The lecture deals with explicit and implicit finite difference and mainly finite volume schemes that have been commonly used in last years for compressible and incompressible fluid flow problems. Mainly we mention schemes used for transonic flow computation (inviscid as well as viscous models) in internal and also external aerodynamics. We prefer modern schemes like RK multistage schemes, TVD and ENO schemes, implicit schemes or higher order schemes. Some results of numerical computation or numerical simulation are presented in the second part of the paper, including 2D and 3D transonic flow through a channel and a cascade (mainly of turbine type), 2D and 3D backward facing step flow (laminar and turbulent), 2D and 3D impinging jet flow (comparisons of some turbulent models). The last two cases have been computed only for incompressible viscous flows. Some tests for the efficiency of higher order scheme (4th-6th order) are presented for the backward facing step problem. In many examples we also present a comparison of numerical and experimental results.
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The contribution reviews our recent research activities on numerical simulations of diesel fuel spray evolution. The simulations are performed by means of an in-house mathematical model. The developed model is capable of predicting the two-phase flows constituted by the dispersed liquid phase (droplets) injected into gaseous environment. Both the multi-component compressible gas-phase flows as well as the "droplet-phase" flows are solved using governing equations written in Eulerian coordinates. The conservation of mass, momentum, and energy is balanced on finite Volumes with arbitralily movable boundaries. Thus, the model enables the computation of movable boundary problems, which facilitates the solution of in-cylinder flow with moving engine piston. The model features the two-way coupling between phases in mas s, momentum, and energy equations. The phenomena as spray induced gaseous flow, gas-to-droplet heat transfer, and fuel evaporation with consecquent vapor transport are, therefore, taken into account. The predictive capabilities of the developed model have been tested in simplified axisymmetric flow cases of diesel fuel injection process. The results of these computations are presented.
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