Bioheat transfer equation : the problem of FDM explicit scheme stability

• Autorzy: Tuzikiewicz W. , Duda M.

Identyfikatory

DOI

10.17512/jamcm.2015.4.14

• Języki publikacji: EN

Abstrakty

EN

In the paper the problem of explicit FDM scheme stability for the bio-heat transfer equation (the Pennes equation) is discussed. To formulate the appropriate condition the von Neumann approach is applied. The first chapter contains the known derivation of FDM stability condition for the Fourier equation. In the second part, a similar condition is found for the case of the bio-heat transfer equation containing both the perfusion and metabolic heat sources.

Słowa kluczowe

EN

bio-heat transfer; finite difference method; stability condition; von Neumann method

PL

wymiana biociepła; metoda różnic skończonych; stan stateczności

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2015
• Tom: Vol. 14, nr 4
• Strony: 139--144
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Tuzikiewicz W.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

autor

Duda M.

• University of Occupational Safety Management in Katowice Katowice, Poland

Bibliografia

• [1] Tzou D.Y., Macro- to Microscale Heat Transfer: The Lagging Behavior, John Wiley & Sons Ltd., 2015.
• [2] Anderson J.D., Computational Fluid Dynamics. The Basics with Applications, McGraw Hill, 1994.
• [3] Mochnacki B., Suchy J.S., Numerical Methods in Computations of Foundry Processes, PFTA, Cracow 1995.
• [4] Mochnacki B., Majchrzak E., Duda M., Numerical modeling of thermal processes in the living tissue domain secured with a layer of protective clothing, Journal of Applied Mathematics and Computational Mechanics 2014, 13, 1, 97-102.
• [5] Mochnacki B., Majchrzak E., Duda M., Simplified model of thermal interactions between environment, protective clothing and skin tissue, Journal of Applied Mathematics and Computational Mechanics 2014, 13, 4, 93-96.
• [6] Ciesielski M., Mochnacki B., Application of the control volume method using the Voronoi polygons for numerical modeling of bio-heat transfer processes, Journal of Theoretical and Applied Mechanics 2014, 52, 4, 927-935.