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Advanced Fluid Reduced Order Models for Compressible Flow

Tezaur, Irina K.; Fike, Jeffrey; Carlberg, Kevin T.; Barone, Matthew F.; Maddix, Danielle; Mussoni, Erin E.; Balajewicz, MacIej

This report summarizes fiscal year (FY) 2017 progress towards developing and implementing within the SPARC in-house finite volume flow solver advanced fluid reduced order models (ROMs) for compressible captive-carriage flow problems of interest to Sandia National Laboratories for the design and qualification of nuclear weapons components. The proposed projection-based model order reduction (MOR) approach, known as the Proper Orthogonal Decomposition (POD)/Least- Squares Petrov-Galerkin (LSPG) method, can substantially reduce the CPU-time requirement for these simulations, thereby enabling advanced analyses such as uncertainty quantification and de- sign optimization. Following a description of the project objectives and FY17 targets, we overview briefly the POD/LSPG approach to model reduction implemented within SPARC . We then study the viability of these ROMs for long-time predictive simulations in the context of a two-dimensional viscous laminar cavity problem, and describe some FY17 enhancements to the proposed model reduction methodology that led to ROMs with improved predictive capabilities. Also described in this report are some FY17 efforts pursued in parallel to the primary objective of determining whether the ROMs in SPARC are viable for the targeted application. These include the implemen- tation and verification of some higher-order finite volume discretization methods within SPARC (towards using the code to study the viability of ROMs on three-dimensional cavity problems) and a novel structure-preserving constrained POD/LSPG formulation that can improve the accuracy of projection-based reduced order models. We conclude the report by summarizing the key takeaways from our FY17 findings, and providing some perspectives for future work.

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TYPE SAND Report YEAR 2017
DOIOSTI

A matrix dependent/algebraic multigrid approach for extruded meshes with applications to ice sheet modeling

SIAM Journal on Scientific Computing

Tuminaro, Raymond S.; Perego, Mauro; Tezaur, Irina K.; Salinger, Andrew G.; Price, Stephen

A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigrid hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. Furthermore, this facilitates integration of the solver with a variety of different extruded mesh applications.

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TYPE Journal Article YEAR 2016
DOIOSTI

Performance Portability of the Aeras Atmosphere Model to Next Generation Architectures using Kokkos

Watkins, Jerry E.; Tezaur, Irina K.

The subject of this report is the performance portability of the Aeras global atmosphere dynamical core (implemented within the Albany multi-physics code) to new and emerging architecture machines using the Kokkos library and programming model. We describe the process of refactoring the finite element assembly process for the 3D hydrostatic model in Aeras and highlight common issues associated with development on GPU architectures. After giving detailed build and execute instructions for Aeras with MPI, OpenMP and CUDA on the Shannon cluster at Sandia National Laboratories and the Titan supercomputer at Oak Ridge National Laboratory, we evaluate the per- formance of the code on a canonical test case known as the baroclinic instability problem. We show a speedup of up to 4 times on 8 OpenMP threads, but we were unable to achieve a speedup on the GPU due to memory constraints. We conclude by providing methods for improving the performance of the code for future optimization.

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TYPE SAND Report YEAR 2016
DOIOSTI

Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier-Stokes equations

Journal of Computational Physics

Balajewicz, MacIej; Tezaur, Irina K.; Dowell, Earl

For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based fluid ROMs in which truncated modes are accounted for a priori via a minimal rotation of the projection subspace. Attention is focused on the full non-linear compressible Navier-Stokes equations in specific volume form as a step toward a more general formulation for problems with generic non-linearities. Unlike traditional approaches, no empirical turbulence modeling terms are required, and consistency between the ROM and the Navier-Stokes equation from which the ROM is derived is maintained. Mathematically, the approach is formulated as a trace minimization problem on the Stiefel manifold. The reproductive as well as predictive capabilities of the method are evaluated on several compressible flow problems, including a problem involving laminar flow over an airfoil with a high angle of attack, and a channel-driven cavity flow problem.

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TYPE Journal Article YEAR 2016
DOIOSTIScopus

Model Reduction for Compressible Cavity Simulations Towards Uncertainty Quantification of Structural Loading

Tezaur, Irina K.; Balajewicz, MacIej; Barone, Matthew F.; Carlberg, Kevin T.; Fike, Jeffrey; Mussoni, Erin E.

This report summarizes FY16 progress towards enabling uncertainty quantification for compressible cavity simulations using model order reduction (MOR). The targeted application is the quantification of the captive-carry environment for the design and qualification of nuclear weapons systems. To accurately simulate this scenario, Large Eddy Simulations (LES) require very fine meshes and long run times, which lead to week-long runs even on parallel state-of-the-art super- computers. MOR can reduce substantially the CPU-time requirement for these simulations. We describe two approaches for model order reduction for nonlinear systems, which can yield significant speed-ups when combined with hyper-reduction: the Proper Orthogonal Decomposition (POD)/Galerkin approach and the POD/Least-Squares Petrov Galerkin (LSPG) approach. The implementation of these methods within the in-house compressible flow solver SPARC is discussed. Next, a method for stabilizing and enhancing low-dimensional reduced bases that was developed as a part of this project is detailed. This approach is based on a premise termed "minimal subspace rotation", and has the advantage of yielding ROMs that are more stable and accurate for long-time compressible cavity simulations. Numerical results for some laminar cavity problems aimed at gauging the viability of the proposed model reduction methodologies are presented and discussed.

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TYPE SAND Report YEAR 2016
DOIOSTI

The Aeras Next Generation Global Atmosphere Model

Bosler, Peter A.; Bova, Steven W.; Demeshko, Irina P.; Fike, Jeffrey; Guba, Oksana; Overfelt, James R.; Roesler, Erika L.; Salinger, Andrew G.; Smith, Thomas M.; Tezaur, Irina K.; Watkins, Jerry E.

The Next Generation Global Atmosphere Model LDRD project developed a suite of atmosphere models: a shallow water model, an x-z hydrostatic model, and a 3D hydrostatic model, by using Albany, a finite element code. Albany provides access to a large suite of leading-edge Sandia high-performance computing technologies enabled by Trilinos, Dakota, and Sierra. The next-generation capabilities most relevant to a global atmosphere model are performance portability and embedded uncertainty quantification (UQ). Performance portability is the capability for a single code base to run efficiently on diverse set of advanced computing architectures, such as multi-core threading or GPUs. Embedded UQ refers to simulation algorithms that have been modified to aid in the quantifying of uncertainties. In our case, this means running multiple samples for an ensemble concurrently, and reaping certain performance benefits. We demonstrate the effectiveness of these approaches here as a prelude to introducing them into ACME.

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TYPE SAND Report YEAR 2016
DOIOSTI

Towards performance-portability of the Albany Finite Element analysis code using the Kokkos library of Trilinos

International Journal of HPC Applications

Demeshko, Irina; Salinger, Andrew G.; Spotz, William S.; Tezaur, Irina K.; Guba, Oksana; Heroux, Michael A.

Performance portability on heterogeneous high-performance computing (HPC) systems is a major challenge faced today by code developers: parallel code needs to execute correctly as well as with high performance on machines with different architectures, operating systems, and software libraries. The Finite Element Method (FEM) is a popular and flexible method for discretizing partial differential equations arising in a wide variety of scientific, engineering, and industry applications that require HPC. This paper presents some preliminary results pertaining to our development of a performance portable implementation of the FEM-based Albany code. Performance portability is achieved using the Kokkos library of Trilinos. We present performance results for two different physics simulations modules in Albany: the Aeras global atmosphere dynamical code and the FELIX land-ice solver. As a result, numerical experiments show that our single code implementation gives reasonable performance across two multi-core/many-core architectures: NVIDIA GPUs and multi-core CPUs.

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TYPE Journal Article YEAR 2016
DOIOSTI
Results 101–150 of 202
Results 101–150 of 202