Low (or ideally zero) numerical dissipation is always critical for high-fidelity scale-resolving flow simulations, as numerical dissipation prevents the physics of inviscid kinetic energy and entropy conservation, which is an essential attribute of compressible turbulence. However, contrary to the requirement, numerical schemes in compressible flow heavily rely on numerical dissipation for stable computation, preventing high-fidelity simulations, especially for flows around complex geometries. We address this challenge by devising a physics-compatible numerical scheme that satisfies the kinetic energy and entropy preservation (KEEP) properties by discretely satisfying the analytical relations of the governing equations. The KEEP scheme is highly stable without introducing numerical dissipation, something that existing numerical schemes fail to do. The stability stems from the significant improvement of entropy preservation in the KEEP scheme. The KEEP scheme allows robust and high-fidelity simulation not only for academic purposes but also for engineering applications with complex geometries. We also discuss an illustrative application to near-stall flows around complex full aircraft configurations with high-lift devices to show the capability of our numerical framework.