scholarly journals Schéma SRNHS Analyse et Application d'un schéma aux volumes finis dédié aux systèmes non homogènes

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
Slah SAHMIM ◽  
Fayssal Benkhaldoun
Keyword(s):  
Shallow Water ◽  
Scalar Case ◽  
Finite Volume Scheme ◽  
Two Phase ◽  
Homogeneous Systems ◽  
Selfsimilar Solution ◽  
International Audience ◽  
The Stability ◽  
New Formulation ◽  
Water Problems

International audience This article is devoted to the analysis, and improvement of a finite volume scheme proposed recently for a class of non homogeneous systems. We consider those for which the corressponding Riemann problem admits a selfsimilar solution. Some important examples of such problems are Shallow Water problems with irregular topography and two phase flows. The stability analysis of the considered scheme, in the homogeneous scalar case, leads to a new formulation which has a naturel extension to non homogeneous systems. Comparative numerical experiments for Shallow Water equations with sourec term, and a two phase problem (Ransom faucet) are presented to validate the scheme. Cet article concerne l'analyse et l'application, d'un schéma proposé récemment por une classe de systèmes non homogènes. Nous considérons ceux pour lesquels le problème de Riemann correpondant admet une solution autosimilaire. Deux exemples importants de tels problèmes sont l'écoulement d'eau peu profonde au-dessus d'un fond non plat et les problèmes diphasiques. l'analyse de stabilité du schéma, dans le cas scalaire homogène, amène à une nouvelle écriture qui a une extension naturelle pour le cas non homogène. Des expériences numériques comparatives pour des équations de saint-Venant avec topographie variable, et un problème diphasique (Robinet de Ransom) sont présentés pour évaluer l'efficacité du schéma.

Mathematical and Numerical Study of an Industrial Scheme for Two-phase Flows in Porous Media under Gravity

2002 ◽  
Vol 2 (4) ◽  
pp. 325-353 ◽  
Author(s):  
G. Enchéry ◽  
R. Masson ◽  
S. Wolf ◽  
R. Eymard
Keyword(s):  
Existence Of Solutions ◽  
Numerical Study ◽  
Multidimensional Space ◽  
Finite Volume Scheme ◽  
Two Phase ◽  
Numerical Tests ◽  
Discrete Equations ◽  
The Stability ◽  
Industrial Scheme ◽  
Convergence Of The Scheme

AbstractIn this paper, we consider a dead-oil model where the capillary pressure is neglected. In a multidimensional space and for a phase-by-phase upstream weigthing cell-centered finite volume scheme, we prove the pressure estimates, the existence of solutions to the discrete equations and the stability of the saturation calculation. This is done in the explicit case as well as in the implicit case. Some numerical tests show the convergence of the scheme.

The influence of the Stokes and Archimedes forces on the stability of a two-phase flow

2003 ◽  
Vol 3 ◽  
pp. 266-270
Author(s):  
B.H. Khudjuyerov ◽  
I.A. Chuliev
Keyword(s):  
Spectral Method ◽  
Stability Region ◽  
Gas Flow ◽  
Two Phase Flow ◽  
Solid Phase ◽  
Stability Characteristic ◽  
Phase Flow ◽  
Two Phase ◽  
The Stability

The problem of the stability of a two-phase flow is considered. The solution of the stability equations is performed by the spectral method using polynomials of Chebyshev. A decrease in the stability region gas flow with the addition of particles of the solid phase. The analysis influence on the stability characteristic of Stokes and Archimedes forces.

scholarly journals Clinical Application and Efficacy of Silver Drug in Ophthalmology: A Literature Review and New Formulation of EYE Drops with Drug Silver (I) Complex of Metronidazole with Improved Dosage Form

Biomedicines ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 210
Author(s):  
Arleta Waszczykowska ◽  
Dominik Żyro ◽  
Justyn Ochocki ◽  
Piotr Jurowski
Keyword(s):  
Dosage Form ◽  
Complex Analysis ◽  
Bacterial Resistance ◽  
Eye Drops ◽  
Ophthalmic Diseases ◽  
The Stability ◽  
New Formulation ◽  
Additional Therapy ◽  
Antibacterial Potential

The use of silver preparations in medicine is becoming increasingly popular. The basic aim of this evaluation was to review the literature on the clinical (in vivo) and antibacterial potential of silver preparations in ophthalmic diseases. The second goal was to summarize the results of experimental research on the use of silver preparations in ophthalmology. The third objective was to present a method for stabilizing eye drops containing silver (I) complex. Analysis of the pH stability of the silver (I) complex with metronidazole in the prepared dosage form (eye drops) was carried out. Most silver preparations are clinically used for topical application. Few experimental results indicate the usefulness of intraocular or systemic administration of silver (I) preparations as an alternative or additional therapy in infectious and angiogenic eye diseases. The development of a new formulation increases the stability of the dosage form. New forms of silver (I) products will certainly find application in the treatment of many ophthalmic diseases. One of the most important features of the silver (I) complex is its capacity to break down bacterial resistance. The new eye drops formula can significantly improve comfort of use. Due to their chemical nature, silver (I) compounds are difficult to stabilize, especially in the finished dosage form.

scholarly journals A relaxation scheme for a hyperbolic multiphase flow model

2019 ◽  
Vol 53 (5) ◽  
pp. 1763-1795 ◽  
Author(s):  
Khaled Saleh
Keyword(s):  
Multiphase Flow ◽  
Flow Model ◽  
Two Phase Flow ◽  
Equations Of State ◽  
Energy Inequality ◽  
Approximation Error ◽  
Finite Volume Scheme ◽  
Phase Flow ◽  
Two Phase ◽  
Relaxation Scheme

This article is the first of two in which we develop a relaxation finite volume scheme for the convective part of the multiphase flow models introduced in the series of papers (Hérard, C.R. Math. 354 (2016) 954–959; Hérard, Math. Comput. Modell. 45 (2007) 732–755; Boukili and Hérard, ESAIM: M2AN 53 (2019) 1031–1059). In the present article we focus on barotropic flows where in each phase the pressure is a given function of the density. The case of general equations of state will be the purpose of the second article. We show how it is possible to extend the relaxation scheme designed in Coquel et al. (ESAIM: M2AN 48 (2013) 165–206) for the barotropic Baer–Nunziato two phase flow model to the multiphase flow model with N – where N is arbitrarily large – phases. The obtained scheme inherits the main properties of the relaxation scheme designed for the Baer–Nunziato two phase flow model. It applies to general barotropic equations of state. It is able to cope with arbitrarily small values of the statistical phase fractions. The approximated phase fractions and phase densities are proven to remain positive and a fully discrete energy inequality is also proven under a classical CFL condition. For N = 3, the relaxation scheme is compared with Rusanov’s scheme, which is the only numerical scheme presently available for the three phase flow model (see Boukili and Hérard, ESAIM: M2AN 53 (2019) 1031–1059). For the same level of refinement, the relaxation scheme is shown to be much more accurate than Rusanov’s scheme, and for a given level of approximation error, the relaxation scheme is shown to perform much better in terms of computational cost than Rusanov’s scheme. Moreover, contrary to Rusanov’s scheme which develops strong oscillations when approximating vanishing phase solutions, the numerical results show that the relaxation scheme remains stable in such regimes.

scholarly journals Variation principle in calculating the flow of a two-phase mixture in the pipes of the cooling systems in high-rise buildings

2018 ◽  
Vol 33 ◽  
pp. 02063 ◽  
Author(s):  
Andrey Aksenov ◽  
Anna Malysheva
Keyword(s):  
Channel Cross Section ◽  
Variation Principle ◽  
Two Phase ◽  
Liquid Phases ◽  
Rate Of Increase ◽  
Annular Layer ◽  
Gas Liquid Flow ◽  
The Stability ◽  
Air Conditioning Systems ◽  
Physical Laws

The analytical solution of one of the urgent problems of modern hydromechanics and heat engineering about the distribution of gas and liquid phases along the channel cross-section, the thickness of the annular layer and their connection with the mass content of the gas phase in the gas-liquid flow is given in the paper.The analytical method is based on the fundamental laws of theoretical mechanics and thermophysics on the minimum of energy dissipation and the minimum rate of increase in the system entropy, which determine the stability of stationary states and processes. Obtained dependencies disclose the physical laws of the motion of two-phase media and can be used in hydraulic calculations during the design and operation of refrigeration and air conditioning systems.

scholarly journals A Well-balanced Finite Volume Scheme for Shallow Water Equations with Porosity: Application to Modelling Flow through Rigid Vegetation

2018 ◽  
Vol 40 ◽  
pp. 05032
Author(s):  
Minh H. Le ◽  
Virgile Dubos ◽  
Marina Oukacine ◽  
Nicole Goutal
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Simple Wave ◽  
Water Model ◽  
Strong Interactions ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Rigid Vegetation ◽  
Vertical Cylinders

Strong interactions exist between flow dynamics and vegetation in open-channel. Depth-averaged shallow water equations can be used for such a study. However, explicit representation of vegetation can lead to very high resolution of the mesh since the vegetation is often modelled as vertical cylinders. Our work aims to study the ability of a single porosity-based shallow water model for these applications. More attention on flux and source terms discretizations are required in order to archive the well-balancing and shock capturing properties. We present a new Godunov-type finite volume scheme based on a simple-wave approximation and compare it with some other methods in the literature. A first application with experimental data was performed.

scholarly journals AN EFFICIENT AND ROBUST GPGPU-BASED SHALLOW WATER MODEL

2020 ◽  
pp. 47
Author(s):  
Fatima-zahra Mihami ◽  
Volker Roeber
Keyword(s):  
Numerical Solution ◽  
Shallow Water ◽  
Computational Cost ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Water Model ◽  
Staggered Grid ◽  
Finite Volume Scheme ◽  
Flow Solver ◽  
Riemann Solvers

We present an efficient and robust numerical model for the solution of the Shallow Water Equations with the objective to develop the numerical foundation for an advanced free surface flow solver. The numerical solution is based on an explicit Finite Volume scheme on a staggered grid to ensure the conservation of mass and momentum across flow discontinuities and wet-dry transitions. This leads to an accurate numerical solution at low computational cost without the need for Riemann solvers. The efficiency of the lean numerical structure is further optimized through a CUDA-GPU implementation.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/xMnK_r7Tj1Q

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