Wyniki wyszukiwania - BazTech

1

Solving the dual-phase lag bioheat transfer equation by the generalized finite difference method

Turchan Ł.

Archives of Mechanics

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2017

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Vol. 69, nr 4-5

389--407

EN

The modeling of bioheat transfer process described by the dual-phase lag equation is considered. The basic equation is supplemented by the appropriate boundary-initial conditions. In the central part of the cylindrical domain the heated sub-domain is located. In this region the additional component determining the capacity of an internal heat source is taken into account. At the stage of numerical computations the generalized finite difference method (GFDM) is used. The GFDM nodes distribution is generated in a random way (with some limitations). The examples of computations for different nodes distribution and comparison with the classical finite difference method are presented. In the final part of the paper the conclusions are formulated.

2

Model hartowania elementu osiowo-symetrycznego z uwzględnieniem ruchów chłodziwa

Kulawik A.

Modelowanie Inżynierskie

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2011

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T. 10, nr 41

213-220

PL

W pracy zaproponowano model matematyczny oraz numeryczny procesu chłodzenia zbudowany z wykorzystaniem uogólnionej metody różnic skończonych. Ruchy chłodziwa, zarówno konwekcyjne jak i wymuszone, zamodelowano, rozwiązując równanie Naviera-Stokesa metodą rzutowania. Rozwiązanie równania przewodzenia ciepła z członem konwekcyjnym uzyskano na podstawie stabilizowanej bezsiatkowej metody różnic skończonych. Do wyznaczenia udziałów przemian fazowych zastosowano makroskopowy model bazujący na analizie wykresów CTPc.

EN

In the paper a mathematical and numerical model for the cooling processes built on the basis of the generalized finite difference method have been proposed. The movements of the coolant, both convective and forced, have been solved using the Navier-Stokes equation with the characteristic based split scheme (CBS). The solution of the heat transport equation with the convective term has been obtained by a stabilized meshless finite difference method. In the paper the macroscopic model of the phase transformations based on an analysis of CCT diagrams has been presented.

3

Numerical solution of heat diffusion equation using the generalized FDM

Lara-Dziembek S., Pawlak E.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2007

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Vol. 6, nr 1

117-125

EN

In the paper the numerical solution of boundary-initial problem described by the Fourier equation and adequate conditions is discussed. The algorithm bases on the concept of generalized finite difference method (GFDM). In the first part the mathematical formulation of the problem and a short description of GFDM algorithm are presented. In the second part the examples of numerical computations are shown. On the stage of computation the explicit version of GFDM is used.

4

Application of generalized finite difference method in numerical modelling of moving boundary problems

Mochnacki B., Lara S.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2003

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Vol. 2, nr 1

129--143

EN

The application of generalized finite difference method for numerical modelling of thermal processes proceeding in the solidifying casting domain is presented. The solidification of pure metals and eutectic alloys is considered. In such case the solidification process takes place at the constant temperature (the Stefan problem). From the numerical point of view the solution of this task is very complex; in particular, in the case of 2D or 3D domains; and in literature one can find the procedures enabling to avoid the difficulties with the direct modelling of the problem discussed. The part of them consist in the substitution of the solidification point T* by the certain interval [T* - ΔT, T* + ΔT]. In this way the subdomain of artificial mushy zone is introduced and the fixed domain approach [1] can be used. On the stage of numerical algorithm construction and numerical simulation the generalized finite difference method is used. In the final part of the paper the examples of computations are shown.