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In this paper, we present a second-order, time- and space-accurate method for solving conservative transport equation in two-dimensional domains. The spatial discretization is based on a finite volume approach using triangular cells of arbitrary shape. A θ-method is employed for the time integration. A second-order upwind scheme with a Local Extremum Diminishing flux limiter formulation is proposed to approximate the advective terms. The numerical method is validated against classical advection test cases, including different characteristic functions and type of grids. Finally, several tests are conducted to demonstrate the capabilities of the proposed scheme.
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Balam et al. (2025) studied this question.
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