A monotonic weighted compact finite difference solution for a non-linear steady advection-diffusion equation

Chivapornthip, Prapol

doi:10.22034/cmde.2024.61722.2680

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	A monotonic weighted compact finite difference solution for a non-linear steady advection-diffusion equation
Computational Methods for Differential Equations
مقاله 3، دوره 14، شماره 2، تیر 2026، صفحه 549-566 اصل مقاله (1.41 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.61722.2680
نویسنده
Prapol Chivapornthip^*
Department of Industrial Engineering, Faculty of Engineering, Kasetsart University, Thailand.
چکیده
This paper introduces a monotonic weighted compact finite difference scheme (WC-FDM) designed to solve the nonlinear one-dimensional steady advection-diffusion equation (ADE). The WC-FDM scheme is validated against the analytical solution and is adaptable to accommodate both uniform and non-uniform grid spacing. Criteria for selecting weights have been developed to ensure scheme monotonicity. Computational performance is benchmarked against other numerical schemes. Numerical analyses reveal that the WC-FDM accurately solves the non-linear steady ADE for both uniform and non-uniform grid spacing scenarios without introducing spurious oscillations. The proposed weight criteria maintain the monotonicity of the WC-FDM scheme resulting the computational stability regardless of the advection dominance level and grid spacing uniformity.
کلیدواژه‌ها
Compact finite difference؛ Monotonic scheme؛ Advection-diffusion؛ Weighted finite difference

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A monotonic weighted compact finite difference solution for a non-linear steady advection-diffusion equation