SUMMARYAn operator-splitting algorithm for the two-dimensional convection-dispersion-reaction equation is developed. The flow domain is discretized into triangular elements which are fixed in time. The governing equation is split into three successive initial value problems: a pure convection problem, a pure dispersion problem and a pure reaction problem. For the pure convection problem, solutions are found by the method of characteristics. The solution algorithm involves tracing the characteristic lines backwards in time from a vertex of an element to an interior point. A cubic polynomial is used to interpolate the concentration and its derivatives on an element. For the pure dispersion problem, an explicit finite element algorithm is employed. Analytical solutions are obtained for the pure reaction problem. The treatment of the boundary conditions is also discussed. Several numerical examples are presented. Numerical results agree well with analytical solutions. Because cubic polynomials are used in the interpolation, very little numerical damping and oscillation are introduced, even for the pure convection problem.

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A model that uses the operator splitting technique based on Eulerian-Lagrangian method and embeds the k-ε turbulence mode is developed. The model is used to simulate a two dimensional flow over a backward-facing step with triangular mesh discrete flow field. The convection operator is solved with the characteristic method and the diffusion operator and pressure-Poisson equation are solved by finite element method. The results from the example showed that numerical results are well agreed with the experimental data, and that the method can be adapted to simulate complex turbulent flow with strong non-linear convection. The treatment of boundary conditions is also studied in the paper. turbulence model, the flow over a backward-facing step, numerical method Citation:Ding D Y, Wu S Q. Numerical application of k-ε turbulence model to the flow over a backward-facing step.