Cattaneo-Vernotte bioheat transfer equation. Stability conditions of numerical algorithm based on the explicit scheme of the finite difference method

• Autorzy: Mochnacki B. , Tuzikiewicz W.

Identyfikatory

DOI

10.17512/jamcm.2016.4.15

• Języki publikacji: EN

Abstrakty

EN

The Cattaneo-Vernotte (CVE) equation is considered. This equation belongs to the group of hyperbolic PDE. Supplementing this equation by two additional terms corresponding to perfusion and metabolic heat sources one can apply the CVE as a mathematical model describing the heat transfer processes proceeding in domain of the soft tissue. Such an approach is recently often preferred substituting the classical Pennes model. At the stage of numerical computations the different numerical methods of the PDE solving can be used. In this paper the problems of stability conditions for the explicit scheme of the finite difference method (FDM) are discussed. The appropriate condition limiting the admissible time step have been found using the von Neumann analysis.

Słowa kluczowe

EN

bioheat transfer; Cattaneo-Vernotte equation; finite difference method; stability conditions of FDM explicit scheme

PL

przepływ biociepła; równanie Cattaneo-Vernotte; metoda różnic skończonych

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 4
• Strony: 137--144
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Mochnacki B.

• University of Occupational Safety Management in Katowice Katowice, Poland

autor

Tuzikiewicz W.

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

Bibliografia

• [1] Pennes H.H., Analysis of tissue and arterial blood temperatures in the resting human forearm, J. Appl. Physiol. 1948, 1, 93-122.
• [2] Majchrzak E., Mochnacki B., Jasinski M., Numerical modelling of bioheat transfer in multilayer skin tissue domain subjected to a flash fire, Computational Fluid and Solid Mechanics 2003, 1-2, 1766-1770.
• [3] Jasinski M., Modelling of tissue thermal injury process with application of direct sensitivity method, Journal of Theoretical and Applied Mechanics 2014, 52, 4, 947-957.
• [4] 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.
• [5] Cattaneo M.C., A form of heat conduction equation which eliminates the paradox of instantaneous propagation, C.R. Acad. Sci. I Math. 1958, 247, 431-433.
• [6] Roetzel W., Putra N., Das S.K., Experiment and analysis for non - Fourier conduction in materials with non-homogeneous inner structure, Int. J. Therm. Sci. 2003, 42, 541-552.
• [7] Antaki P.J., New interpretation of non-Fourier heat conduction in processed meat, ASME J. Heat Transfer 2005, 127, 189-193.
• [8] Mochnacki B., Suchy J.S., Numerical Methods in Computations of Foundry Processes, PFTA, Cracow 1995.
• [9] Tzou D.Y., Macro - to Microscale Heat Transfer: The Lagging Behavior, John Wiley & Sons, Ltd 2015.
• [10] Majchrzak E., Mochnacki B., Dual-phase-lag equation. Stability conditions of a numerical algorithm based on the explicit scheme of the finite difference method, Journal of Applied Mathematics and Computational Mechanics 2016, 15(3), 89-96.
• [11] Tuzikiewicz W., Duda M., Bioheat transfer equation. The problem of FDM explicit scheme stability, Journal of Applied Mathematics and Computational Mechanics 2015, 14(4), 139-144.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.