Godunov method Chebyshev method of local iteration 1 Chebyshev method of local iterations 1 Chebyshev's methods 1 Compressibility of gases 1 Compressible Euler system 1 Compressible euler system 1 Consistency formulation 1 Diffuse interface 1 Diffusion process 1 Error estimates 1 Errors 1 Euler equations 1 Euler system 1 Gas dynamics 1 Governing equations 1 Heat conduction 1 Interface relaxations 1 Iterative methods 1 L 1 norm 1 Multiphase flow 1 Multiphases 1 Numerical methods 1 Numerical solution 1 Relative energies 1 Relative energy 1 Shock tubes 1 Strong solution 1 Thermal conduction 1 Two phase 1