APPLICATION OF TVD SCHEMES TO NUMERICAL MODELING OF FRONTAL SALINITY ZONES IN A SHALLOW SEA

V. V. Fomin

Characteristics of TVD (Total Variation Diminishing) schemes [7] are studied to approximate advective operators in numerical modeling problems of frontal salinity zones in a shallow sea. The most commonly used TVD schemes are compared by the example of a two-dimensional problem with discontinuities in the initial data. The problem on the instability of a freshwater lens and the problem on the formation of the alongshore salinity by river runoff are considered within the framework of a three-dimensional hydrodynamic model [3]. Based on comparative analysis, it is shown that TVD schemes provide a more realistic description of frontal zones than monotonic first-order approximation schemes. The TVD schemes yield the best results in calculating both the salinity advection and the velocity advection.