High-order physical-constraints-preserving velocity-consistent schemes for compressible multicomponent five-equation model with the Mie-Grüneisen equation of state

This work presents the first extension of the velocity-consistent (VC) framework for compressible multicomponent flows to the five-equation model with Mie-Grüneisen equation of state, thereby significantly broadening its applicability to materials such as solid metals, detonation products, and geomaterials. This generalization is nontrivial, as density-dependent material properties require more elaborate proofs to preserve equilibrium. The proposed high-order scheme employs velocity-consistent Lax-Friedrichs fluxes, which have been theoretically shown to preserve exact velocity-pressure equilibrium at material interfaces. To improve robustness and efficiency, the proposed schemes feature stabilized numerical diffusion in the global Lax-Friedrichs fluxes, combined with third-order TVD Runge-Kutta time-stepping to achieve efficiency and stability at larger time steps. Further accuracy and physical admissibility are achieved through affine-invariant WENO reconstruction and a hybrid flux limiter that adaptively blends high-order and first-order VC fluxes. Fourteen benchmark tests validate the scheme, showing fifth-order convergence, robust shock capture up to Mach 10, and successful simulations of Richtmyer-Meshkov instability, underwater explosions, and convergent shocks. These results collectively confirm that VC schemes effectively capture shocks, maintain high-resolution interface tracking, and strictly adhere to physical admissibility constraints across a wide range of materials.