Efficient High-Order Accurate Methods using Unstructured Grids for Hydrodynamics and Acoustics

摘要

The objective of this project has been the development of high-order accurate simulation techniques for fluid flow problems of interest to the US Navy, such as hydrodynamics and acoustics. Efficient solution techniques for high-order Discontinuous Galerkin methods have been investigated from both a theoretical and practical standpoint. An h-p multigrid solution strategy which delivers optimal convergence rates which are independent of both the order of accuracy p of the discretization, and the resolution h of the mesh has been developed and demonstrated on steady and unsteady problems, showing good efficiency and parallel scalability using up to 2000 processors. Sensitivity analysis techniques-based on the solution of the adjoint problem have also been developed, and used to drive h and p adaptive refinement techniques for increasing accuracy at optimal cost. Future work will concentrate on extending these techniques to three dimensional Reynolds-averaged Navier-Stokes (RANS) simulations and large eddy simulations LES for important flows of Naval interest.