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In this paper, we construct a robust adaptive central-upwind scheme onunstructured triangular grids for two-dimensional shallow water equations withvariable density. The method is well-balanced, positivity-preserving, andoscillation-free at the curve where two types of fluid merge. The proposedapproach is an extension of the adaptive well-balanced, positivity-preservingscheme developed in Epshteyn and Nguyen (arXiv preprint arXiv:2011.06143,2020). In particular, to preserve "lake-at-rest" steady states, we utilize theRiemann Solver with appropriately rotated coordinates to obtain the pointvalues in the neighborhood of the fluid interface. In addition, to improve theefficiency of an adaptive method in the multifluid flow, the curve of densitydiscontinuity is reconstructed by using the level set method and volumefraction method. To demonstrate the accuracy, high resolution, and efficiencyof the new adaptive central-upwind scheme, several challenging tests forShallow water models with variable density are performed.

Adaptive Central-Upwind Scheme on Triangular Grids for the Shallow Water Model with variable density