Calculation of Complicated Flows, Using First and Second-Order Schemes (RESEARCH NOTE)

The first-order schemes used for discretisation of the convective terms are straightforward and easy to use, with the drawback of introducing numerical diffusion. Application of the secondorder schemes, such as QUICK scheme, is a treatment to reduce the numerical diffusion, but increasing convergence oscillation is unavoidable. The technique used in this study is a compromise between the above-mentioned problem, i.e. reducing the numerical diffusion and increasing the stability of the solution. This double folded task is achieved by introducing a modified second-order hybrid scheme. In addition to that by means of this formulation it is possible to show that the coefficients of the discretised equation at all neighboring points are positive and the value of a coefficient at a pole point is equal to the sum of its neighboring points, which means the two basic conditions defined by Patankar are satisfied. Therefore, this scheme has the benefits of the both first and second order schemes together. Results obtained by this scheme to predict the complicated flow regimes were promising and agreed well with experimental data.

Keywords:

Second , order Hybrid Scheme , Stability , boundedness , Numerical Diffusion , Laminar Flows