Аннотация:A numerical approach for modeling heterogeneous media composed of multiple compressible materials with different physical properties is considered. The model is singlevelocity, and the governing equations represent mass conservation for each component, conservation of the total momentum and energy, and advection of N-1 characteristic functions that depend on volume fractions of N components. The isobaric assumption is used to close the model equations. We consider the second-order accurate Godunov-type numerical scheme for solving the system of governing equations. It is shown that for meeting the PV and monotonicity properties of the numerical solutions, different characteristic functions should be taken for the advection operator and for the face-interpolator, and such functions are proposed. We test the proposed model and numerical method with several benchmark problems. The results obtained show that the method is robust and effective in capturing interfaces in multimaterial compressible hydrodynamics, providing non-oscillatory and physically admissible solutions.