The principal objective of this work is to investigate, develop and demonstrate advanced solution strategies for current and emerging high-order CFD discretizations, which are both robust and…

The National Aeronautics and Space Administration (NASA) awarded a $596,092.77 cooperative agreement to the University of Wyoming, Sponsored Programs to investigate, develop, and demonstrate advanced solution strategies for high-order computational fluid dynamics (CFD) discretizations that are robust and efficient for large-scale transient problems on massively parallel exascale architectures. The objective is to leverage a spectrum of linear and nonlinear solution techniques to optimize the robustness, efficiency, and scalability of CFD solvers for various discretizations on emerging hardware. The developed solvers will be demonstrated with continuous and discontinuous high-order finite-element discretizations, as well as high-order kinetic energy or entropy preserving schemes for aerospace engineering applications. This award is not associated with any set-aside program and will be performed in Laramie, Wyoming with a completion date of September 30, 2022.

The principal objective of this work is to investigate, develop and demonstrate advanced solution strategies for current and emerging high-order CFD discretizations, which are both robust and efficient, for the solution of large-scale transient problems on massively parallel exascale architectures. Although local nonlinear solvers enjoyed early success in CFD solvers, particularly when used as smoothers within a non-linear multigrid approach, these have increasingly been replaced by linear solver techniques used as drivers for newton or quasi-newton methods due to robustness issues encountered with local nonlinear methods for more demanding CFD problems, including higher resolution cases, more challenging flow physics, and stiffer nonlinear systems resulting from emerging high-order discretization schemes. While newton-krylov methods are well suited for delivering tight convergence tolerances, particularly in the final stages of convergence, these methods can be extremely costly overall, due to the requirement of overcoming strong nonlinear transients in the initial stages of convergence. On the other hand, local nonlinear solvers are generally very effective at overcoming these initial strong nonlinearities, but lack the rigorous properties of contractivity that can be developed for linear methods such as krylov techniques, which in turn can be used to drive a newton method at low residual levels, where nonlinear effects become vanishingly small. Furthermore, the emergence of heterogeneous architectures with low memory bandwidth and massive parallelism would seem to put global linearization methods at a disadvantage, due to the large memory requirements of (approximate) matrix factorization and poor scalability potential at the high end. However, the use of linear and nonlinear methods need not be mutually exclusive, and techniques for combining the advantages of both approaches offer the possibility of developing superior solvers that are provably robust, numerically efficient, and highly scalable. The principal idea of this proposal is to devise strategies that make use of a spectrum of both linear and nonlinear solution techniques at different scales, providing an avenue for optimizing robustness, efficiency and scalability for various CFD discretizations on various types of hardware. Examples include the use of nonlinear residual smoothing methods used in conjunction with newton-krylov methods, the application of nonlinear (FAS) multigrid methods for newton method continuation, and the tailoring of local linear solvers and/or nonlinear smoothers to block sizes that enable optimal use of emerging hardware configurations. Additionally, these methods are devised for use in multilevel or multigrid methods in order to ensure an overall numerically optimal solution scheme. For high-order temporal discretizations, an additional degree of time parallelism can be leveraged to enhance overall scalability. The developed solvers are to be demonstrated with different discretizations, including continuous and discontinuous high-order finite-element discretizations, as well as highorder kinetic energy or entropy preserving schemes for aerodynamic problems of relevance to the aerospace engineering community. Rather than attempting to develop a monolithic new solver approach for specific CFD problems, we seek to extend knowledge about the performance, strength and weaknesses of various linear and nonlinear solver techniques, while attempting to combine these component technologies in optimal ways for specific CFD discretizations and applications. Our goal is to revolutionize aerospace simulation capabilities through the development and adoption of solver technology that is optimally suited for existing and novel discretizations as well as emerging HPC hardware.