Transient solution of compressible viscous flows on high performance computing platforms using finite volume methods

摘要

The work presented in this dissertation is the result of u22application-drivenu22 research, with the need to solve complex large-scale engineering problems of significance and relevance to the Army and NASA using state-of-the-art high performance computing (HPC) platforms as its primary motivation. Currently, a majority of commercially available computational fluid dynamics (CFD) simulation algorithms in use by Army and NASA researchers and scientists solve the Navier-Stokes equations using a finite volume method (FVM) framework. Although these codes are extremely mature and take advantage of the numerical schemes complimentary to FVM, many do lack in computational performance for second-order accurate time integration schemes, due to the resulting nonlinear system of equations for large-scale applications, and exhibit poor scalability on a number of supercomputing platforms. Therefore, the purpose of this work is the development of a fully implicit, finite volume solver for large-scale transient compressible viscous flows, optimized for implementation on parallel, vector, and multi-streaming architectures. Optimization will include reduction in memory requirements, increasing computation speed, and obtaining near-linear code scalability. This is accomplished through implementation of innovative Jacobian-free/matrix-free iterative algorithms and code parallelization and vectorization. The Jacobian-free Generalized Minimal RESidual (GMRES) method is used to solve the resulting linear system inside each nonlinear Newton-Raphson iteration. Furthermore, the matrix-free Lower-Upper Symmetric Gauss Seidel (LU-SGS) method is employed as a preconditioning technique to the GMRES solver. Massively parallel implicit computations of both 2-dimensional and 3-dimensional aerodynamic applications using vector/multi-streaming and cluster supercomputers are presented to demonstrate the performance of the present solver in several aspects. These applications show the current implementation to be highly robust and accurate for problems of all flow regimes, subsonic, transonic, and supersonic. Though not originally intended for subsonic flows within the incompressible limit, i.e. flows with Mach numbers of 0.3 or less, results are presented which show that the solution accuracy of this solver is maintained for this class of problem. However, additional cases would need to be studied to determine the full scope of application to subsonic flows. The scalability of the current implementation is shown to be near-linear and super-linear across multiple supercomputing platforms.