Numerical Simulation of Tidal Hydrodynamics in the Mahakam Estuary using MacCormack and Lax-Wendroff Schemes

Hadi Hermansyah (Balikpapan State Polytechnic, Balikpapan, 76129, Indonesia)
Emil Azmanajaya (Balikpapan State Polytechnic, Balikpapan, 76129, Indonesia)
Indriasri Raming (Mathematics Department, Mulawarman University, Samarinda, 75119, Indonesia)
Faisal Faisal (Mathematics Department, Lambung Mangkurat University, Banjarbaru, 70714, Indonesia)
Fahruddin Fahruddin (Geophysics Department, HasanuddinUniversity, Makassar, 90245, Indonesia)

Zero : Jurnal Sains, Matematika, dan Terapan
Vol 10, No 2 (2026): Zero: Jurnal Sains Matematika dan Terapan

Tidal hydrodynamics in the Mahakam Estuary are influenced by intricate tidal propagation and river–estuary interactions, necessitating precise numerical modeling. This research analyzed the MacCormack and Lax–Wendroff methods for addressing the one-dimensional Saint–Venant equations influenced by semi-diurnal tides, with an average depth of 10 m and a river flow rate of 3000 m³/s. Simulations were performed with uniform discretization under chosen CFL conditions and confirmed against analytical tidal propagation traits using RMSE, MAE, correlation coefficient, and wave amplitude retention. Both models effectively replicated flood–ebb cycles and tidal damping with similar precision. The MacCormack scheme generated more refined solutions with reduced numerical oscillations, while the Lax–Wendroff scheme maintained sharper gradients but exhibited slight dispersive errors. In general, both methods proved to be dependable and numerically consistent for tidal simulations in the Mahakam Estuary.