Model Numerik Transportasi Polutan 2-D di Teluk Balikpapan Menggunakan Skema Beda Hingga Dufort-Frankel

Abstract

Pollutant transport in coastal waters, such as Balikpapan Bay, is a complex phenomenon influenced by advection and diffusion mechanisms. Mathematical modeling using the two-dimensional (2-D) advection-diffusion equation is a primary approach; however, analytical solutions are very limited, necessitating accurate and stable numerical methods. This study aims to implement an explicit finite difference method using the Dufort-Frankel scheme to solve the 2-D advection-diffusion equation for modeling pollutant dispersion in Balikpapan Bay. The Dufort-Frankel scheme was chosen because it offers better numerical stability compared to conventional explicit schemes such as Forward-Time Central-Space (FTCS) and does not require matrix inversion like implicit schemes. Simulations were conducted on a two-dimensional square domain of size 1×1 unit with a 51×51 grid, using a centered Gaussian distribution as the initial condition and homogeneous Dirichlet (zero) boundary conditions on all domain edges. The physical parameters used were advection velocities vₓ = 0.1 m/s, vᵧ = 0.05 m/s, and diffusion coefficient D = 0.01 m²/s, with a time step Δt = 0.001 seconds over a total simulation time of 0.05 seconds (50 iterations). The simulation results show that the pollutant spreads progressively from the initial distribution center throughout the domain, with the dominant direction toward the northeast following the advection velocity vector. The maximum pollutant concentration decreases exponentially over time, while the center of mass moves away from the initial point. No numerical oscillations or instability were observed during the simulation period. The Dufort-Frankel scheme proves to be effective, numerically stable, and computationally efficient for modeling pollutant transport in tropical open waters such as Balikpapan Bay