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Compressible Mathematical Model

The computational model solves following system of equations:

1 3
3 3
2 3
3 3
5 3
6 2
7 1
8 2
  • Mass conservation [*]
  • Momentum conservation [*]
  • Energy conservation [*] and [*], two options
  • where: Einstein summation is used, $ \color{white} \partial$ is partial derivative, $ \color{white} x_i$ is i-th Cartesian coordinate, $ \color{white} \rho$ is density, $ \color{white} u_i$ is i-th velocity vector component, $ \color{white} t$ is time, $ \color{white} p$ is static pressure, $ \color{white} \tau$ shear stress tensor, $ \color{white} \delta_{ij}$ is Kronecker delta, $ \color{white} e_0$ is total specific energy, $ \color{white} \mu$ is dynamic viscosity, $ \color{white} S_{ij}$ is rate-of-deformation tensor, $ \color{white} T$ is static temperature, $ \color{white} Pr$ is Prandtl number, $ \color{white} R$ specific gas constant, $ \color{white} C_p$ specific heat capacity (at constant pressure), $ \color{white} C_v$ specific heat capacity (at constant volume), $ \color{white} q_i$ i-th heat flux component (Fourier law), $ \color{white} \lambda$ heat conductivity coefficient.
  • The whole system is closed with boundary conditions.