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The integral-equation methods first proposed for solving filtration problems by Barenblatt [1] were subsequently used to good effect when studying cracked and porous media [2, 3].
      
However, the realization of the integral-equation method in the latter two cases [2, 3] contradicted the idea of interpenetrating continua which was used as a basis for the model of filtration in cracked and porous media [4].
      
A universal one-equation model for turbulent viscosity
      
The calculations are performed in the local conical approximation using the system of Reynolds equations and the differential one-equation turbulence model.
      
The flow past a circular cylinder with an isothermal surface at Mach numbers M∞=2 and 5 and Reynolds numbers ranging from 104 to 108 is investigated on the basis of the Reynolds equations using a differential two-equation turbulence model.
      
We present a new version of the two-equation turbulence model, which makes it possible to calculate continuously the entire flow range from laminar to turbulent, including transition, in the case of a time-periodic, high-turbulence-level freestream.
      
The propagation of an instability wave over an active segment of finite length is calculated using an integral-equation method based on solving the problem of boundary layer flow receptivity to surface vibration.
      
The problem of how the parameters of the underwater sound channel affect the sound field calculated in the ray and parabolic-equation approximations is studied.
      
The experimental data qualitatively agree with the numerical calculations performed in the kinetic-equation approximation including the viscous damping of waves.
      
The master integrals are evaluated as a series in ratio m/M and in ε with the help of a differential-equation method.
      
A theory is devised on the basis of a numerical solution of the electromagnetic field equations in an integral-equation formulation.
      
Numerical solution of the nonstationary Stokes system by methods of adjoint-equation theory and optimal control theory
      
Methods in optimal control and the adjoint-equation theory are applied to the design of iterative algorithms for the numerical solution of the nonstationary Stokes system perturbed by a skew-symmetric operator.
      
The problem of electromagnetic-wave diffraction from a group of bodies solved via the pattern-equation method
      
The modified two-equation model and the EDC turbulent combustion model are used for the gas phase.
      
A DSM closure is applied in the former, and a one-equation model is solved in the latter.
      
Algebraic stress model with RNG ε-equation for simulating confined strongly swirling turbulent flows
      
An explicit Harten-Yee Non-MUSCL Modified-flux-type TVD scheme has been used to solve the system of equations, and a zero-equation algebraic turbulence model to calculate the eddy viscosity coefficient.
      
The presented analysis is based on numerical simulations by means of N-S compressible solver with a two-equation turbulence model.
      
An explicit Harten-Yee Non-MUSCL Modified-flux-type TVD scheme has been used to solve the system of equations, and a zero-equation algebraic turbulence model to calculate the eddy viscosity coefficient.
      
 

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