Mathematical Modeling of Multiphase Mixture Inflow into a Stratified Reservoir and the Breakdown of the Layered Structure
DOI:
https://doi.org/10.71310/pcam.3_73.2026.01Keywords:
stratified reservoir, multiphase flow, Rakhmatulin model, phase separation, plunging, Richardson number, Kelvin–Helmholtz instability, operator splitting, re-erosion, Garcia–Parker formulaAbstract
A three-dimensional mathematical model is proposed for the inflow of a turbid (sediment-laden) river flow into a density-stratified reservoir, accounting for phase separation and the breakdown of the layered structure. The model is based on Kh.A. Rakhmatulin’s theory of interpenetrating continua: the carrier fluid and the dispersed particles each have their own velocity field, and the interphase drag represents particle settling. The vertical mixing coefficient depends on the local Richardson number, capturing stratification breakdown through Kelvin–Helmholtz instability; re-erosion near the bed is modeled by the Garcia–Parker formula. The problem is solved on a Harlow–Welch staggered grid by a five-stage operator-splitting scheme. A simulation of the subcritical plunging regime reproduces the inflow plume, the plunge point, the bottom underflow, and the intrusion layer, and is verified against classical criteria and mass balance.
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