scholarly journals Non-overlapping Schwarz algorithms  for the Incompressible  Navier-Stokes equations with DDFV discretizations

2021 ◽  
Author(s):  
Thierry Goudon ◽  
Stella Krell ◽  
Giulia Lissoni
Keyword(s):  
Stokes Equations ◽  
Stokes Problem ◽  
Navier Stokes ◽  
Crucial Issue ◽  
Navier Stokes Equations ◽  
Numerical Fluxes ◽  
Schwarz Algorithms ◽  
The Impact ◽  
Asymptotic Problem ◽  
Overlapping Schwarz

We propose and analyze   non-overlapping Schwarz algorithms for the domain decomposition of the unsteady incompressible Navier-Stokes problem with Discrete Duality Finite Volume discretizations. The design of suitable transmission conditions for the velocity and the pressure is a crucial issue. We establish the well-posedness of the method and the convergence of the iterative process, pointing out how the numerical fluxes influence  the asymptotic problem which is intended to be a discretization of the Navier-Stokes equations on the entire computational  domain.Finally we numerically illustrate the behavior and performances of the algorithm. We discuss on numerical grounds the impact of the parameters for several mesh geometries and we perform  simulations of the  flow past an obstacle with several domains.

scholarly journals Fluid-kinetic modelling for respiratory aerosols with variable size and temperature

2020 ◽  
Vol 67 ◽  
pp. 100-119 ◽  
Author(s):  
Laurent Boudin ◽  
Céline Grandmont ◽  
Bérénice Grec ◽  
Sébastien Martin ◽  
Amina Mecherbet ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Kinetic Modelling ◽  
Type Equation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Aerosol Dynamics ◽  
Convection Diffusion Equation ◽  
Time Marching ◽  
Branched Structure ◽  
The Impact

In this paper, we propose a coupled fluid-kinetic model taking into account the radius growth of aerosol particles due to humidity in the respiratory system. We aim to numerically investigate the impact of hygroscopic effects on the particle behaviour. The air flow is described by the incompressible Navier-Stokes equations, and the aerosol by a Vlasov-type equation involving the air humidity and temperature, both quantities satisfying a convection-diffusion equation with a source term. Conservations properties are checked and an explicit time-marching scheme is proposed. Twodimensional numerical simulations in a branched structure show the influence of the particle size variations on the aerosol dynamics.

scholarly journals Flow Pressure Behavior Downstream of Ski Jumps

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 168 ◽  
Author(s):  
Agostino Lauria ◽  
Giancarlo Alfonsi ◽  
Ali Tafarojnoruz
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Dynamic Pressure ◽  
Pressure Head ◽  
Navier Stokes ◽  
Maximum Pressure ◽  
Navier Stokes Equations ◽  
Free Jet ◽  
Jet Characteristics ◽  
The Impact

Ski jump spillways are frequently implemented to dissipate energy from high-speed flows. The general feature of this structure is to transform the spillway flow into a free jet up to a location where the impact of the jet creates a plunge pool, representing an area for potential erosion phenomena. In the present investigation, several tests with different ski jump bucket angles are executed numerically by means of the OpenFOAM® digital library, taking advantage of the Reynolds-averaged Navier–Stokes equations (RANS) approach. The results are compared to those obtained experimentally by other authors as related to the jet length and shape, obtaining physical insights into the jet characteristics. Particular attention is given to the maximum pressure head at the tailwater. Simple equations are proposed to predict the maximum dynamic pressure head acting on the tailwater, as dependent upon the Froude number, and the maximum pressure head on the bucket. Results of this study provide useful suggestions for the design of ski jump spillways in dam construction.

scholarly journals Development of An Integrated Numerical Model for Simulating Wave Interaction with Permeable Submerged Breakwaters Using Extended Navier–Stokes Equations

2020 ◽  
Vol 8 (2) ◽  
pp. 87 ◽  
Author(s):  
Paran Pourteimouri ◽  
Kourosh Hejazi
Keyword(s):  
Porous Medium ◽  
Wave Propagation ◽  
Numerical Model ◽  
Analytical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Stokes Wave ◽  
Navier Stokes Equations ◽  
Numerical Predictions ◽  
The Impact

An integrated two-dimensional vertical (2DV) model was developed to investigate wave interactions with permeable submerged breakwaters. The integrated model is capable of predicting the flow field in both surface water and porous media on the basis of the extended volume-averaged Reynolds-averaged Navier–Stokes equations (VARANS). The impact of porous medium was considered by the inclusion of the additional terms of drag and inertia forces into conventional Navier–Stokes equations. Finite volume method (FVM) in an arbitrary Lagrangian–Eulerian (ALE) formulation was adopted for discretization of the governing equations. Projection method was utilized to solve the unsteady incompressible extended Navier–Stokes equations. The time-dependent volume and surface porosities were calculated at each time step using the fraction of a grid open to water and the total porosity of porous medium. The numerical model was first verified against analytical solutions of small amplitude progressive Stokes wave and solitary wave propagation in the absence of a bottom-mounted barrier. Comparisons showed pleasing agreements between the numerical predictions and analytical solutions. The model was then further validated by comparing the numerical model results with the experimental measurements of wave propagation over a permeable submerged breakwater reported in the literature. Good agreements were obtained for the free surface elevations at various spatial and temporal scales, velocity fields around and inside the obstacle, as well as the velocity profiles.

A Simplified Parallel Two-Level Iterative Method for Simulation of Incompressible Navier-Stokes Equations

2015 ◽  
Vol 7 (6) ◽  
pp. 715-735
Author(s):  
Yueqiang Shang ◽  
Jin Qin
Keyword(s):  
Stokes Equations ◽  
Stokes Problem ◽  
Coarse Grid ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Step Flow ◽  
Grid Solution ◽  
Oseen Problem ◽  
Parallel Iterative

AbstractBased on two-grid discretization, a simplified parallel iterative finite element method for the simulation of incompressible Navier-Stokes equations is developed and analyzed. The method is based on a fixed point iteration for the equations on a coarse grid, where a Stokes problem is solved at each iteration. Then, on overlapped local fine grids, corrections are calculated in parallel by solving an Oseen problem in which the fixed convection is given by the coarse grid solution. Error bounds of the approximate solution are derived. Numerical results on examples of known analytical solutions, lid-driven cavity flow and backward-facing step flow are also given to demonstrate the effectiveness of the method.

scholarly journals Two-Dimensional Modelling of a Quayside Floating System

2020 ◽  
Vol 8 (11) ◽  
pp. 903
Author(s):  
Sixtine Neuvéglise ◽  
Gaële Perret ◽  
Hassan Smaoui ◽  
François Marin ◽  
Philippe Sergent
Keyword(s):  
Stokes Equations ◽  
Numerical Models ◽  
Navier Stokes ◽  
Intermediate Water ◽  
Navier Stokes Equations ◽  
Quadratic Drag ◽  
Floating System ◽  
Physical Tests ◽  
Comparison Of The Results ◽  
The Impact

This paper studies the behaviour of a quayside floater oscillating in front of a vertical dike. In order to study the floater motion and the impact of the dike on the floater, a linear analytical model based on 2D potential flow theory in intermediate water depth conditions and a numerical model resolving 2D Navier–Stokes equations are developed. Physical tests performed for different floater dimensions in a wave tank are used as references for the analytical and numerical models. The comparison of the results obtained analytically, numerically and experimentally leads to the validity domain of the potential model. A correction of this model is proposed, based on the optimization of the radiated coefficients, and a quadratic drag term is added according to Morison equation. The impact of the different parameters of the system on floater behaviour is considered. Results show that the draft has the most important impact on floater motion.

scholarly journals Characteristic Local Discontinuous Galerkin Methods for Incompressible Navier-Stokes Equations

2017 ◽  
Vol 22 (1) ◽  
pp. 202-227
Author(s):  
Shuqin Wang ◽  
Weihua Deng ◽  
Jinyun Yuan ◽  
Yujiang Wu
Keyword(s):  
Discontinuous Galerkin ◽  
Stokes Equations ◽  
Local Discontinuous Galerkin Method ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Local Discontinuous Galerkin ◽  
Priori Estimates ◽  
Numerical Fluxes ◽  
Theoretical Results ◽  
Variational Formulations

AbstractBy combining the characteristic method and the local discontinuous Galerkin method with carefully constructing numerical fluxes, variational formulations are established for time-dependent incompressible Navier-Stokes equations in ℝ2. The nonlinear stability is proved for the proposed symmetric variational formulation. Moreover, for general triangulations the priori estimates for the L2–norm of the errors in both velocity and pressure are derived. Some numerical experiments are performed to verify theoretical results.

The Effect of Blade Lean, Twist and Bow on the Performance of Axial Turbine at Design Point

2011 ◽  
Author(s):  
Hadi Karrabi ◽  
Mohsen Rezasoltani
Keyword(s):  
Stokes Equations ◽  
Numerical Data ◽  
Navier Stokes ◽  
Minor Effect ◽  
Complex Flow ◽  
Navier Stokes Equations ◽  
Axial Turbine ◽  
Twisted Blade ◽  
The Impact ◽  
Good Agreement

An investigation to understand the impact of twisted, leaned and bowed blades on the performance of axial turbine was undertaken. A CFD code, which solves the Reynolds-averaged Navier–Stokes equations, was used to compute the complex flow field of axial turbine. The code was validated against existing Hannover turbine experimental data. Numerical data showed good agreement with measured data. Finally, the effect of geometry changes, focusing on blade lean, twist and bow, on the Avon turbine blade performance, was analyzed. Results show that twisted blade affects performance significantly. Leaned and bowed blade has minor effect on performance.

scholarly journals An Oseen Two-Level Stabilized Mixed Finite-Element Method for the 2D/3D Stationary Navier-Stokes Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Aiwen Wang ◽  
Xin Zhao ◽  
Peihua Qin ◽  
Dongxiu Xie
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Mesh Size ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stabilized Finite Element ◽  
Stabilized Finite Element Method ◽  
Element Method

We investigate an Oseen two-level stabilized finite-element method based on the local pressure projection for the 2D/3D steady Navier-Stokes equations by the lowest order conforming finite-element pairs (i.e.,Q1−P0andP1−P0). Firstly, in contrast to other stabilized methods, they are parameter free, no calculation of higher-order derivatives and edge-based data structures, implemented at the element level with minimal cost. In addition, the Oseen two-level stabilized method involves solving one small nonlinear Navier-Stokes problem on the coarse mesh with mesh sizeH, a large general Stokes equation on the fine mesh with mesh sizeh=O(H)2. The Oseen two-level stabilized finite-element method provides an approximate solution (uh,ph) with the convergence rate of the same order as the usual stabilized finite-element solutions, which involves solving a large Navier-Stokes problem on a fine mesh with mesh sizeh. Therefore, the method presented in this paper can save a large amount of computational time. Finally, numerical tests confirm the theoretical results. Conclusion can be drawn that the Oseen two-level stabilized finite-element method is simple and efficient for solving the 2D/3D steady Navier-Stokes equations.

Heat Transfer Generated by the Interaction of Single and Multiple Tandem Jets in Crossflow

2010 ◽  
Author(s):  
Amina Radhouane ◽  
Nejla Mahjoub ◽  
Hatem Mhiri ◽  
George Lepalec ◽  
Philippe Bournot
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Uniform Grid ◽  
Cooling Power ◽  
Small Scale ◽  
Fluid Composition ◽  
Navier Stokes Equations ◽  
The Impact

“Twin jets in Crossflow” is a common configuration that finds application in several large and/or small scale industrial fields. The interest in such a configuration is further enhanced by its dependence in several parameters, that may be geometric, dynamic, thermal, or relative to the handled fluid composition. We propose to focus in the present work on the effect of the number of the emitted jets on the generated heat transfer, in presence of an unchanged uniform crossflow. To reach this goal, single, double and triple jet configurations were simulated, based upon the resolution of the Navier Stokes equations by means of the RSM (Reynolds Stress Model) second order turbulent closure model, together with a non uniform grid system particularly tightened near the emitting nozzles. After validation, we tried to find out the impact of the number of the handled jets on their cooling “power” by tracking the temperature distribution of the resulting flowfield. Since in practically all applications we are in need of higher efficiencies and then of higher operating temperatures, we are constantly concerned about not going beyond the shielding material melting temperature. If the use of cooling jets proves to be efficient, this may bring a significant progress in the technological field.

scholarly journals An Algorithm for the Navier-Stokes Problem

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
F.Z. Nouri ◽  
K. Amoura
Keyword(s):  
Nonlinear Problem ◽  
Numerical Experiments ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Navier Stokes ◽  
Nous Proposons ◽  
Navier Stokes Equations ◽  
International Audience ◽  
The One ◽  
Work First

International audience This study is a continuation of the one done in [7],[8] and [9] which are based on the work, first derived by Glowinski et al. in [3] and [4] and also Bernardi et al. [1] and [2]. Here, we propose an Algorithm to solve a nonlinear problem rising from fluid mechanics. In [7], we have studied Stokes problem by adapting Glowinski technique. This technique is userful as it decouples the pressure from the velocity during the resolution of the Stokes problem. In this paper, we extend our study to show that this technique can be used in solving a nonlinear problem such as the Navier Stokes equations. Numerical experiments confirm the interest of this discretisation. Cette étude est la continuation des travaux [7],[8] et [9] qui sont basés sur l'étude faite par Glowinski et al. [3] et [4] ainsi que Bernardi et al. (voir [1] et [2]). Ici nous proposons un Algorithme pour résoudre un problème non-linéaire issu de la mécanique des fluides. Dans [7] nous avons étudié le problème de Stokes en adaptant la technique de Glowinski, grace à aquelle, on peut découpler la pression de la vitesse lors de la résolution du problème de Stokes. Dans ce travail, nous étendons notre étude et montrons que cette technique peut être utilisée dans la résolution d'un probème non-linéaire comme les quations de Navier Stokes. Des tests numériques confirment l'intérêt de la discrétisation.

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