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This paper focuses on the construction of accurate and predictive data-driven reduced models of large-scale numerical simulations with complex dynamics and sparse training data sets. In these settings, standard, single-domain approaches may be too inaccurate or may overfit and hence generalize poorly. Moreover, processing large-scale data sets typically requires significant memory and computing resources which can render single-domain approaches computationally prohibitive. To address these challenges, we introduce a domain decomposition formulation into the construction of a data-driven reduced model. In doing so, the basis functions used in the reduced model approximation become localized in space, which can increase the accuracy of the domain-decomposed approximation of the complex dynamics. The decomposition furthermore reduces the memory and computing requirements to process the underlying large-scale training data set. We demonstrate the effectiveness and scalability of our approach in a large-scale three-dimensional unsteady rotating detonation rocket engine simulation scenario with over $75$ million degrees of freedom and a sparse training data set. Our results show that compared to the single-domain approach, the domain-decomposed version reduces both the training and prediction errors for pressure by up to $13 \%$ and up to $5\%$ for other key quantities, such as temperature, and fuel and oxidizer mass fractions. Lastly, our approach decreases the memory requirements for processing by almost a factor of four, which in turn reduces the computing requirements as well., Comment: 27 pages, 14 figures

In this project we aim to construct a high fidelity boundary condition module for Maxwell's equations that can be interfaced with major time-domain electromagnetics solver systems. There is ample need in the EM modeling community for reliable and stable far field boundary conditions of high accuracy. Most existing methods are limited in one or more of these requirements, and recent developments in the CRBC procedure (as originally presented by Hagstrom and Warburton in 2009), have made the technique an attractive candidate for implementation in multi-purpose solvers. In phase-I of this project we implemented and improved upon many aspects of this method, particularly in light of the needs of high order accurate Maxwell equations solvers (based on the discontinuous Galerkin method). Error bounds were computed and demonstrated for a number of cases. We continue in the second phase of this project to improve upon the robustness of this method, as we develop a software platform which shall be its flagship (and open source) implementation. In this first quarterly report we present initial progress to this end, showing recent mathematical developments, project coordination plans and some results from our initial experience with MEEP., The original document contains color images.

In this project, a team comprising of HyPerComp Inc. and NASA-JPL aims to develop modular parallel adaptive meshing capability for problems involving implicitly captured interfaces such as free surface capture using the level set method. In specific, these models will be demonstrated along with the appropriate software interfaces for the US Army PROTEUS toolkit. The foundation for this development will be an existing full-featured mesh generation program which has capabilities to handle geometries defined by CAD models as well as pointwise/mesh based data. This code will be interfaced with the open source software PYRAMID (developed and supported at JPL) and an API-based communication between PROTEUS (and other internally developed solvers) and the mesh modules will be developed. The effects of curved geometry (which can be important in high order modeling), scalability and efficiency of the parallel adaptive algorithm, smoothness of the mesh, preserving high order accuracy and stability in the simulation process shall be the highlights of the proposed project. HyPerComp has a long record of accomplishments in mesh generation for large scale fluid mechanics and electromagnetics problems, as well as modern high performance computing techniques in these areas. The parallel adaptive mesh software at JPL is one among a select group of computer programs with well demonstrated capabilities.

Detailed understanding of turbulent combustion in liquid rocket engines (LRE) requires an ability to predict the coupling between the transient features, acoustics, vortex/shear layer dynamics and the unsteady combustion heat release. Conventional and ad hoc models that mimic or match one set of conditions but fail in another test case cannot be used for reliable predictions. This paper presents a simulation strategy based on Large-Eddy Simulation (LES) that uses a finite-volume scheme on multi-block, structured grids and solves the full multi-species, compressible LES equations using a hybrid central-upwind scheme to capture both turbulence shear flow and large density gradients. The sensitivity of predictions to the real gas equation of state such as the Peng-Robinson one is addressed in this study. The main modeling challenges concern the simultaneous capture of the flame structure, the flame-turbulence interactions and the regions of compressibility. The current work focuses on turbulent combustion in three single injector configurations for these objectives: (a) trans-critical liquid oxygen (LOX) / gaseous hydrogen (GH2) combustion, (b) trans-critical LOX/methane combustion and (c) high-pressure GOX/methane combustion with thermo-acoustic instabilities. Results will be reported on the flame structure, liquid core length and spreading rate, and comparison with data where appropriate. Finally, for LES of such problems, a more fundamental challenge is to determine the implication of the LES subgrid closures for real gas flame dynamics. As a preliminary effort, the Linear-Eddy sub-grid model (LEM) is being applied to some of these cases., The original document contains color images.

HyPerComp is developing advanced computational tools to model high speed flows with MHD effects. Unstructured, multi-dimensional hypersonic MHD codes have been developed at HyPerComp to study supersonic viscous flows in a self-consistent, fully coupled manner. Effects of thermal, chemical and internal mode dis-equilibrium with and without the presence of electro-magnetic fields have been included in these codes. An existing parallel code environment using generalized mesh structure (prisms, tetrahedra, etc.) developed for Computational Electromagnetics, was adapted to model MHD with (a) Finite rate chemistry of ionizing air, (b) Thermal Non-equilibrium (Distribution of energy across various modes of storage), and (c) Electromagnetic effects. The effect of boundary conditions such as conducting/non-conducting walls, applied or extracted electric power and so forth, render this predictive capability invaluable in the study of MHD accelerators, power generators, turbulence control, and integrated analysis of fluid mechanics and time-varying electromagnetic fields. The subject of inlet flow control for hypersonic vehicles with MHD has attracted attention due to the possibility of flow modifications without the need for moving parts. There are numerous proposed designs to reduce drag, decrease total pressure loss and enhance air mass capture using MHD. Additionally, proposed MHD based concepts can even serve as a source of auxiliary onboard power, and as means to increase thrust produced by nozzles in hypersonic vehicles. The code development activity at HyPerComp has resulted in a high performance toolkit by which these ideas can be tested computationally.

The objective of Phase-I of this project was to demonstrate feasibility of exploiting the commonality in the structure of the governing equations in fluid dynamics and electromagnetics to develop a higher order Magneto-Gas-Dynamics (MGD) solver, based on the 3D, unstructured, parallel discontinuous Galerkin (DG) CEM (Computational ElectroMagnetics) code TEMPUS under development at HyPerComp. This objective was met by demonstrating conversion of the TEMPUS code, to an inviscid flow solver with minimal modifications. The only required changes to the code were the incorporation of appropriate flux computations and boundary conditions, while the structure of the code remained essentially same. This code conversion was preceded by the development of an implicit scheme based on a novel linearization technique for the flux terms, and the application of the DG scheme to classical problems in 1D and quasi 1D. The 1D demonstration included extension of the DG formulation to MGD equations, and successful application of the scheme to the Brio-Wu shock-tube problem and Wu's intermediate shock problem. It has been concluded that a strong platform for high order multi-physics computations may be built on the code structure and formulation developed in this activity, with extensions to elliptic and parabolic differential equation systems., The original document contains color images.