Advection scheme with 3rd high-order spatial interpolation at the middle temporal level and its application to saltwater intrusion in the Changjiang Estuary

A non-oscillatory advection scheme with 3rd high-order spatial interpolation at the middle temporal level coupled with a TVD limiter (the 3rd HSIMT-TVD scheme) was developed with the following features: (1) It uses a parabola to characterize a substance's local distribution at nΔ t; (2) it determines the cell interface value at (n+0.5)Δ t by one-step backward tracing to its position at nΔ t; and (3) it uses Sweby's TVD limiter to constrain the derived cell interface value to eliminate numerical oscillation. The 3rd HSIMT-TVD scheme was derived based on Sweby's original TVD formula directly, thus the symmetric assumption of a TVD limiter is not necessary. 1D/2D tests suggest that the present scheme performs quite robustly compared to some other well-established schemes. The wavenumber two freshwater eddy instability has been successfully simulated using the present scheme.The derived model was then used to simulate the saltwater intrusion into the Changjiang Estuary, and the in situ data collected in February 2003 and February-March 2007 were used for validation. The model results were quite close to the measured data, and the main features of saltwater intrusion, such as saltwater spilling over from the North Branch, the salt wedge, and the stratification introduced by the wedge-like saltwater intrusion and the plume-like extension of diluted water, were simulated correctly. Furthermore, some other schemes were also used for comparison, and their differences are discussed.