the purpose of this paper is to studying nonlinear k-ε turbulence models and its advantages in internal combustion engines, since the standard k-ε model is incapable of representing the anisotropy of turbulence intensities and fails to express the reynolds stresses adequately in rotating flows. therefore, this model is not only incapable of expressing the anisotropy of turbulence in an engine c...

The purpose of this paper is to studying nonlinear k-ε turbulence models and its advantages in internal combustion engines, since the standard k-ε model is incapable of representing the anisotropy of turbulence intensities and fails to express the Reynolds stresses adequately in rotating flows. Therefore, this model is not only incapable of expressing the anisotropy of turbulence in an engine c...

The commonly used linear k-ε turbulence model is shown to be incapable of accurate prediction of turbulent flows, where non-isotropy is dominant. Two examples of non-isotropic flows, which have a wide range of applications in marine waters, are saline water flow and the stratified flows due to temperature gradients. These relate to stratification and consequently, variation of density through...

In this paper we present a penalty method for solving a complementarity problem involving 2nd-order nonlinear parabolic differential operators. In this work we first rewrite the complementarity problem as a nonlinear variational inequality. Then, we define a nonlinear parabolic partial differential equation (PDE) approximating the variational inequality using a power penalty term with a penalty...

In this paper we present numerical methods for the nonlinear Schrödinger equations (NLS) in the semiclassical regimes: iε uεt = − ε 2 ∆u + V (x)u + f(|u|)u, x ∈ R, with nonzero far-field conditions. A time-splitting cosine-spectral (TS-Cosine) method is presented when the nonzero far-field conditions are or can be reduced to homogeneous Neumann conditions, a time-splitting Chebyshev-spectral (T...

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