Modelling atmospheric flows

Acta Numerica ◽  
2007 ◽  
Vol 16 ◽  
pp. 67-154 ◽  
Author(s):  
Mike Cullen
Keyword(s):  
Current Practice ◽  
Stokes Equations ◽  
Numerical Algorithms ◽  
Navier Stokes ◽  
Atmospheric Models ◽  
Navier Stokes Equations ◽  
Atmospheric Flows ◽  
Production Models ◽  
Weather And Climate ◽  
Limit Solutions

This article demonstrates how numerical methods for atmospheric models can be validated by showing that they give the theoretically predicted rate of convergence to relevant asymptotic limit solutions. This procedure is necessary because the exact solution of the Navier–Stokes equations cannot be resolved by production models. The limit solutions chosen are those most important for weather and climate prediction. While the best numerical algorithms for this purpose largely reflect current practice, some important limit solutions cannot be captured by existing methods. The use of Lagrangian rather than Eulerian averaging may be required in these cases.

scholarly journals Numerical modelling of bank failures during reservoir draw-down

2018 ◽  
Vol 40 ◽  
pp. 03001 ◽  
Author(s):  
Nils Reidar B. Olsen ◽  
Stefan Haun
Keyword(s):  
Stokes Equations ◽  
Limit Equilibrium ◽  
Numerical Algorithms ◽  
High Viscosity ◽  
Navier Stokes ◽  
Bank Failures ◽  
Navier Stokes Equations ◽  
Order Of Magnitude ◽  
Sediment Layers ◽  
Hydropower Reservoir

Numerical algorithms are presented for modeling bank failures during reservoir flushing. The algorithms are based on geotechnical theory and the limit equilibrium approach to find the location and the depth of the slides. The actual movements of the slides are based on the solution of the Navier-Stokes equations for laminar flow with high viscosity. The models are implemented in the SSIIM computer program, which also can be used for modelling erosion of sediments from reservoirs. The bank failure algorithms are tested on the Bodendorf hydropower reservoir in Austria. Comparisons with measurements show that the resulting slides were in the same order of magnitude as the observed ones. However, some scatter on the locations were observed. The algorithms were stable for thick sediment layers, but instabilities were observed for thin sediment layers.

A Godunov-Type Scheme for Atmospheric Flows on Unstructured Grids: Euler and Navier-Stokes Equations

2007 ◽  
Vol 164 (1) ◽  
pp. 217-244 ◽  
Author(s):  
Nash'at Ahmad ◽  
Zafer Boybeyi ◽  
Rainald Löhner ◽  
Ananthakrishna Sarma
Keyword(s):  
Stokes Equations ◽  
Unstructured Grids ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Atmospheric Flows

The structure and stabilization by boundary conditions of an annular flow of Kolmogorov type

2017 ◽  
Vol 32 (4) ◽  
Author(s):  
Andrei A. Kornev
Keyword(s):  
Boundary Conditions ◽  
Annular Flow ◽  
Stokes Equations ◽  
Numerical Algorithms ◽  
Main Flow ◽  
Secondary Flows ◽  
Navier Stokes ◽  
Internal Boundary ◽  
Navier Stokes Equations ◽  
Quasistationary Solutions

AbstractA system of Navier-Stokes equations with a right-hand side is considered in the case when the system approximately describes the motion of a thin layer of a viscous incompressible fluid in an annular domain under the action of external electromagnetic force. The problem possesses an unstable two-stream nonstationary main flow and a set of quasistationary solutions of vortex type for the tested range of parameters. A method of study of the general dynamic pattern is proposed in the paper. The method is based on the construction of control boundary conditions specified on the internal boundary of the annulus and providing the stabilization of considered unstable modes. The problem of boundary stabilization of the main and secondary flows is also solved numerically and we obtained that it is sufficient to take into account only a part of unstable modes in the construction of stabilizing conditions for the main flow. The method based on the partial stabilization of the main flow is first proposed for stabilization of secondary flows, which essentially simplifies the implementation of the algorithm. Formulations of the problems and numerical algorithms are presented.

scholarly journals Well-posedness analysis of a stationary Navier–Stokes hemivariational inequality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Min Ling ◽  
Weimin Han
Keyword(s):  
Stokes Equations ◽  
Normal Component ◽  
Numerical Algorithms ◽  
Hemivariational Inequality ◽  
Navier Stokes ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Navier Stokes Equations ◽  
Solution Existence And Uniqueness ◽  
Stationary Navier Stokes Equations

AbstractThis paper provides a well-posedness analysis for a hemivariational inequality of the stationary Navier-Stokes equations by arguments of convex minimization and the Banach fixed point. The hemivariational inequality describes a stationary incompressible fluid flow subject to a nonslip boundary condition and a Clarke subdifferential relation between the total pressure and the normal component of the velocity. Auxiliary Stokes hemivariational inequalities that are useful in proving the solution existence and uniqueness of the Navier–Stokes hemivariational inequality are introduced and analyzed. This treatment naturally leads to a convergent iteration method for solving the Navier–Stokes hemivariational inequality through a sequence of Stokes hemivariational inequalities. Equivalent minimization principles are presented for the auxiliary Stokes hemivariational inequalities which will be useful in developing numerical algorithms.

scholarly journals Secondary frequencies in the wake of a circular cylinder with vortex shedding

1991 ◽  
Vol 225 ◽  
pp. 557-574 ◽  
Author(s):  
Saul S. Abarbanel ◽  
Wai Sun Don ◽  
David Gottlieb ◽  
David H. Rudy ◽  
James C. Townsend
Keyword(s):  
Circular Cylinder ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Numerical Algorithms ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Reynolds Numbers ◽  
Two Dimensional Flow

A detailed numerical study of two-dimensional flow past a circular cylinder at moderately low Reynolds numbers has been conducted using three different numerical algorithms for solving the time-dependent compressible Navier–Stokes equations. It was found that if the algorithm and associated boundary conditions were consistent and stable, then the major features of the unsteady wake were well predicted. However, it was also found that even stable and consistent boundary conditions could introduce additional periodic phenomena reminiscent of the type seen in previous wind-tunnel experiments. However, these additional frequencies were eliminated by formulating the boundary conditions in terms of the characteristic variables. An analysis based on a simplified model provides an explanation for this behaviour.

scholarly journals Closed-form shock solutions

2014 ◽  
Vol 745 ◽  
Author(s):  
B. M. Johnson
Keyword(s):  
Mach Number ◽  
Closed Form ◽  
Evolution Equations ◽  
Stokes Equations ◽  
Numerical Algorithms ◽  
Ideal Gas ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Closed Form Solutions ◽  
Nonlinear Character

AbstractIt is shown here that a subset of the implicit analytical shock solutions discovered by Becker and by Johnson can be inverted, yielding several exact closed-form solutions of the one-dimensional compressible Navier–Stokes equations for an ideal gas. For a constant dynamic viscosity and thermal conductivity, and at particular values of the shock Mach number, the velocity can be expressed in terms of a polynomial root. For a constant kinematic viscosity, independent of Mach number, the velocity can be expressed in terms of a hyperbolic tangent function. The remaining fluid variables are related to the velocity through simple algebraic expressions. The solutions derived here make excellent verification tests for numerical algorithms, since no source terms in the evolution equations are approximated, and the closed-form expressions are straightforward to implement. The solutions are also of some academic interest as they may provide insight into the nonlinear character of the Navier–Stokes equations and may stimulate further analytical developments.

scholarly journals On Parallel Numerical Algorithms for Simulating Industrial Filtration Problems

2007 ◽  
Vol 7 (2) ◽  
pp. 118-134 ◽  
Author(s):  
R. Čiegis ◽  
O. Iliev ◽  
Z. Lakdawala
Keyword(s):  
Parallel Algorithm ◽  
Stokes Equations ◽  
Data Communication ◽  
Numerical Algorithms ◽  
Time Discretization ◽  
Solid Particles ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Parallel Numerical Algorithms

AbstractThe performance of oil filters used in the automotive industry can be significantly improved, especially when computer simulation is an essential component of the design process. In this paper, we consider parallel numerical algorithms for solving mathematical models describing the process of filtration, filtering solid particles out of liquid oil. The Navier — Stokes — Brinkmann system of equations is used to describe the laminar flow of incompressible isothermal oil. The space discretization in the complicated filter geometry is based on the finite-volume method. Special care is taken for an accurate approximation of the velocity and pressure on the interface between the fluid and the porous media. The time discretization used here is a proper modification of the fractional time step discretization (cf. Chorin scheme) of the Navier- Stokes equations, where the Brinkmann term is considered in both the prediction and the correction substeps. A data decomposition method is used to develop a parallel algorithm, where the domain is distributed among the processors by using a structured reference grid. The MPI library is used to implement the data communication part of the algorithm. A theoretical model is proposed for the estimation of the complexity of the given parallel algorithm and a scalability analysis is done on the basis of this model. The results of the computational experiments are presented, and the accuracy and efficiency of the parallel algorithm is tested on real industrial geometries.

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