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Compressible Mathematical Model

The computational model solves following system of equations: img152 1 img154 1 img155 img156 img157 img158 img159 img162img153img163 img164
  • Mass conservation [*]
  • Momentum conservation [*]
  • Energy conservation [*] and [*], two options
  • where: Einstein summation is used, $ \partial$ is partial derivative, $ x_i$ is i-th Cartesian coordinate, $ \rho$ is density, $ u_i$ is i-th velocity vector component, $ t$ is time, $ p$ is static pressure, $ \tau$ shear stress tensor, $ \delta_{ij}$ is Kronecker delta, $ e_0$ is total specific energy, $ \mu$ is dynamic viscosity, $ S_{ij}$ is rate-of-deformation tensor, $ T$ is static temperature, $ Pr$ is Prandtl number, $ R$ specific gas constant, $ C_p$ specific heat capacity (at constant pressure), $ C_v$ specific heat capacity (at constant volume), $ q_i$ i-th heat flux component (Fourier law), $ \lambda$ heat conductivity coefficient.
  • The whole system is closed with boundary conditions.
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