SIMULATION OF UNSTEADY TRANSPORT PHENOMENA USING NEW FINITE VOLUME METHOD

Arafat Hussain, Zahoor Iqbal, Khalid Abdulkhaliq M. Alharbi, N. Ameer Ahammad, Fahima Hajjej, Manasik M. Nour, Zakaria M. M. Mahmoud and Syed M. Eldin
Additional contact information
Arafat Hussain: Institute of Applied System Analysis, Jiangsu University, Zhenjiang, Jiangsu 212013, P. R. China
Zahoor Iqbal: College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China3Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan
Khalid Abdulkhaliq M. Alharbi: Mechanical Engineering Department, College of Engineering, Umm Al-Qura University, Makkah, Saudi Arabia
N. Ameer Ahammad: Department of Mathematics, Faculty of Science, University of Tabuk, P. O. Box 741, Tabuk 71491, Saudi Arabia
Fahima Hajjej: Department of Information Systems, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P. O. Box 84428, Riyadh 11671, Saudi Arabia
Manasik M. Nour: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Zakaria M. M. Mahmoud: Department of Physics, College of Sciences, King Khalid University, P. O. Box 9004, Abha, Saudi Arabia
Syed M. Eldin: Center of Research, Faculty of Engineering, Future University in Egypt, New Cairo 11835, Egypt

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-13

Abstract: Based on the finite volume method (FVM), a numerical scheme is constructed to simulate the unsteady convection–diffusion transport problem. New expressions are obtained for interface approximation of the field variable, subsequently, these newly obtained interface expressions are used to develop the numerical scheme. Convection-dominant and diffusion-dominant phenomena are simulated by taking different values of convective velocity (V ) and diffusion coefficient (k). This newly proposed numerical scheme gives second order of convergence along space and time. Experiments are carried out to test the new proposed upwind approach. Numerical results produced by the proposed approach are compared with the conventional finite volume method, step-wise approach FVM and quadratic upwind interpolation finite volume approach. This comparative study indicates that for different cases for convection-dominant and diffusion-dominant problems, our proposed approach gives highly accurate and stable solution. The conventional finite volume method and other approaches result solution with non-physical oscillations. Our obtained numerical results are consistent and support our theoretical approach.

Keywords: Finite Volume Method; Convection–Diffusion Problem; Convergence Order; Interface Approximation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400911

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