Abstract
In the numerical analysis of the flow field with FDM or other discretization methods, any grid discretization to fit the complicated boundary configuration could be selected arbitrarily with generalized curvilinear coordinates. Generalized coordinates are much available considering the variety of the shape of the physical region of interest, while orthogonal coordinates can only be applied to simple space because they are the specific ones of generalized coordinates. As the first step of study, two-dimensional k〜εmodel equations and their boundary conditions are worked out. The conservative expressions of k〜εmodel equations based on them are indicated here. Discretization of de-pendent variables with the control volume method and formulation of the boundary conditions (i.e. power-law of the velocity, free-slip condition of the turbulence kinetic energy k, wall-law of the dissipatiobn rate of turbulence energy ε) are proposed. The poisson equation of the pressure is formulated, where the second-order derivatives of the pressure are integrated conservatively over each control volume. The pressure at the boundary is solved as being unknown. Then the flow rate balances through the control volumes adjacent to the boundary are converged accurately as well as within the region.
