فهرست نشریات علمی دسترسی آزاد ایران

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.