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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Block-Structured Operator Inference for Coupled Multiphysics Model Reduction

This work presents a block-structured formulation of Operator Inference as a way to learn structured reduced-order models for multiphysics systems. The approach specifies the governing equation structure for each physics component and the structure of the coupling terms. Once the multiphysics structure is specified, the reduced-order model is learned from snapshot data following the nonintrusive Operator Inference methodology. In addition to preserving physical system structure, which in turn permits preservation of system properties such as stability and second-order structure, the block-structured approach has the advantages of reducing the overall dimensionality of the learning problem and admitting tailored regularization for each physics component. The numerical advantages of the block-structured formulation over a monolithic Operator Inference formulation are demonstrated for aeroelastic analysis, which couples aerodynamic and structural models. For the benchmark test case of the AGARD 445.6 wing, block-structured Operator Inference provides an average 20% online prediction speedup over monolithic Operator Inference across subsonic and supersonic flow conditions in both the stable and fluttering parameter regimes while preserving the accuracy achieved with monolithic Operator Inference.

42 ENGINEERING↗
NASA NTRS2001

Development of a Hybrid RANS/LES Method for Compressible Mixing Layer Simulations

A hybrid method has been developed for simulations of compressible turbulent mixing layers. Such mixing layers dominate the flows in exhaust systems of modem day aircraft and also those of hypersonic vehicles currently under development. The hybrid method uses a Reynolds-averaged Navier-Stokes (RANS) procedure to calculate wall bounded regions entering a mixing section, and a Large Eddy Simulation (LES) procedure to calculate the mixing dominated regions. A numerical technique was developed to enable the use of the hybrid RANS/LES method on stretched, non-Cartesian grids. The hybrid RANS/LES method is applied to a benchmark compressible mixing layer experiment. Preliminary two-dimensional calculations are used to investigate the effects of axial grid density and boundary conditions. Actual LES calculations, performed in three spatial directions, indicated an initial vortex shedding followed by rapid transition to turbulence, which is in agreement with experimental observations.

Georgiadis, Nicholas J.↗
DOE OSTI2014

Results from the US-German Benchmark Initiative for FY14

Sandia recently joined the third phase of and is a contributing partner to a U.S.-German “Joint Project” entitled “Comparison of current constitutive models and simulation procedures on the basis of model calculations of the thermo-mechanical behavior and healing of rock salt.” The first goal of the project is to check the ability of numerical modeling tools to correctly describe the relevant deformation phenomena in rock salt under various influences. Achieving this goal will lead to increased confidence in the results of numerical simulations related to the secure storage of radioactive wastes in rock salt, thereby enhancing the acceptance of the results. These results may ultimately be used to make various assertions regarding both the stability analysis of an underground repository in salt during the operating phase and the long-term integrity of the geological barrier against the release of harmful substances into the biosphere in the post-operating phase. Among the numerical modeling tools are constitutive models that are used in computer simulations for the description of the thermal, mechanical, and hydraulic behavior of the host rock under various influences and for the long-term prediction of this behavior into the future. A second goal of the project is to investigate and demonstrate the possibilities for further potential development and improvement of these constitutive models. This report summarizes the efforts undertaken during FY14 in support of these international benchmark calculations of field experiments.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2017

Highly Efficient and Scalable Compound Decomposition of Two-Electron Integral Tensor and Its Application in Coupled Cluster Calculations

The representation and storage of two-electron integral tensors are vital in large- scale applications of accurate electronic structure methods. Low-rank representation and efficient storage strategy of integral tensors can significantly reduce the numerical overhead and consequently time-to-solution of these methods. In this paper, by combining pivoted incomplete Cholesky decomposition (CD) with a follow-up truncated singular vector decomposition (SVD), we develop a decomposition strategy to approximately represent the two-electron integral tensor in terms of low-rank vectors. A systematic benchmark test on a series of 1-D, 2-D, and 3-D carbon-hydrogen systems demonstrates high efficiency and scalability of the compound two-step decomposition of the two-electron integral tensor in our implementation. For the size of atomic basis set N_b ranging from ~ 100 up to ~ 2, 000, the observed numerical scaling of our implementation shows O(N_b^{2.5~3}) versus O(N_b^{3~4}) of single CD in most of other implementations. More importantly, this decomposition strategy can significantly reduce the storage requirement of the atomic-orbital (AO) two-electron integral tensor from O(N_b^4) to O(N_b^2 log_{10}(N_b)) with moderate decomposition thresholds. The accuracy tests have been performed using ground- and excited-state formulations of coupled- cluster formalism employing single and double excitations (CCSD) on several bench- mark systems including the C_{60} molecule described by nearly 1,400 basis functions. The results show that the decomposition thresholds can be generally set to 10^{-4} to 10^{-3} to give acceptable compromise between efficiency and accuracy.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Investigation of Natural Circulation Instability and Transients in Passively Safe Small Modular Reactors

The NEUP funded project, NEUP-3496, aims to experimentally investigate two-phase natural circulation flow instability that could occur in Small Modular Reactors (SMRs), especially for natural circulation SMRs. The objective has been achieved by systematically performing tests to study the general natural circulation instability characteristics and the natural circulation behavior under start-up or design basis accident conditions. Experimental data sets highlighting the effect of void reactivity feedback as well as the effect of power ramp-up rate and system pressure have been used to develop a comprehensive stability map. The safety analysis code, RELAP5, has been used to evaluate experimental results and models. Improvements to the constitutive relations for flashing have been made in order to develop a reliable analysis tool. This research has been focusing on two generic SMR designs, i.e. a small modular Simplified Boiling Water Reactor (SBWR) like design and a small integral Pressurized Water Reactor (PWR) like design. A BWR-type natural circulation test facility was firstly built based on the three-level scaling analysis of the Purdue Novel Modular Reactor (NMR) with an electric output of 50 MWe, namely NMR-50, which represents a BWR-type SMR with a significantly reduced reactor pressure vessel (RPV) height. The experimental facility was installed with various equipment to measure thermalhydraulic parameters such as pressure, temperature, mass flow rate and void fraction. Characterization tests were performed before the startup transient tests and quasi-steady tests to determine the loop flow resistance. The control system and data acquisition system were programmed with LabVIEW to realize the realtime control and data storage. The thermal-hydraulic and nuclear coupled startup transients were performed to investigate the flow instabilities at low pressure and low power conditions for NMR-50. Two different power ramps were chosen to study the effect of startup power density on the flow instability. The experimental startup transient results showed the existence of three different flow instability mechanisms, i.e., flashing instability, condensation induced flow instability, and density wave oscillations. In addition, the void-reactivity feedback did not have significant effects on the flow instability during the startup transients for NMR-50. ii Several initial startup procedures with different power ramp rates were experimentally investigated to eliminate the flow instabilities observed from the startup transients. Particularly, the very slow startup transient and pressurized startup transient tests were performed and compared. It was found that the very slow startup transients by applying very small power density can eliminate the flashing oscillations in the single-phase natural circulation and stabilize the flow oscillations in the phase of net vapor generation. The initially pressurized startup procedure was tested to eliminate the flashing instability during the startup transients as well. The pressurized startup procedure included the initial pressurization, heat-up, and venting process. The startup transient tests showed that the pressurized startup procedure could eliminate the flow instability during the transition from single-phase flow to two-phase flow at low pressure conditions. The experimental results indicated that both startup procedures were applicable to the initial startup of NMR. However, the pressurized startup procedures might be preferred due to short operating hours required. In order to have a deeper understanding of natural circulation flow instability, the quasi-steady tests were performed using the test facility installed with preheater and subcooler. The effect of system pressure, core inlet subcooling, core power density, inlet flow resistance coefficient, and void reactivity feedback were investigated in the quasi-steady state tests. The experimental stability boundaries were determined between unstable and stable flow conditions in the dimensionless stability plane of inlet subcooling number and Zuber number. To predict the stability boundary theoretically, linear stability analysis in the frequency domain was performed at four sections of the natural circulation test loop. The flashing phenomena in the chimney section was considered as an axially uniform heat source. And the dimensionless characteristic equation of the pressure drop perturbation was obtained by considering the void fraction effect and outlet flow resistance in the core section. The theoretical flashing boundary showed some discrepancies with previous experimental data from the quasi-steady state tests. In the future, thermal non-equilibrium was recommended to improve the accuracy of flashing instability boundary. As another part of the funded research, flow instabilities of a PWR-type SMR under low pressure and low power conditions were investigated experimentally as well. The NuScale reactor design was selected as the prototype for the PWR-type SMR. In order to experimentally study the natural circulation behavior of NuScale iii reactor during accidental scenarios, detailed scaling analyses are necessary to ensure that the scaled phenomena could be obtained in a laboratory test facility. The three-level scaling method is used as well to obtain the scaling ratios derived from various non-dimensional numbers. The design of the ideally scaled facility (ISF) was initially accomplished based on these scaling ratios. Then the engineering scaled facility (ESF) was designed and constructed based on the ISF by considering engineering limitations including laboratory space, pipe size, and pipe connections etc. PWR-type SMR experiments were performed in this well-scaled test facility to investigate the potential thermal hydraulic flow instability during the blowdown events, which might occur during the loss of coolant accident (LOCA) and loss of heat sink accident (LOHS) of the prototype PWR-type SMR. Two kinds of experiments, normal blowdown event and cold blowdown event, were experimentally investigated and compared with code predictions. The normal blowdown event was experimentally simulated since an initial condition where the pressure was lower than the designed pressure of the experiment facility, while the code prediction of blowdown started from the normal operation condition. Important thermal hydraulic parameters including reactor pressure vessel (RPV) pressure, containment pressure, local void fraction and temperature, pressure drop and natural circulation flow rate were measured and analyzed during the blowdown event. The pressure and water level transients are similar to the experimental results published by NuScale [51], which proves the capability of current loop in simulating the thermal hydraulic transient of real PWR-type SMR. During the 20000s blowdown experiment, water level in the core was always above the active fuel assemble during the experiment and proved the safety of natural circulation cooling and water recycling design of PWR-type SMR. Besides, pressure, temperature, and water level transient can be accurately predicted by RELAP5 code. However, the oscillations of natural circulation flow rate, water level and pressure drops were observed during the blowdown transients. This kind of flow oscillations are related to the water level and the location upper plenum, which is a path for coolant flow from chimney to steam generator and down comer. In order to investigate the transients start from the opening of ADS valve in both experimental and numerical way, the cold blow-down experiment is conducted. For the cold blowdown event, different from setting both reactor iv pressure vessel (RPV) and containment at high temperature and pressure, only RPV was heated close to the highest designed pressure and then open the ADS valve, same process was predicted using RELAP5 code. By doing cold blowdown experiment, the entire transients from the opening of ADS can be investigated by code and benchmarked with experimental data. Similar flow instability observed in the cold blowdown experiment. The comparison between code prediction and experiment data showed that the RELAP5 code can successfully predict the pressure void fraction and temperature transient during the cold blowdown event with limited error, but numerical instability exists in predicting natural circulation flow rate. Besides, the code is lack of capability in predicting the water level related flow instability observed in experiments.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity

In this paper, we present a first-order Stress-Hybrid Virtual Element Method (SH-VEM) on six-noded triangular meshes for linear plane elasticity. Here, we adopt the Hellinger–Reissner variational principle to construct a weak equilibrium condition and a stress based projection operator. In each element, the stress projection operator is expressed in terms of the nodal displacements, which leads to a displacement based formulation. This stress-hybrid approach assumes a globally continuous displacement field while the stress field is discontinuous across each element. The stress field is initially represented by divergence-free tensor polynomials based on Airy stress functions, but we also present a formulation that uses a penalty term to enforce the element equilibrium conditions, referred to as the Penalty Stress-Hybrid Virtual Element Method (PSH-VEM). Numerical results are presented for PSH-VEM and SH-VEM, and we compare their convergence to the composite triangle FEM and B-bar VEM on benchmark problems in linear elasticity. The SH-VEM converges optimally in the L 2 norm of the displacement, energy seminorm, and the L 2 norm of hydrostatic stress. Furthermore, the results reveal that PSH-VEM converges in most cases at a faster rate than the expected optimal rate, but it requires the selection of a suitably chosen penalty parameter.

42 ENGINEERING↗
DOE OSTI2019

A Low-Rank Solver for the Navier--Stokes Equations with Uncertain Viscosity

In this work, we study an iterative low-rank approximation method for the solution of the steady-state stochastic Navier--Stokes equations with uncertain viscosity. The method is based on linearization schemes using Picard and Newton iterations and stochastic finite element discretizations of the linearized problems. For computing the low-rank approximate solution, we adapt the nonlinear iterations to an inexact and low-rank variant, where the solution of the linear system at each nonlinear step is approximated by a quantity of low rank. This is achieved by using a tensor variant of the GMRES method as a solver for the linear systems. We explore the inexact low-rank nonlinear iteration with a set of benchmark problems, using a model of flow over an obstacle, under various configurations characterizing the statistical features of the uncertain viscosity, and we demonstrate its effectiveness by extensive numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Summary of FY15 Results of Benchmark Modeling Activities

Sandia is participating in the third phase of and is a contributing partner to a U.S.- German “Joint Project” entitled “Comparison of current constitutive models and simulation procedures on the basis of model calculations of the thermo-mechanical behavior and healing of rock salt.” The first goal of the project is to check the ability of numerical modeling tools to correctly describe the relevant deformation phenomena in rock salt under various influences. Achieving this goal will lead to increased confidence in the results of numerical simulations related to the secure storage of radioactive wastes in rock salt, thereby enhancing the acceptance of the results. These results may ultimately be used to make various assertions regarding both the stability analysis of an underground repository in salt, during the operating phase, and the long-term integrity of the geological barrier against the release of harmful substances into the biosphere, in the post-operating phase. Among the numerical modeling tools required to address this are constitutive models that are used in computer simulations for the description of the thermal, mechanical, and hydraulic behavior of the host rock under various influences and for the long-term prediction of this behavior into the future. A second goal of the project is to investigate and demonstrate the possibilities for further potential development and improvement of these constitutive models. This report summarizes the efforts undertaken during FY15 in support of this international U.S.-German benchmark initiative.

58 GEOSCIENCES↗
NASA NTRS1997

Second Computational Aeroacoustics (CAA) Workshop on Benchmark Problems

The proceedings of the Second Computational Aeroacoustics (CAA) Workshop on Benchmark Problems held at Florida State University are the subject of this report. For this workshop, problems arising in typical industrial applications of CAA were chosen. Comparisons between numerical solutions and exact solutions are presented where possible.

Tam, C. K. W.↗
DOE OSTI2012

Dense LU Factorization on Multicore Supercomputer Nodes

Dense LU factorization is a prominent benchmark used to rank the performance of supercomputers. Many implementations, including the reference code HPL, use block-cyclic distributions of matrix blocks onto a two-dimensional process grid. The process grid dimensions drive a trade-off between communication and computation and are architecture- and implementation-sensitive. We show how the critical panel factorization steps can be made less communication-bound by overlapping asynchronous collectives for pivot identification and exchange with the computation of rank-k updates. By shifting this trade-off, a modified block-cyclic distribution can beneficially exploit more available parallelism on the critical path, and reduce panel factorization's memory hierarchy contention on now-ubiquitous multi-core architectures. The missed parallelism in traditional block-cyclic distributions arises because active panel factorization, triangular solves, and subsequent broadcasts are spread over single process columns or rows (respectively) of the process grid. Increasing one dimension of the process grid decreases the number of distinct processes in the other dimension. To increase parallelism in both dimensions, periodic 'rotation' is applied to the process grid to recover the row-parallelism lost by a tall process grid. During active panel factorization, rank-1 updates stream through memory with minimal reuse. In a column-major process grid, the performance of this access pattern degrades as too many streaming processors contend for access to memory. A block-cyclic mapping in the more popular row-major order does not encounter this problem, but consequently sacrifices node and network locality in the critical pivoting steps. We introduce 'striding' to vary between the two extremes of row- and column-major process grids. As a test-bed for further mapping experiments, we describe a dense LU implementation that allows a block distribution to be defined as a general function of block to processor. Other mappings can be tested with only small, local changes to the code.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2020

Team Dynamics and Development in Chemical Emergency Response

This presentation is focused on Team Dynamics and Development in Chemical Emergency Response. While regulatory requirements focus on defining the performance requirements associated with this category of response team, there is very little information and guidance provided to team leaders on the criticality of team dynamics of development in performance. These elements are essential to achieving successfully integrated team operations. NREL has worked to expand chemical response team participation to include operational personnel from research, support operations, and various technical areas. Since this team expansion has encompassed integration from numerous levels and areas within the organization, a systematic approach was adopted to better understand how organization culture, dynamics, and diversity can be used to be more effective. Benchmarking other organizations and reviewing relevant literature assisted in laying the foundation to develop a strategy that incorporates team development principles, dynamics, and leadership practices to increase the effectiveness of emergency response operations. This presentation focuses on the valuable lessons learned and the team-based approaches that can be used to develop a successful response team.

emergency response↗
DOE OSTI2017

Adaptive local basis set for Kohn–Sham density functional theory in a discontinuous Galerkin framework II: Force, vibration, and molecular dynamics calculations

Recently, we have proposed the adaptive local basis set for electronic structure calculations based on Kohn–Sham density functional theory in a pseudopotential framework. The adaptive local basis set is efficient and systematically improvable for total energy calculations. In this paper, we present the calculation of atomic forces, which can be used for a range of applications such as geometry optimization and molecular dynamics simulation. We demonstrate that, under mild assumptions, the computation of atomic forces can scale nearly linearly with the number of atoms in the system using the adaptive local basis set. We quantify the accuracy of the Hellmann–Feynman forces for a range of physical systems, benchmarked against converged planewave calculations, and find that the adaptive local basis set is efficient for both force and energy calculations, requiring at most a few tens of basis functions per atom to attain accuracies required in practice. Since the adaptive local basis set has implicit dependence on atomic positions, Pulay forces are in general nonzero. However, we find that the Pulay force is numerically small and systematically decreasing with increasing basis completeness, so that the Hellmann–Feynman force is sufficient for basis sizes of a few tens of basis functions per atom. We verify the accuracy of the computed forces in static calculations of quasi-1D and 3D disordered Si systems, vibration calculation of a quasi-1D Si system, and molecular dynamics calculations of H{sub 2} and liquid Al–Si alloy systems, where we show systematic convergence to benchmark planewave results and results from the literature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Extending TOUGH + HYDRATE with a parallel particle transport simulator: numerical investigation of sand production during gas production from hydrate deposits

A new parallel code for simulating particle transport in porous media is integrated with the TOUGH + HYDRATE simulator to investigate sand production associated with gas production from unconsolidated gas hydrate-bearing sediments (HBS). Here, the parallel coupled simulator is named THMPT and uses the integral finite difference method to describe the Darcian and non-Darcian flow of fluids and heat transport, the finite element method to describe the associated geomechanical changes, and the discrete element method to track the trajectory of individual sand particles within the HBS. The THMPT simulator is written in Fortran, incorporates multiple optimized algorithms, and can comprehensively address the coupled flow, thermal, chemical, geomechanical, and particle transport processes that characterize the system behaviors during gas production from HBS. The simulator can capture all processes involved in sand particle transport in porous media, including sand detachment, collision, clogging (i.e., bridging), and migration. A benchmark case study of sand production in the course of depressurization-induced gas production from a representative HBS reveals various distinct microscopic particle migration mechanisms and the adverse impact of sand particle detachment, transport, and clogging. The numerical investigation also examines the effect of bottomhole pressure on mitigating sand production. The simulation results indicate that sand clogging near the wellbore significantly reduces permeability, decreasing gas production by at least 50%. Lastly, the efficiency of gravel packing in mitigating sand production is numerically evaluated, revealing that the structure of the porous media appears to profoundly influence the macroscopic motion behavior of sand particles and sand clogging characteristics.

discrete element method↗
DOE OSTI2019

Long-duration direct drive hydrodynamics experiments on the National Ignition Facility: Platform development and numerical modeling with CHIC

Here, we report on a novel planar direct-drive platform for hydrodynamics experiments on the National Ignition Facility (NIF). Its commissioning has been performed as part of the NIF Discovery Science Program. This platform enables the use of a 30 ns drive at an average intensity of 200 TW/cm 2 , creating a planar shock and ablation front over a 2 mm radius. To benchmark the performance of this design, the planarity of both the shock and ablation fronts has been measured between 26 ns and 28 ns after the start of the laser drive in a 3 mm-thick CH foil. The platform was then used to measure late-time Rayleigh-Taylor instability (RTI) growth at the ablation front for a 2D-rippled 300 μm-thick CH foil. Simultaneously, a numerical platform has been developed with the CHIC radiation hydrodynamics code at the CELIA laboratory. The CHIC numerical platform allows, for the first time, a complete simulation of the experiments over 30 ns to be performed. Large-scale simulations recover the trajectory and the 2D RTI growth measurements. They are additionally compared with half-mode simulations performed with identical parameters. We demonstrate that both numerical techniques fit with analytical modeling of RTI growth and discuss plans for future campaigns.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Benchmark oxygen-oxygen pair-distribution function of ambient water from x-ray diffraction measurements with a wide Q-range

Four recent x-ray diffraction measurements of ambient liquid water are reviewed here. Each of these measurements represents a significant development of the x-ray diffraction technique applied to the study of liquid water. Sources of uncertainty from statistical noise, Q-range, Compton scattering, and self-scattering are discussed. The oxygen-hydrogen contribution to the measured x-ray scattering pattern was subtracted using literature data to yield an experimental determination, with error bars, of the oxygen-oxygen pair-distribution function, g{sub OO}(r), which essentially describes the distribution of molecular centers. The extended Q-range and low statistical noise of these measurements has significantly reduced truncation effects and related errors in the g{sub OO}(r) functions obtained. From these measurements and error analysis, the position and height of the nearest neighbor maximum in g{sub OO}(r) were found to be 2.80(1) A and 2.57(5) respectively. Numerical data for the coherent differential x-ray scattering cross-section I{sub X}(Q), the oxygen-oxygen structure factor S{sub OO}(Q), and the derived g{sub OO}(r) are provided as benchmarks for calibrating force-fields for water.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Incorporating Full Elastodynamic Effects and Dipping Fault Geometries in Community Code Verification Exercises for Simulations of Earthquake Sequences and Aseismic Slip (SEAS)

ABSTRACT Numerical modeling of earthquake dynamics and derived insight for seismic hazard relies on credible, reproducible model results. The sequences of earthquakes and aseismic slip (SEAS) initiative has set out to facilitate community code comparisons, and verify and advance the next generation of physics-based earthquake models that reproduce all phases of the seismic cycle. With the goal of advancing SEAS models to robustly incorporate physical and geometrical complexities, here we present code comparison results from two new benchmark problems: BP1-FD considers full elastodynamic effects, and BP3-QD considers dipping fault geometries. Seven and eight modeling groups participated in BP1-FD and BP3-QD, respectively, allowing us to explore these physical ingredients across multiple codes and better understand associated numerical considerations. With new comparison metrics, we find that numerical resolution and computational domain size are critical parameters to obtain matching results. Codes for BP1-FD implement different criteria for switching between quasi-static and dynamic solvers, which require tuning to obtain matching results. In BP3-QD, proper remote boundary conditions consistent with specified rigid body translation are required to obtain matching surface displacements. With these numerical and mathematical issues resolved, we obtain excellent quantitative agreements among codes in earthquake interevent times, event moments, and coseismic slip, with reasonable agreements made in peak slip rates and rupture arrival time. We find that including full inertial effects generates events with larger slip rates and rupture speeds compared to the quasi-dynamic counterpart. For BP3-QD, both dip angle and sense of motion (thrust versus normal faulting) alter ground motion on the hanging and foot walls, and influence event patterns, with some sequences exhibiting similar-size characteristic earthquakes, and others exhibiting different-size events. These findings underscore the importance of considering full elastodynamics and nonvertical dip angles in SEAS models, as both influence short- and long-term earthquake behavior and are relevant to seismic hazard.

Geochemistry & Geophysics↗
DOE OSTI2016

Tensor integrand reduction via Laurent expansion

We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C++ library Ninja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface Ninja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the Ninja library and interfaced it to MadLoop, which is part of the public MadGraph5_aMC@NLO framework. We performed a detailed performance study, comparing against other public reduction tools, namely CutTools, Samurai, IREGI, PJFry++ and Golem95. We find that Ninja out-performs traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool Golem95 which is however more limited and slower than Ninja. Lastly, we considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that Ninja’s performance scales well with both the rank and multiplicity of the considered process.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

An enhanced AUSM + -up scheme for high-speed compressible two-phase flows on hybrid grids

Here in this work, an enhanced AUSM + -up scheme is presented for high-speed compressible two-phase flows using a six-equation two-fluid single-pressure model. Based on the observation that the AUSM + -up flux function does not take into account relative velocity between the two phases and thus is not stable and robust for computation of two-phase flows involving interaction of strong shock waves and material interfaces, the enhancement is in the form of a volume fraction coupling term and a modification of the velocity diffusion term, both proportional to the relative velocity between the two phases. These modifications in the flux function obviate the need to employ the exact Riemann solver, leading to a significantly less expensive yet robust flux scheme. Furthermore, the Tangent of Hyperbola for INterface Capturing (THINC) scheme is used in order to provide a sharp resolution for material interfaces. A number of benchmark test cases are presented to assess the performance and robustness of the enhanced AUSM + -up scheme for compressible two-phase flows on hybrid unstructured grids. Lastly, the numerical experiments demonstrate that the enhanced AUSM + -up scheme along with THINC scheme can efficiently compute high-speed two-fluid flows such as shock–bubble interactions, while accurately capturing material interfaces.

42 ENGINEERING↗