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1
Content available remote Solution of energy equation using the interval boundary element method
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EN
In the paper the 1D energy equation with an interval source function is considered. For this type of equation the 1st scheme of the interval boundary element method is presented. As an example the pure metal crystallization process is analyzed. In the final part of the paper the results of numerical computations for the cooper crystallization process with the interval source function are shown.
2
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EN
In the paper, the description of an unsteady heat transfer for a two-dimensional problem is presented. It is assumed that all the thermophysical parameters appearing in the mathematical model of the problem analyzed are given as fuzzy numbers. The problem discussed has been solved by means of the 1st scheme of the fuzzy boundary element method using α-cuts. The application of α-cuts allows one to avoid complicated arithmetical operations in the fuzzy numbers set. The interval Gauss elimination method with the decomposition procedure has been applied to solve the obtained fuzzy system of equations. In the final part of the paper, the results of numerical computations are shown.
3
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EN
In this paper an application of the interval boundary element method for solving problems with interval thermal parameters and interval source function in a system casting-mould is presented. The task is treated as a boundary-initial problem in which the crystallization model proposed by Mehl-Johnson-Avrami-Kolmogorov has been applied. The numerical solution of the problem discussed has been obtained on the basis of the interval boundary element method (IBEM). The interval Gauss elimination method with the decomposition procedure has been applied to solve the obtained interval system of equations. In the final part of the paper, results of numerical computations are shown.
4
Content available remote Solution of 2D transient diffusion problem with interval source function
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EN
In this paper an application of the interval boundary element method for solving 2D problems with interval heat source is presented. The numerical solution of the problem discussed has been obtained on the basis of the 1st scheme of the interval boundary element method. In the final part of the paper, results of numerical computations are shown.
EN
In the paper the two-dimensional numerical modelling of heat transfer in crystalline solids is considered. In the mathematical description the relaxation time and the boundary conditions are given as interval numbers. The problem formulated has been solved by means of the interval lattice Boltzmann method using the rules of directed interval arithmetic.
PL
W artykule zaprezentowano dwuwymiarowy model numeryczny przepływu ciepła w ciele krystalicznym. W opisie matematycznym czas relaksacji i warunki brzegowe są zdefiniowane jako liczby przedziałowe. Sformułowane zagadnienie rozwiązano za pomocą interwałowej metody siatek Boltzmanna stosując skierowaną arytmetykę interwałową.
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Content available remote Modelowanie zadań z ostrym frontem krzepnięcia z wykorzystaniem II schematu MEB
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PL
W pracy przedstawiono sposób modelowania procesu krzepnięcia zachodzącego w stałej temperaturze (problem Stefana), przy czym rozpatrywano zadanie 1D. Wykorzystano II schemat metody elementów brzegowych. Omówiono algorytm rozwiązania oraz pokazano przykład obliczeń numerycznych.
EN
The numerical model of 1D Stefan problem is solved using the 2nd scheme of the BEM. The theoretical background and also the example of numerical simulation are presented.
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