To address physical modeling of supercritical multicomponent §uid §ows, ideal-gas law must be changed to real-gas equation of state (EoS), thermodynamic and transport properties have to incorporate dense §uid corrections, and turbulence modeling has to be reconsidered compared to classical approaches. Real-gas thermodynamic is presently investigated with validation by NIST (National Institute of Standards and Technology) data. Two major issues of Liquid Rocket Engines (LRE) are also presented. The ¦rst one is the supercritical §uid §ow inside small cooling channels. In a context of LRE, a strong heat §ux coming from the combustion chamber (locally φ ≈ 80 MW/m 2 ) may lead to very steep density gradients close to the wall. These gradients have to be thermodynamically and numerically captured to properly reproduce in the simulation the mechanism of heat transfer from the wall to the §uid. This is done with a shock-capturing weighted essentially nonoscillatory (WENO) numerical discretization scheme. The second issue is a supercritical §uid injection following experimental conditions [1] in which a trans-or supercritical nitrogen is injected into warm nitrogen. The two-dimensional results show vortex structures with high §uid density detaching from the main jet and persisting in the low-speed region with low §uid density.