A multimaterial Eulerian approach for fluid-solid interaction - Obadia, Benjamin (Cranfield University, 2012)
This thesis is devoted to understanding and modeling multimaterial interactions, and to develop accordingly a robust scheme taking into account the largest variety of those, with a particular interest in resolving solid/fluid configurations. This very general frame of studies can be tackled with numerous different approaches as several issues arise and need to be addressed before attempting any modelisation of these problems. A first questioning should be the frame of reference to be used for the materials considered. Eulerian shock-capturing schemes have advantages for modeling problems involving complex non-linear wave structures and large deformations. If originally reserved mostly to fluids components, recent work has focused on extending Eulerian schemes to other media such as solid dynamics, as long as the set of equations employed is written under a hyperbolic system of conservation laws. Another matter of interest when dealing with multiple immiscible materials it the necessity to include some means of tracking material boundaries within a numerical scheme. Interface tracking methods based on the use of level set functions are an attractive alternative for problems with sliding interfaces since it allows discontinuous velocity profiles at the material boundaries whilst employing fixed grids. However, its intrinsic lack of variables conservation needs to be circumvented by applying an appropriate fix near the interface, where cells might comprise multiple components. Another requirement is the ability to correctly predict the physical interaction at the interface between the materials. For that purpose, the Riemann problem corresponding to the interfacial conditions needs to be formulated and solved. This implies in turn the need of appropriate Riemann solvers; if they are largely available when the materials are identical (i.e. governed by the same set of equations), a specific Riemann solver will be developed to account for fluid/solid interaction. Eventually, these newly developed methods will be tested on a wide range of different multimaterial problems, involving several materials undergoing large deformations. The materials used, whether modelling fluid/fluid or solid/fluid interactions, will be tested using various initial conditions from both sides of the interface, to demonstrate the robustness of the solver and its flexibility. These testcases will be carried out in 1D, 2D and 3D frames, and compared to exact solutions or other numerical experiments conducted in previous studies.