The main objective of the current work is to introduce a new conceptual linearization strategy to improve the performance of a primitive shock-capturing pressure-based finite-volume method. To avoid a spurious oscillatory solution in the chosen collocated grids, both the primitive and extended methods utilize two convecting and convected momentum expressions at each cell face. The expressions are obtained via a physical-based discretization of two inclusive statements, which are constructed via a novel incorporation of the continuity and momentum governing equations. These two expressions in turn provide a strong coupling among the Euler conservative statements. Contrary to the primitive work, the linearization in the current work respects the definitions and essence of physics behind deriving the Euler governing equations. The accuracy and efficiency of the new formulation are then investigated by solving the shock tube as a problem with moving normal and expansion waves and the converging-diverging nozzle as a problem with strong stationary normal shock. The results show that there is good improvement in performance of the primitive pressure-based shock-capturing method while its superior accuracy is not deteriorated at all.

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