Multiple stream superposition of a two-stream combined analytical numerical initial value problem solver for aerodynamic mixing

In spite of the rapid advances in both scalar and parallel computational flow simulation tools, the large number and breadth of variables involved in both design and inverse problems make the use of complex fluid flow models impractical. With this restriction, it may be concluded that an important family of methods for mathematical/computational development are reduced or approximate models. An approximate model for two stream mix problems utilizing a combined perturbation/numerical modelling methodology has been developed [1]. The numerical portion of the model uses a compact finite difference scheme, while analytical solutions are used to resolve singular behavior that is inherent to this flow. Approximate representation of the flow in terms of flux variables yields a linear transport operator, thus facilitating the additive decomposition of the solution into numerical and analytical portions. Additionally, linearity permits superposition of the basic two-stream initial value problem to construct multiple stream mixing problems. Multiple stream results are presented to illustrate the efficiency of this methodology.     

Mixed analytical/numerical method for flow equations with a source term

A mixed analytical/numerical approach is studied for flow problems described by partial differential equations with source terms which are analytically integrable and which may involve a time scale (S-scale) much smaller than the mean flow time scale (M-scale). A rigorous error analysis based on the modified equation is conducted for a linear model equation and it is shown, both analytically and numerically, that the mixed scheme is more accurate than a conventional numerical method. Most interestingly, the mixed approach has a good accuracy for the M-scale structure even though the time step is larger than the S-scale, while a conventional scheme fails to work in this case by producing errors of order O(1) or larger.