Various authors have developed finite volume methods for hyperbolic conservation laws, including the classical Godunov and HLL Riemann solvers. This work aims to expand central-upwind methods to triangular meshes, specifically addressing the transport equation with a heterogeneous storage coefficient. The foundation of central and central-upwind schemes was established by Kurganov and Tadmor, followed by Kurganov, Noelle, and Petrova, and Kurganov and Petrova. While Correa and Borges successfully extended the central method for heterogeneous storage coefficients on quadrilateral meshes, and Correa and Murad recently introduced a central-upwind version for the Black-Oil problem, a general formulation for triangular grids remains an open challenge. To date, such methods exist primarily for quadrilateral meshes or for triangles with unitary storage coefficients. Our work focuses on developing a new method for modeling flow problems in porous media by defining a general high-order central-upwind scheme that incorporates heterogeneous storage coefficients on unstructured triangular meshes. To validate the proposed method, we perform numerical tests considering the transport equation with a velocity field governed by Darcy’s law. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001