flow ◽  
Unsteady Flow ◽  
Heat Exchangers ◽  
Arbitrary Shape ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Computational Domain ◽  
Two Dimensional ◽  
Navier Stokes Equations

Reasonable development and creation of any device in which there is an interaction between the fluid flow and the elements of the flow parts (for example, heat exchangers, transport and power machines, main pipelines), is impossible without detailed information about the characteristics of the flow, about the forces on the surfaces that are around, about vibroacoustic phenomena, etc. Among the various methods of obtaining information about the characteristics of the flow, about the forces on surfaces that are flown around, about vibroacoustic phenomena, an important role is played by theoretical methods that rely on the equation of hydrodynamics and numerous ways to solve them. In this case, the main efforts are aimed at solving the system of Navier-Stokes equations. In this paper, a general method is described for the numerical solution of the problem of unsteady flow of a viscous incompressible fluid in flat channels of an arbitrary shape of heat exchangers. An effective solution to the problem is achieved by using adaptive networks. The mathematical model of the flow is based on the two-dimensional Navier-Stokes equations in the variables "flow function - vortex" and the Poissonequation for pressure, which are solved on the basis of the finite-difference method. A numerical simulation of the fluid flow in a flat curvilinear elbow is carried out at the Reynolds number Re = 1000. This form reflects the most characteristic features of the flow paths of various hydraulic machines, heat exchangers, hydraulic and pipeline systems. The presentation of the numerical results was carried out on the basis of the VISSIM graphic processing package. One of the main problems (difficulties) in the numerical solution of problems of mathematical physics is the representation of boundary conditions for regions of arbitrary shape. The implementation of various artificial methods that are now used in the approximation of both the curvilinear boundaries themselves and the boundary conditions on them can lead to significant losses in the accuracy of the solution. This is especially evident in problems in which solutions in the boundary region have maximum gradients. An effective method for solving this problem is the use of adapted grids for the computational domain. The essence of this method lies in the fact that such a coordinate system, not necessarily orthogonal, is found in which the boundary lines (surfaces) of the region coincide with the coordinate lines (surfaces). In the flat case, the computational domain is transformed into a rectangular one, and the limit curve is displayed on the sides of the rectangle. In practice, the problem of constructing an adapted mesh is reduced to finding functions that describe the mappings of the canonical (rectangular) region onto the region for which the problem was originally formulated, that is, for the two-dimensional case, the functions x (ξ, η), y (ξ, η) are determined.

The enstrophy cascade in forced two-dimensional turbulence

2011 ◽  
Vol 671 ◽  
pp. 168-183 ◽  
Author(s):  
ANDREAS VALLGREN ◽  
ERIK LINDBORG
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Cascade Range ◽  
Navier Stokes ◽  
Logarithmic Correction ◽  
Computational Domain ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Grid Points ◽  
Enstrophy Cascade

We carry out direct numerical simulations of two-dimensional turbulence with forcing at different wavenumbers and resolutions up to 327682 grid points. In the absence of large-scale drag, a state is reached where enstrophy is quasi-stationary while energy is growing. In the enstrophy cascade range the energy spectrum has the form E(k) = εω2/3k−3, without any logarithmic correction, where εω is the enstrophy dissipation and is of the order of unity. However, is varying between different simulations and is thus not a perfect constant. This variation can be understood as a consequence of large-scale dissipation intermittency, following the argument by Landau (Landau & Lifshitz, Fluid Mechanics, 1959, Pergamon). In the presence of a large-scale drag, we obtain a slightly steeper spectrum. When forcing is applied at a scale which is somewhat smaller than the computational domain, no vortices are formed, and the statistics remain close to Gaussian in the enstrophy cascade range. When forcing is applied at a smaller scale, long-lived coherent vortices form at larger scales than the forcing scale, and intermittency measures become very large at all scales, including the scales of the enstrophy cascade. We conclude that the enstrophy cascade with a k−3-spectrum is a robust feature of the two-dimensional Navier–Stokes equations. However, there is a complete lack of universality of higher-order statistics of vorticity increments in the enstrophy cascade range.

Direct simulation of transition in an oscillatory boundary layer

1998 ◽  
Vol 371 ◽  
pp. 207-232 ◽  
Author(s):  
G. VITTORI ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Temporal Development ◽  
Direct Simulation ◽  
Navier Stokes Equations ◽  
Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

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