The main objective of this thesis is to accelerate the solvers used for solving the pressure Poisson equation, for the simulation of low-Mach number flows on unstructured meshes. This goal is completed with a need for stability, in particular when dealing with complex geometries. To this effect, several modifications of the deflated Conjugate Gradient method have been assessed. A restart method based on an estimation of the effect of numerical errors has been implemented and validated. Then, a method consisting in computing piecewise-linear or piecewise-quadratic solutions on the coarse grid level has proven unstable in the unstructured solver YALES2. The new method developed then consists in turning the standard two-level deflated Conjugate Gradient solver into a three-level method. Therefore, the high number of iterations on the newly created third level slows down the solver, which we have corrected thanks to two methods developed in order to reduce the number of iterations on the coarse levels. The first method is the creation of initial guesses thanks to a well-suited projection method. The second one consists in adapting the convergence criterion on the coarse grids. Numerical results on massively parallel simulations, with the standard two-level solver, show a drastic reduction of the computational times of the solver and an important improvement of its weak scaling. The implementation of these techniques to the three-level deflation induces additional gains in terms of computational times. Besides perfecting this solver, complementary research has to be conducted regarding dynamic load balancing, which could become a key development of the solver.
from HAL : Dernières publications http://ift.tt/1xKQX96
from HAL : Dernières publications http://ift.tt/1xKQX96
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