Solutions to increase the accuracy of Godunov-type schemes range from extending the number of cells used in the discretization, which increases significantly the computational cost, to introducing flux limiters that may be overcompressive, although monotonicity preserving. The Modified DPM presented here is a Godunov-type numerical scheme for the resolution of linear advection equation, on a Cartesian grid. It is a generalization of the Discontinous Profile Method (DPM) scheme. In the proposed method the stencil remains small and higher-order accuracy is achieved by considering the point value at the cell interfaces and the mean cell value as two different variables. This additional information is included in the reconstruction of a discontinuous profile in the cell, and has a central role in constructing a low-diffusive scheme. Thus, only the current cell and the four neighbouring ones are necessary to achieve good accuracy, at reasonable computational cost. The two-dimensional generalization of the Modified DPM presented here is shown to give a good representation of the theoretical solution on a set of two-dimensional test cases. Its performance is compared to that of the MUSCL scheme on the same test cases.
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