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1

A note on the regularity of weak solutions to the coupled 2D Allen-Cahn-Navier-Stokes system

Medjo T. Tachim

Journal of Applied Analysis

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2019

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Vol. 25, nr 1

111--117

EN

In this article,we study a coupled Allen-Cahn-Navier-Stokes model in a two-dimensional domain. The model consists of the Navier-Stokes equations for the velocity, coupled with an Allen-Cahn model for the order (phase) parameter.We present an equivalent weak formulation for the model, and we prove a new regularity result for the weak solutions.

2

Numerical Calculations of the Cast Solidification with the Complex Shape Including the Movement of the Liquid Phase

Gawrońska E., Dyja R.

Archives of Foundry Engineering

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2018

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Vol. 18, iss. 3

65--70

EN

The paper presents the results of the computer simulations of solidification with consideration of the liquid phase movement. Simulations were conducted in a real, complex cast. There is a multi-stage resolution to the problem of convection in solidification simulations. The most important resolution concerns the development of the numerical model with the momentum and continuity equations, as well as conditions which are determined by the convection. Simulations were carried out with the use of our authorial software based on stabilized finite elements method (Petroy-Galerkin). In order to solve Navier-Stokes equation (with the convection element), Boussinesq’s approximation were used. Finite Elements Method (FEM) was responsible for the solidification. FEM is close to the heat conduction equation solution (with the internal heat source responsible for the heat released during phase transformation). Convection causes movement in the liquid phase in the solidifying cast and can significantly influence the process of heat transfer from the cast. It may change the distribution of the defects. Results of this article make it possible to assess the conditions in which the influence of the convection on solidification is significant.

3

Numeryczna ocena cząstkowej rezerwy przepływu wieńcowego (FFR)

Mirota K., Wasilewski J., Poloński L.

Inżynieria i Aparatura Chemiczna

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2014

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Nr 5

355--356

PL

Istnieje duża zgodność między zmierzoną wartością cząstkowej rezerwy przepływu wieńcowego (FFR) a stopniem istotności hemodynamicznej zmiany miażdżycowej. Poważnym ograniczeniem w upowszechnieniu zastosowań diagnostycznych FFR jest konieczność inwazyjnego pomiaru ciśnień. W niniejszej pracy przedstawiono alternatywną metodykę bazującą na numerycznych obliczeniach przepływu wieńcowego. Omówiono aspekty związane z segmentacją tętnic wieńcowych oraz wpływu właściwości reologicznych krwi na symulacje numeryczne.

EN

There is a good agreement between the invasive measurements of fractional flow reserve (FFR) and hemodynamic significance of the coronary artery stenosis. A major limitation of widespread applications of FFR is its invasive nature. In this paper authors present the methodology of non-invasive numerical FFR calculation. Some issues concerning the coronary artery segmentation and the influence of blood rheological properties on FFR simulation results are discussed.

4

Foundations of the Navier-Stokes boundary conditions in fluid mechanics

Badur J., Karcz M., Lemański M., Nastałek L.

Transactions of the Institute of Fluid-Flow Machinery

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2011

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nr 123

3-55

EN

Until recently it was believed that Navier’s boundary condition could be given as a rigorous foundation for slip phenomena. Due to the latest measurements in the mass flow rate of a gas flowing through nano- and microchannels, several discrepancies in the mathematical modelling have been found. Thus, in the literature, the opinion persists for the Navier slip condition to be correct only under certain circumstances, particularly those restricted to the first order boundary conditions. One of many ways to eliminate this discrepancy, which is extensively employed in the contemporary literature, is to develop a variety of the so-called second order boundary conditions. This path, however, seems incorrect since it lacks consistency between the bulk stress tensor and its boundary representation. In the paper we propose to replace the classical Navier slip condition with the new, more general Navier-Stokes slip boundary condition. Instead of the usual method of consideration, the boundary condition is presented as following from the mass and momentum balances within a thin, shell-like moving layer. Owing to this, the problem of consistency between the internal and external friction in a viscous fluid is solved within the framework of new layer balances, and a proper form of constitutive relations for friction and mobility forces. Finally, the common features of the Navier, Stokes, Maxwell and Reynolds concepts of a boundary slip layer are compared and revalorized. The classifications of different mobility mechanisms, important for flows in nano-, microchannels are also discussed.

5

Shape derivatives for general objective functions and the incompressible Navier-Stokes equations

Schmidt S., Schulz V.

Control and Cybernetics

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2010

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Vol. 39, no 3

677-713

EN

The aim of this paper is to present the shape derivative for a wide array of objective functions using the incompressible Navier-Stokes equations as a state constraint. Most real world applications of computational fluid dynamics are shape optimization problems in nature, yet special shape optimization techniques are seldom used outside the field of elliptic partial differential equations and linear elasticity. This article tries to be self contained, also presenting many useful results from the literature. We conclude with a comparison of different objective functions for the shape optimization of an obstacle in a channel, which can be done quite conveniently when one knows the general form of the shape gradient.

6

High-lift behaviour of half-models at flight reynolds numbers

Szulc O., Doerffer P.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2006

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Vol. 10, No 2

191-206

EN

A peniche is designed to offset a half-span aircraft model from the wind tunnel wall boundary layer. This strategy of model mounting results in large influence on the meas-ured aerodynamic coefficients, compared with full-span data, The negative influence is especially important in high-lift conditions leading to incorrect maximum lift behaviour, A very time-consuming set of python scripts was constructed to allow automatic meshing of the wing-body configuration of the DLR F11 high-lift model placed in the European Transonic Wind tunnel (ETW, Germany). Variations due to different concepts of model mountings (peniches) were included. A block-structured FLOWer solver (DLR, Germany) was used for all flow simulations, simplifying the mesh generation process by using the chimera overlapping grids technique, Preliminary results are available for a full-span configuration obtained with a symmetry condition at the mirror plane. Computations of the half-span model placed directly at the wall or mounted using a standard peniche are also presented.

7

Numerical resolution of incompressible navier-stokes equations in the stream function formulation

Kosma Z.

Inżynieria Chemiczna i Procesowa

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2006

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T. 27, z. 3/1

737-760

EN

The method of lines is applied to simulate the motion of viscous incompressible fluid in a driven cavity and around an aerofoil at a large angle of attack. The numerical algorithms are based on the solution of an initial-boundary value problem for the full incompressible Navier-Stokes equations in the form of the fourth order equation for the stream function. Calculations for the cavity flow configuration have been obtained for Reynolds numbers ranging from 5000 to 30 000 on the non-uniform grids 100x100 and a uniform grid 150x150. Computations for the flow around the aerofoil have been performed at Reynolds numbers Re = or < 1000.

PL

Przedstawiono algorytmy numeryczne do symulacji płaskiego, niestacjonarnego ruchu cieczy lepkiej. Do rozwiązywania równań Naviera-Stokesa zastosowano metodę prostych, polegającą na sprowadzaniu zagadnień początkowo-brzegowych dla równania czwartego rzędu dla funkcji prądu do zagadnień początkowych dla układów równań różniczkowych zwyczajnych. Wykonano symulację ruchu cieczy lepkiej w kwadratowym zagłębieniu z jedną poruszającą się ścianką dla liczby Reynoldsa w zakresie 5000-30 000 na siatkach: nierównomiernej 100x100 i równomiernej 150x150 oraz symulację opływu profilu lotniczego nachylonego pod dużym kątem natarcia do napływającego strumienia w nieskończoności dla Re = lub < 1000.