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High-Order Numerical Methods for Shock-Bubble Interaction Computations

Abstract : The importance of modelling two-phase flows involving shock waves arises from many engineering and medical applications. The presence of strong shock waves, their interactions with bubble interfaces and the large variation of material properties make the resolution of such problems a complicated task for the numerical methods. While the variety of numerical techniques to solve these problems exist, e.g. the sharp interfaceor the diffuse interface methods, these strategies can lead to spurious oscillations of the solution near the interface. It is well known that it is difficult to achieve both a high order accuracy of the scheme and the monotonicity of the solution.In this thesis a four-equation mixture model is employed and integrated in an explicit finite-volume solver with different numerical schemes and reconstruction methods. The construction of a high-order numerical tool for solving stiff 2D and 3D shock-bubble interactions is proposed. The numerical validation of the methods is performed on various 1D problems (shock-tube problems) and on air-helium shock-bubble case in 2D. The study is then ex- tended to the collapse of a gas bubble immersed in water and located in the vicinity of a wall. While the high-order numerical schemes lead to the high-accuracy reconstruction, the question of computational cost emerges. The physical phenomena involved into considered problems require a fine grid to achieve the detailed solution. For instance, a computational isotropic grid can reach over 1 billion nodes in 3D, leading to a huge cost. Thus, there is a need of CPU reduction techniques. Different mesh-stretching techniques have been studied and implemented in the code, leading to a reduction of the computational cost by a factor of 5 for the problem of shock-bubble collapse. Finally, the computations of the latter problem have been successfully extended to 3D with implementation of parallel paradigms (OpenMP and MPI). The solutions computed on one billion points with third order accuracy are presented and discussed. The evolution of the maximum wall pressure is analysed when the stand-off distance varies, suggesting potential wall damages.
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Submitted on : Thursday, May 12, 2022 - 4:41:43 PM
Last modification on : Friday, May 13, 2022 - 3:36:49 AM


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  • HAL Id : tel-03666688, version 1



Ksenia Kozhanova. High-Order Numerical Methods for Shock-Bubble Interaction Computations. Other. ISAE-ENSMA Ecole Nationale Supérieure de Mécanique et d'Aérotechique - Poitiers, 2022. English. ⟨NNT : 2022ESMA0001⟩. ⟨tel-03666688⟩



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