Numerical modelling and High Performance Computing for sediment flows

The dynamic of sediment flows is a subject that covers many applications in geophysics, ranging from estuary silting issues to the comprehension of sedimentary basins. This PhD thesis deals with high resolution numerical modeling of sediment flows and implementation of the corresponding algorithms on hybrid calculators. Sedimentary flows involve multiple interacting phases, giving rise to several types of instabilities such as Rayleigh-Taylor instabilities and double diffusivity. The difficulties for the numerical simulation of these flows arise from the complex fluid/sediment interactions involving different physical scales. Indeed, these interactions are difficult to treat because of the great variability of the diffusion parameters in the two phases. When the ratio of the diffusivities, given by the Schmidt number, is too high, conventional methods show some limitations. This thesis extends the recent results obtained on the direct resolution of the transport of a passive scalar at high Schmidt number on hybrid CPU-GPU architectures and validates this approach on instabilities that occur in sediment flows. This work first reviews the numerical methods which are adapted to high Schmidt flows in order to apply effective accelerator implementation strategies and proposes an open source reference implementation named HySoP. The proposed implementation makes it possible, among other things, to simulate flows governed by the incompressible Navier-Stokes equations entirely on accelerator or coprocessor thanks to the OpenCL standard and tends towards optimal performances independently of the hardware. The numerical method and its implementation are first validated on several classical test cases and then applied to the dynamics of sediment flows which involve a two-way coupling between the transported scalars and the Navier-Stokes equations. We show that the joint use of adapted numerical methods and their implementation on accelerator makes it possible to describe accurately, at a very reasonable cost, sediment transport for Schmidt numbers difficult to reach with other methods.