Mathematics

The motivation behind the thesis work has its origin in the applications of perforatedplates to the flow control of transonic Aircrafts, as well as the eusive cooling forgas turbine engines. Aside the prior work done by P. Doerer and T. Lewandowskiin this area using the Finite Volume Method, there was an interest to explore theapplicability of the Meshfree particle methods to simulate certain congurations ofgas flow through microchannels, and whether such methods are practical enough toextend the model to further configurations.For that purpose, the Weakly Compressible Smoothed Particle Hydrodynamicswas chosen to model low Reynolds number incompressible gas flows through microchannel,including heat transfer through the channel walls. A proposed schemewas implemented via LAMMPS software and the results were processed via a developpedC++ code for cartesian interpolation using the SPH formula. Finally, a databank was provided for all the test cases.In general, the SPH results well captures the various flow features in the domain. Acareful choice regarding the parameters of the state equation is crucial to the solutionaccuracy as well as avoiding any unphysical behaviours. From a computational aspect,the implemented SPH scheme is much more expensive than traditional Euleriansolvers; hence it may not be suitable for practical situations. Further investigationsare still required regarding the transient behavior of the model; and the effect of the model parameters needs to be quantied in order to stand on the best accuracy.