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When fully conservative methods are used to simulate transcritical flow,spurious pressure oscillations and numerical instability are generated. Thestrength and speed of propagation of shock waves cannot be representedcorrectly using a semi-conservative or primitive method. In this research, anadaptive primitive-conservative scheme is designed to overcome the aforesaidtwo difficulties. The underlying cause for pressure oscillation is analyzedwithin the framework of Finite Volume Method (FVM). We found that thenonlinearity of the thermodynamic properties of transcritical fluids rendersstandard conservative numerical methods ineffective. In smooth regions, schemesbased on primitive variable are used to eliminate spurious pressureoscillations. For the purpose of correctly capturing shock waves, the modifiedRoe Riemann solver for real fluid is utilized in regions where shock wavesinduce discontinuity. The adaptive numerical approach relies only on the speedof sound, eliminating the requirement to calculate the derivatives ofthermodynamic quantities. A large number of numerical test cases conducted inone- and two-dimensional spaces have shown the robustness and accuracy of theproposed adaptive scheme for the simulations of high speed transcritical flows.

An adaptive primitive-conservative scheme for high speed transcritical flow with an arbitrary equation of state