Numerical Simulation of Compressible Flows with Interfaces

Compressible interfacial flows exist in a variety of applications: reacting fronts, droplet break up, jets and sprays in high speed, shock passage in foams, etc. These flows behave in a complex multi-scale way including interface deformation, wave interface interaction and complex transport phenomena.\nIn the first section, the interaction of a laminar flame with a compression wave is investigated. More precisely, the evolution of the burning interface is investigated and discussion over different compression waves and their effects on the flame geometry and burning rate are made.\nIn the second part, a numeral framework for simulation of compressible multiphase flows using adaptive wavelet collocation method is developed. This study was originally motivated by the desire for a numerical tool capable of simulating the atomization process during start-up conditions in a supersonic combustor. To model such physics, the solver needs to handle high density ratios, transport terms and capillary effects.\nThe multi-scale behaviour of these flows requires a multi-scale approach. Parallel Adaptive\nWavelet Collocation Method (PAWCM) makes use of second generation wavelets to dynamically adapt the grid to localized structures in the flow in time and space. This approach allows the solution to be approximated using a subset of the points that would normally be used with a uniform grid scheme. Thus, computation on this subset is efficient and high levels of data compression is achieved.