A Numerical Solution by Finite Volume Method to Solving Three-Dimensional System

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DOI: https://doi.org/10.28924/2291-8639-24-2026-81
Published: Mar 19, 2026
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Badran Jasim Salim, A Numerical Solution by Finite Volume Method to Solving Three-Dimensional System, Int. J. Anal. Appl., 24 (2026), 81.

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Badran Jasim Salim

Abstract

A 3D system of partial differential equation was studied about heat propagation on the vascular tissue along time. The system was numerically solved by using Finite Volume Method (FVM). In the case of a specific numerical cube method, the governing equations were integrated through control volume. Forward and central differences were subsequently used to discretize the time (∂t) and spatial derivatives (∂x). All aforementioned numerical scheme was implemented in MATLAB. The method was validated by selecting a time step within the discovered stability limits. We applied this to a reference problem with known initial and boundary conditions. When the numerical solution was used, it showed great agreement with the exact analytical solution, and the final volumetric solution was almost identical to both solutions, the very small error values ​​shown in the table and figures highlight this excellent accuracy. It was determined that the FVM represents a sound and effective method for solution of this type heat diffusion problem. The results show that as long as numerical stability is not affected, smaller lattice spacing can lead to higher accuracy.

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