An elliptic blending Reynolds stress transport equation model for Newtonian fluids has been extended to predict polymer-induced drag reduction FENE-P fluids. The conformation tensor equation which is related to the polymer stress is adopted from the model form of Resende et al., and the models of redistribution and dissipation rate terms for the Reynolds stress transport equation are considered by the elliptic blending equation. Also, the new model terms for viscoelastic turbulent transport and viscoelastic dissipation in the Reynolds stress transport equation are introduced to consider the polymer additives effect. The prediction results are directly compared to the DNS data to assess the performance of the present model predictions.

Nodal transport methods are proposed for solving the simplified even-parity neutron transport (SEP) equation. These new methods are attributed to the success of existing nodal diffusion methods such as the Polynomial Expansion Nodal and the Analytic Function Expansion Nodal Methods, which are known to be very effective for solving the neutron diffusion equation. Numerical results show that the simplified even-parity transport equation is a valid approximation to the transport equation and that the two nodal methods developed in this study also work for the SEP transport equation, without conflict. Since accuracy of methods is easily increased by adding node unknowns, the proposed methods will be effective for coarse mesh calculation and this will also lead to computation efficiency.

An algebraic model for turbulent heat fluxes is proposed on the basis of the elliptic blending equation. The algebraic model satisfies the temperature-pressure gradient correlation characteristics of near-wall region and the flow center region far away from the wall. That is, the turbulent heat flux conditions for both regions are connected by the solution of the elliptic blending equation. The predictions of turbulent heat transfer in a plane channel flow have been carried out with constant wall heat flux and constant wall temperature difference boundary conditions respectively. Also, the rotating channel flow with constant wall temperature difference is considered to test the applicability of the model. The prediction results show that the distributions of the turbulent heat fluxes and mean temperature are well captured by the present algebraic heat flux model.

수송방정식의 양면적은 특성으로 인하여 이송항이 지배적인 흐름에 있어서 수송방정식의 수채해석은 매우 난해하다. 특히 유한요소법을 사용하여 수치해석할 때, 상류방향으로 더 많은 가중치를 두기 위하여 변화된 시행함수를 사용한다. 이러한 방법을 Petrov-Galerkin 방법이라고 한다. 본 논문에서는 N+1 과 N+2 Petrov-Galerkin 방법을 격자 Peclet 수가 큰 수송문제에 적용하였다. 주파수맞춤 기법을 사용하여 N+2 Petrov- Gal