Wyniki wyszukiwania - BazTech

1

Simulation of Sea-ice Thermodynamics by a Smoothed Particle Hydrodynamics Method

Staroszczyk R.

Archives of Hydro-Engineering and Environmental Mechanics

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2018

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Vol. 65, nr 4

277--299

EN

The paper deals with the problem of sea-ice pack motion and deformation under the action of wind and water drag forces. Differential equations describing the behaviour of ice, with its very distinct material responses in converging and diverging flows, express the mass and linear momentum balances on a horizontal plane (the free surface of the ocean). The thermodynamic effects (ice melting and lead water freezing) are accounted for by adding source terms to the equations describing the evolution of the ice thickness and area fraction (concentration). These thermodynamic source terms are described by means of a single function that idealizes typical ice growth-rates observed in winter in the Arctic. The equations governing the problem are solved by a fully Lagrangian method of the smoothed particle hydrodynamics (SPH). Assuming that the ice behaviour can be approximated by a non-linearly viscous rheology, the proposed SPH model was used to simulate the flow of a sea-ice pack driven by wind drag stresses and varying seasonal temperatures. The results of numerical simulations illustrate the evolution of an ice pack, including distributions of ice thickness and ice area fraction in space and time for assumed temperature distributions.

2

SPH Modelling of Sea-ice Pack Dynamics

Staroszczyk R.

Archives of Hydro-Engineering and Environmental Mechanics

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2017

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Vol. 64, nr 2

115--137

EN

The paper is concerned with the problem of sea-ice pack motion and deformation under the action of wind and water currents. Differential equations describing the dynamics of ice, with its very distinct mateFfigrial responses in converging and diverging flows, express the mass and linear momentum balances on the horizontal plane (the free surface of the ocean). These equations are solved by the fully Lagrangian method of smoothed particle hydrodynamics (SPH). Assuming that the ice behaviour can be approximated by a non-linearly viscous rheology, the proposed SPH model has been used to simulate the evolution of a sea-ice pack driven by wind drag stresses. The results of numerical simulations illustrate the evolution of an ice pack, including variations in ice thickness and ice area fraction in space and time. The effects of different initial ice pack configurations and of different conditions assumed at the coast–ice interface are examined. In particular, the SPH model is applied to a pack flow driven by a vortex wind to demonstrate how well the Lagrangian formulation can capture large deformations and displacements of sea ice.

3

Computer implementation of mass transport in Matlab environment for modeling Epitaxial growth process with moving boundary problem

Gulkowski S.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2015

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Vol. 19, No 1

15--23

EN

Due to the possibility of producing high quality and low cost silicon substrates the Epitaxial Lateral Overgrowth technology may find its application in the photovoltaic industry. However, a lateral growth process depends on many technological parameters such as the temperature of the system, the cooling rate, the solvent or the geometry of the mask. For this reason finding optimized settings for these factors in experimental research is difficult and time consuming. Numerical analysis of the growth process leads to better understanding of the fundamentals of the growth process. For this reason a computational model of epitaxial growth was proposed. This paper focuses on the accuracy of the numerical solution of the mass transport process during epitaxial growth. The method was implemented in the Matlab environment for the moving boundary application. The results of the calculations are presented.

4

Problem of the moving boundary in continuous casting solved by the analytic-numerical method

Grzymkowski R., Pleszczyński M., Hetmaniok E.

Archives of Foundry Engineering

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2013

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Vol. 13, iss. 1

33--38

EN

Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase – liquid phase leads to formulation of the parabolic or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use some sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, applied for finding the approximate solutions of the selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.

5

Application of the analytic - numerical method in solving the problem with moving boundary

Hetmaniok E., Pleszczyński M.

Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska

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2012

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z. 2

57--74

EN

The paper presents a method of the analytic-numerical nature applied for finding the approximate solutions of the selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Presented method is attractive from the engineer’s point of view since it is relatively easy for using and does not require either sophisticated numerical techniques or far advanced mathematical tools.

PL

W pracy przedstawiono metodę o analityczno–numerycznym charakterze zastosowaną do przybliżonego rozwiązywania wybranej klasy problemów, które można sprowadzić do jednofazowego zagadnienia krzepnięcia płyty z nieznaną a priori, zmienną w czasie granicą obszaru, w którym poszukiwane jest rozwiązanie. Prezentowana metoda jest atrakcyjna z inżynierskiego punktu widzenia, gdyż jest stosunkowo łatwa w użyciu i nie wymaga stosowania wyszukanych technik numerycznych ani zaawansowanych narzędzi matematycznych.

6

Analytic-numerical method of determining the freezing front location

Grzymkowski R., Hetmaniok E., Pleszczyński M.

Archives of Foundry Engineering

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2011

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Vol. 11, iss. 3 spec.

75--80

EN

Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase – liquid phase leads to formulation of the parabolic boundary problems with the moving boundary. Solution of such defined problem requires, most often, to use sophisticated numerical techniques and far advanced mathematical tools. Excellent illustration of the complexity of considered problems, as well as of the variety of approaches used for finding their solutions, gives the papers [1-4]. In the current paper, the authors present the, especially attractive from the engineer point of view, analytic-numerical method for finding the approximate solution of selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of the sought function describing the temperature field into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of the function defining the location of freezing front with the broken line, parameters of which are numerically determined.

7

Solution of the solidification problem by using the variational iteration method

Hetmaniok E., Słota D., Zielonka A.

Archives of Foundry Engineering

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2009

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Vol. 9, iss. 4

63-68

EN

The paper presents the approximated solution of the solidification problem, modelled with the aid of the one-phase Stefan problem with the boundary condition of the second kind, by using the variational iteration method. For solving this problem one needs to determine the distribution of temperature in the given domain and the position of the moving interface. The proposed method of solution consists of describing the considered problem with a system of differential equations in a domain with known boundary, and solving the received system with the aid of VIM method. The accuracy of the obtained approximated solution is verified by comparing it with the analytical solution.