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Spécialité : Mécanique des fluides


Vineet SONI

Soutenue le 9 décembre 2016

Parallel Adaptive Multiscale Numerical Methods for Complex Compressible Flows

M. Kai Schneider, Professeur, Aix-Marseille Université, France
M. Gabi Ben–Dor, Professeur, Ben Gurion University of the Negev, Israel

M. Jean–François Haas, Ingénieur Chercheur, CEA, France
M. Dany Vandromme, Professeur, INSA de Rouen Normandie, France
M. Olivier Roussel, Chercheur, Umeå University, Sweden

Directeur de thèse
M. Abdellah Hadjadj, Professeur, INSA de Rouen Normandie, France

Parallel Adaptive Multiscale Numerical Methods for Complex Compressible Flows

The challenges of the real world problems with respect to perform high–fidelity numerical simulations of large–scale computations inflict a huge computational hurdle due to the necessity of handling complex multiscale problems which require dynamically adaptive solutions. To address this issue, a conventional solution would be to embrace some sort of local solution adaption. In this work, a wavelet based adaptive point–value multiresolution (MR) method is developed in a framework of a finite–differences method. Higher–order spatial and temporal discretization schemes are used. The flow solver is further strengthened by employing a ghost–cell based immersed boundary method in conjunction with the ray tracing technique to facilitate simulations using non–conforming grids over complex shape obstacles. A series of multidimensional numerical problems are conducted exhibiting excellent performance of the grid adaption in terms of reduction in the computational efforts as well as the accuracy of the MR method. Moreover, in order to take advantage of the computing power of the most prevalent supercomputers, three new parallel load–balancing algorithms are tailored for the point–value MR method for the multi–core and the multi–processor architectures. The algorithms include a new concept of the multiresolution forest structure (MFS). A careful assessment of these methods are discussed in detail exposing their benefits as well as their limitations. Rigorous performance analysis of these methods reveals an immense potential to exploit the parallelism using the concept of the proposed MFS ; and lay down the new paths to enhance the speedup performance of MR methods. Application to shock waves including shock–obstacle interaction in double–concave cylindrical reflectors, for ignition detonation or high–speed combustion problems, shows two new shock bifurcations revealing a greater insight into the phenomenology of the reflection configurations. It is shown, for the first time, that the transition from a single–triple–point wave configuration (STP) to a double–triple–point wave configuration (DTP) and back occurs several times on the second reflector, indicating that the flow is capable of retaining the memory of the past events over the entire process.

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