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\(u^{n+1}_f \), \( \omega_p^{n+1} \), \( \alpha^{n+1}\), \( u_p^{n+1} \) -…

- - - - \( \kappa\)
      - \( \alpha^n \)
  - - - \( A_u\)
      - \( \hat{u}_f^n\)
        
        \((1-\hat{\psi}_s)u_f+\hat{\psi}_s u_s \)
        
        \( u_s^n\)
        
        \( u_p+\omega_p \times (x_i-x_p)\)
        
        \( u_p^n \)
        
        \( \omega_p^n\)
        
        \( \hat{\psi}_s \)
        
        \( \frac{\phi_s \rho_s}{\rho} \)
        
        \( \rho \)
        
        \( (1-\phi_s)\rho_f+\phi_s\rho_s \)
        
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        \( \phi_s^n \)
        
        \( \frac{\sum_{in} \phi_{v,i}}{\sum_{all} \phi_{v,i }}\)
- - - - \( M_n \)
        
        \(-\frac{\partial \omega(x,\theta)}{\partial\theta } \)
- - - - \( F_n \)
        
        \(-\frac{\partial \omega(x,\theta)}{\partial x } \)
      - \( F_s^{'}\)
        
        \( F_{st}^{'} \frac{F_s}{\sqrt{F_s^2+F_t^2}}\)
        
        \( F_s\)
        
        \( F_s^0-k_s\delta_s \)
      - \( F_t^{'}\)
        
        \( F_{st}^{'} \frac{F_t}{\sqrt{F_s^2+F_t^2}}\)
        
        \( F_t\)
        
        \( F_t^0-k_t\delta_t \)
        
        \( F_{st}^{'}\)
        
        \( min(\sqrt{F_s^2+F_t^2},\mu F_n) \)