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This paper aims to perform a comparative study between capabilities of two numerical schemes from two main branches of numerical methods for solving hyperbolic conservation equations.

The accuracy and performance of a newly developed high‐resolution central scheme vs a higher‐order Godunov‐based method are evaluated in the context of black‐oil reservoir simulations. Both methods are modified enabling study of applications that are not strictly hyperbolic and exhibit local linear degeneracies in their wave structure.

The numerical computations show that while both schemes produce results with virtually the same accuracy, the Godunov method reproduces slightly more accurate results at the expense of calculation of eigen‐structures.

The paper investigates only one dimensional problems, but the idea can be easily extended to multi‐dimensional problems.

The paper shows the strengths and weaknesses of two practical numerical methods.

Such comparative study has not been published elsewhere and in particular, the performance of numerical methods on simulating hysteresis effect in hydrocarbon reservoirs has not been investigated in detail before.