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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Parallel Particle Advection Bake-Off for Scientific Visualization Workloads

There are multiple algorithms for parallelizing particle advection for scientific visualization workloads. While many previous studies have contributed to the understanding of individual algorithms, our study aims to provide a holistic understanding of how algorithms perform relative to each other on various workloads. To accomplish this, we consider four popular parallelization algorithms and run a “bake-off” study (i.e., an empirical study) to identify the best matches for each. The study includes 216 tests, going to a concurrency of up to 8192 cores and considering data sets as large as 34 billion cells with 300 million particles. Overall, our study informs three important research questions: (1) which parallelization algorithms perform best for a given workload?, (2) why?, and (3) what are the unsolved problems in parallel particle advection? In terms of findings, we find that the seeding box is the most important factor in choosing the best algorithm, and also that there is a significant opportunity for improvement in execution time, scalability, and efficiency.

Pugmire, Dave↗
DOE OSTI2025

Building a new multiphysics workflow in MOOSE: application to tritium migration, trapping and advection in TMAP8

Fusion devices are anticipated to produce and consume several kilograms of tritium per year. This rare fuel resource is both highly mobile and radioactive, making tracking inventories a priority for operation and safety. The fusion safety program at the Idaho National Laboratory has been developing the Tritium Migration and Analysis Program (TMAP), of which the latest version is a MOOSE-based application. TMAP8 is verified against its predecessors and possesses additional multi-dimensional tritium migration modeling capabilities. As we extend its capabilities towards both whole device (in multiple dimensions) and whole plant (with multiple components) simulations, the syntax of inputs must become compact, descriptive, compatible with quality assurance processes, and as error-proof as achievable. The new Physics system developed MOOSE can set up equations and instantiating them on plant components. The system permits the automatic definition of complex discretization with a consistency between object parameters achieved programmatically. The Physics system can currently instantiate the equations for heat conduction and Navier Stokes weakly compressible flow. In MOOSE-terms, it automates the definition of kernels, boundary conditions, and several core and helper materials and fields. As part of this effort, Physics classes were developed for tritium migration, trapping and advection within either a multi-dimensional Navier Stokes fluid dynamics simulation, or a 1D thermal hydraulics piping system. In this presentation, we will showcase the new syntax, its application to several verification and validation cases which were already studied using the classical TMAP8 syntax, and a demonstration of the new coupling capabilities for the migration of tritium into blanket coolant channels and the subsequent advection into the coolant loop.

70 - PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

PCG method with Strang’s circulant preconditioner for Hermitian positive definite linear system in Riesz space fractional advection–dispersion equations

In this paper, preconditioned conjugate gradient (PCG) method with Strang’s circulant preconditioner is investigated to solve the Hermitian positive definite linear systems, which is result from the Crank–Nicolson (C-N) finite difference scheme with the weighted and shifted Grünwald difference (WSGD) operators to discretize the Riesz space fractional advection–dispersion equation (RSFADE). We show that the spectrum of the preconditioned matrix is clustered around 1, and the singular values of the preconditioned matrix are uniformly bounded away from zero under a certain condition, respectively; hence the PCG method, when applied to solving the preconditioned system, converges superlinearly. Moreover, the complexity in each iteration of the PCG method is O(Nlog N) via using the fast Fourier transforms, where N is the matrix size. Numerical experiments are included to demonstrate the effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Two-Relaxation-Time Lattice Boltzmann Method and its Application to Advective-Diffusive-Reactive Transport

The lattice Boltzmann method (LBM) based on single-relaxation-time (SRT) or multiple-relaxation-time (MRT) collision operators is widely used in simulating flow and transport phenomena. The LBM based on two-relaxation-time (TRT) collision operators possesses strengths from the SRT and MRT LBMs, such as its simple implementation and good numerical stability, although tedious mathematical derivations and presentations of the TRT LBM hinder its application to a broad range of flow and transport phenomena. This paper describes the TRT LBM clearly and provides a pseudocode for easy implementation. Various transport phenomena were simulated using the TRT LBM to illustrate its applications in subsurface environments. These phenomena include advection-diffusion in uniform flow, Taylor dispersion in a pipe, solute transport in a packed column, reactive transport in uniform flow, and bacterial chemotaxis in porous media. Finally, the TRT LBM demonstrated good numerical performance in terms of accuracy and stability in predicting these transport phenomena. Therefore, the TRT LBM is a powerful tool to simulate various geophysical and biogeochemical processes in subsurface environments.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

SUPG stabilization for the nonconforming virtual element method for advection–diffusion–reaction equations

We present here the design, convergence analysis and numerical investigations of the nonconforming virtual element method with Streamline Upwind/Petrov–Galerkin (VEM-SUPG) stabilization for the numerical resolution of convection–diffusion–reaction problems in the convective-dominated regime. According to the virtual discretization approach, the bilinear form is split as the sum of a consistency and a stability term. The consistency term is given by substituting the functions of the virtual space and their gradients with their polynomial projection in each term of the bilinear form (including the SUPG stabilization term). Polynomial projections can be computed exactly from the degrees of freedom. The stability term is also built from the degrees of freedom by ensuring the correct scalability properties with respect to the mesh size and the equation coefficients. The nonconforming formulation relaxes the continuity conditions at cell interfaces and a weaker regularity condition is considered involving polynomial moments of the solution jumps at cell interface. Optimal convergence properties of the method are proved in a suitable norm, which includes contribution from the advective stabilization terms. Experimental results confirm the theoretical convergence rates.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Matrix-free subcell residual distribution for Bernstein finite element discretizations of linear advection equations

In this work, we introduce a new residual distribution (RD) framework for the design of bound-preserving high-resolution finite element schemes. The continuous and discontinuous Galerkin discretizations of the linear advection equation are modified to construct local extremum diminishing (LED) approximations. To that end, we perform mass lumping and redistribute the element residuals in a manner which guarantees the LED property. The hierarchical correction procedure for high-order Bernstein finite element discretizations involves localization to subcells and definition of bound-preserving weights for subcell contributions. Using strong stability preserving (SSP) Runge–Kutta methods for time integration, we prove the validity of discrete maximum principles under CFL-like time step restrictions. The low-order version of our method has roughly the same accuracy as the one derived from a piecewise (multi)-linear approximation on a submesh with the same nodal points. In high-order extensions, we use an element-based flux-corrected transport (FCT) algorithm which can be interpreted as a nonlinear RD scheme. The proposed LED corrections are tailor-made for matrix-free implementations which avoid the rapidly growing cost of matrix assembly for high-order Bernstein elements. The results for 1D, 2D, and 3D test problems compare favorably to those obtained with the best matrix-based approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Sylvester-preconditioned adaptive-rank implicit time integrators for advection-diffusion equations with variable coefficients

Here, we consider the adaptive-rank integration of multi-dimensional time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled with high-order diagonally implicit Runge-Kutta temporal schemes. The discrete equation is a generalized Sylvester equation (GSE), which we solve with a projection-based adaptive-rank algorithm structured around two key strategies: (i) constructing dimension-wise subspaces using a novel atypical extended Krylov strategy, and (ii) efficiently solving the basis coefficient matrix with a preconditioned GMRES solver. The low-rank decomposition is performed in 2D using SVD and with high-order SVD (HOSVD) in 3D to represent the tensor in a compressed Tucker format. For d-dimensional problems (here, d = 2 or 3), the computational complexity and memory storage of the approach are found numerically to scale as and $\mathscr{O}(Nr^2) + \mathscr{O} (r^{d+1})$ and $\mathscr{O}(Nr) + \mathscr{O} (r^{d})$, respectively, with the one-dimensional resolution and the maximal rank during the Krylov iteration (which we find to be largely independent of on our numerical examples). We present numerical examples that illustrate the advertised properties of the algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Approximation rates of DeepONets for learning operators arising from advection–diffusion equations

Here we present the analysis of approximation rates of operator learning in Chen and Chen (1995) and Lu et al. (2021), where continuous operators are approximated by a sum of products of branch and trunk networks. In this work, we consider the rates of learning solution operators from both linear and nonlinear advection–diffusion equations with or without reaction. We find that the approximation rates depend on the architecture of branch networks as well as the smoothness of inputs and outputs of solution operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Evaluation of Stratocumulus Evolution Under Contrasting Temperature Advections in CESM2 Through a Lagrangian Framework

Abstract This study leveraged a Lagrangian framework to examine the evolution of stratocumulus clouds under cold and warm advections (CADV and WADV) in the Community Earth System Model 2 (CESM2) against observations. We found that CESM2 simulates a too rapid decline in low‐cloud fraction (LCF) and cloud liquid water path (CLWP) under CADV conditions, while it better aligns closely with observed LCF under WADV conditions but overestimates the increase in CLWP. Employing an explainable machine learning approach, we found that too rapid decreases in LCF and CLWP under CADV conditions are related to overestimated drying effects induced by sea surface temperature, whereas the substantial increase in CLWP under WADV conditions is associated with the overestimated moistening effects due to free‐tropospheric moisture and surface winds. Our findings suggest that overestimated drying effects of sea surface temperature on cloud properties might be one of crucial causes for the high equilibrium climate sensitivity in CESM2.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

STANDING SHOCK INSTABILITY IN ADVECTION-DOMINATED ACCRETION FLOWS

Depending on the values of the energy and angular momentum per unit mass in the gas supplied at large radii, inviscid advection-dominated accretion flows can display velocity profiles with either preshock deceleration or preshock acceleration. Nakayama has shown that these two types of flow configurations are expected to have different stability properties. By employing the Chevalier and Imamura linearization method and the Nakayama instability boundary conditions, we discover that there are regions of parameter space where disks/shocks with outflows can be stable or unstable. In regions of instability, we find that preshock deceleration is always unstable to the zeroth mode with zero frequency of oscillation, but is always stable to the fundamental mode and overtones. Furthermore, we also find that preshock acceleration is always unstable to the zeroth mode and that the fundamental mode and overtones become increasingly less stable as the shock location moves away from the horizon when the disk half-height expands above ∼12 gravitational radii at the shock radius. In regions of stability, we demonstrate the zeroth mode to be stable for the velocity profiles that exhibit preshock acceleration and deceleration. Moreover, for models that are linearly unstable, our model suggests the possible existence of quasi-periodic oscillations (QPOs) with ratios 2:3 and 3:5. These ratios are believed to occur in stellar and supermassive black hole candidates, for example, in GRS 1915+105 and Sgr A*, respectively. We expect that similar QPO ratios also exist in regions of stable shocks.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2022

Continuum Covariance Propagation for Understanding Variance Loss in Advective Systems

Motivated by the spurious variance loss encountered during covariance propagation in atmospheric and other large-scale data assimilation systems, we consider the problem for state dynamics governed by the continuity and related hyperbolic partial differential equations. This loss of variance has been attributed to reduced-rank representations of the covariance matrix, as in ensemble methods for example, or else to the use of dissipative numerical methods. Through a combination of analytical work and numerical experiments, we demonstrate that significant variance loss, as well as gain, typically occurs during covariance propagation, even at full rank. The cause of this unusual behavior is a discontinuous change in the continuum covariance dynamics as correlation lengths become small, for instance in the vicinity of sharp gradients in the velocity field. This discontinuity in the covariance dynamics arises from hyperbolicity: the diagonal of the kernel of the covariance operator is a characteristic surface for advective dynamics. Our numerical experiments demonstrate that standard numerical methods for evolving the state are not adequate for propagating the covariance, because16they do not capture the discontinuity in the continuum covariance dynamics as correlations lengths tend to zero. Our analytical and numerical results show that this leads to significant, spurious variance loss in certain regions, and gain in others. The results suggest that developing local covariance propagation methods designed specifically to capture covariance evolution near the diagonal may prove a useful alternative to current methods of covariance propagation.

covariance propagation↗
DOE OSTI2018

A method of alternating characteristics with application to advection-dominated environmental systems

We present a numerical method for solving a class of systems of partial differential equations (PDEs) that arises in modeling environmental processes undergoing advection and biogeochemical reactions. The salient feature of these PDEs is that all partial derivatives appear in linear expressions. As a result, the system can be viewed as a set of ordinary differential equations (ODEs), albeit each one along a different characteristic. The method then consists of alternating between equations and integrating each one step-wise along its own characteristic, thus creating a customized grid on which solutions are computed. Since the solutions of such PDEs are generally smoother along their characteristics, the method offers the potential of using larger time steps while maintaining accuracy and reducing numerical dispersion. The advantages in efficiency and accuracy of the proposed method are demonstrated in two illustrative examples that simulate depth-resolved reactive transport and soil carbon cycling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Optimization-based, property-preserving finite element methods for scalar advection equations and their connection to Algebraic Flux Correction

In this paper, we continue our efforts to exploit optimization and control ideas as a common foundation for the development of property-preserving numerical methods. Here we focus on a class of scalar advection equations whose solutions have fixed mass in a given Eulerian region and constant bounds in any Lagrangian volume. Our approach separates discretization of the equations from the preservation of their solution properties by treating the latter as optimization constraints. This relieves the discretization process from having to comply with additional restrictions and makes stability and accuracy the sole considerations in its design. A property-preserving solution is then sought as a state that minimizes the distance to an optimally accurate but not property-preserving target solution computed by the scheme, subject to constraints enforcing discrete proxies of the desired properties. Furthermore, we consider two such formulations in which the optimization variables are given by the nodal solution values and suitably defined nodal fluxes, respectively. A key result of the paper reveals that a standard Algebraic Flux Correction (AFC) scheme is a modified version of the second formulation obtained by shrinking its feasible set to a hypercube. In conclusion, we present numerical studies illustrating the optimization-based formulations and comparing them with AFC

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

The influence of permeability anisotropy in the upper ocean crust on advective heat transport by a ridge-flank hydrothermal system

Here, in this study, we highlight the importance of permeability anisotropy on the hydrogeological regime of a ridge-flank hydrothermal system. Our study site, North Pond, is a marine sediment pond on ~8 Ma seafloor in the North Atlantic, and represents a low-temperature, end-member ridge-flank hydrothermal system. Previous simulations of North Pond elucidated long-standing hypotheses concerning hydrothermal fluid and heat transport in the upper volcanic crust but failed to fully explain observed patterns of seafloor heat flux in this area. Here we use variography, a geostatistical method, to quantify relations between seafloor heat-flux measurements, and coupled numerical simulations of fluid and heat flow to simulate the hydrogeologic regime. Directional variography shows that heat-flux observations are correlated along-strike of the regional crustal fabric. Three-dimensional simulations that include permeability anisotropy are able to replicate seafloor heat-flux patterns across North Pond. The simulations that result in the best match to thermal data incorporate permeability anisotropy in the horizontal plane. We find that the feedback between permeability anisotropy and the asymmetric geometry of North Pond combine to promote advective removal of heat and mass within the crustal aquifer. These findings suggest that permeability anisotropy in the oceanic crust may influence ridge-flank hydrothermal circulation more broadly.

58 GEOSCIENCES↗
DOE OSTI2020

Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements

Physics-informed neural networks (PINNs) were recently proposed in [18] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution, while a PDE-induced NN is coupled to the solution NN, and all differential operators are treated using automatic differentiation. Here, we first employ the standard PINN and a stochastic version, sPINN, to solve forward and inverse problems governed by a non-linear advection–diffusion–reaction (ADR) equation, assuming we have some sparse measurements of the concentration field at random or pre-selected locations. Subsequently, we attempt to optimise the hyper-parameters of sPINN by using the Bayesian optimisation method (meta-learning) and compare the results with the empirically selected hyper-parameters of sPINN. In particular, for the first part in solving the inverse deterministic ADR, we assume that we only have a few high-fidelity measurements, whereas the rest of the data is of lower fidelity. Hence, the PINN is trained using a composite multi-fidelity network, first introduced in [12], that learns the correlations between the multi-fidelity data and predicts the unknown values of diffusivity, transport velocity and two reaction constants as well as the concentration field. For the stochastic ADR, we employ a Karhunen–Loève (KL) expansion to represent the stochastic diffusivity, and arbitrary polynomial chaos (aPC) to represent the stochastic solution. Correspondingly, we design multiple NNs to represent the mean of the solution and learn each aPC mode separately, whereas we employ a separate NN to represent the mean of diffusivity and another NN to learn all modes of the KL expansion. For the inverse problem, in addition to stochastic diffusivity and concentration fields, we also aim to obtain the (unknown) deterministic values of transport velocity and reaction constants. The available data correspond to 7spatial points for the diffusivity and 20 space–time points for the solution, both sampled 2000 times. We obtain good accuracy for the deterministic parameters of the order of 1–2% and excellent accuracy for the mean and variance of the stochastic fields, better than three digits of accuracy. In the second part, we consider the previous stochastic inverse problem, and we use Bayesian optimisation to find five hyper-parameters of sPINN, namely the width, depth and learning rate of two NNs for learning the modes. Here, we obtain much deeper and wider optimal NNs compared to the manual tuning, leading to even better accuracy, i.e., errors less than 1% for the deterministic values, and about an order of magnitude less for the stochastic fields.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Predictive Inverse Model for Advective Heat Transfer in a Short–Circuited Fracture: Dimensional Analysis, Machine Learning, and Field Demonstration

Identifying fluid flow maldistribution in planar geometries is a well–established problem in subsurface science/engineering. Of particular importance to the thermal performance of enhanced (or “engineered”) geothermal systems is identifying the existence of nonuniform (i.e., heterogeneous) permeability and subsequently predicting advective heat transfer. Here, machine learning via a genetic algorithm (GA) identifies the spatial distribution of an unknown permeability field in a two–dimensional Hele–Shaw geometry (i.e., parallel plates). The inverse problem is solved by minimizing the L2 norm between simulated residence time distribution (RTD) and measurements of an inert tracer breakthrough curve (BTC) (C–Dot nanoparticle). Principal component analysis (PCA) of spatially correlated permeability fields enabled reduction of the parameter space by more than a factor of 10 and restricted the inverse search to reservoir–scale permeability variations. Thermal experiments and tracer tests conducted at the mesoscale Altona Field Laboratory (AFL) demonstrate that the method accurately predicts the effects of extreme flow channeling on heat transfer in a single bedding–plane rock fracture. However, this is only true when the permeability distributions provide adequate matches to both tracer RTD and frictional pressure loss. Without good agreement to frictional pressure loss, it is still possible to match a simulated RTD to measurements, but subsequent predictions of heat transfer are grossly inaccurate. Here, the results of this study suggest that it is possible to anticipate the thermal effects of flow maldistribution, but only if both simulated RTDs and frictional pressure loss between fluid inlets and outlets are in good agreement with measurements.

42 ENGINEERING↗
DOE OSTI2024

Kinetic corrections to heat-flow and Nernst advection for laser heated plasmas

Reduced models for approximating the impact of kinetic electron behavior on the transport of thermal energy and magnetic field are investigated. The thermal flux limiter has improved agreement with Vlasov–Fokker–Planck data when a harmonic form is used that adjusts the electron mean free path to account for electron–electron collisions; these results apply to both unmagnetized and magnetized plasmas. Once a magnetic field is incorporated, the mean free path should also be modified using the electron gyroradius. A flux limiter on Nernst advection of magnetic fields is also required; a form that limits Nernst by the same fraction as the thermal heat-flow best reproduces kinetic simulations. A flux limiter form for the cross terms (Righi–Leduc and cross-gradient-Nernst) is also suggested. Hohlraum simulations relevant to fusion experiments on the National Ignition Facility are found to be sensitive to all of these details.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Quantum dynamics simulation of the advection-diffusion equation

The advection-diffusion equation is simulated via several quantum algorithms. Three formulations are considered: (1) Trotterization, (2) variational quantum time evolution (VarQTE), and (3) adaptive variational quantum dynamics simulation (AVQDS). These schemes were originally developed for the Hamiltonian simulation of many-body quantum systems. The finite-difference discretized operator of the transport equation is formulated as a Hamiltonian and solved without the need for ancillary qubits. Computations are conducted on a quantum simulator (IBM Qiskit Aer) and a superconducting quantum hardware (IBM Fez). The former emulates the latter without the noise. The actual hardware implementation experiences significant noise. The results of the quantum simulator are compared with data from direct numerical simulation (DNS) with infidelities of the order 10 −5 . In the quantum simulator, Trotterization is observed to have the lowest infidelity and is suitable for fault-tolerant computation. The AVQDS algorithm requires the lowest gate count and circuit depth. The VarQTE algorithm is the next best in terms of gate counts, but the number of its optimization variables is directly proportional to the number of qubits. Due to current hardware limitations, Trotterization cannot be implemented, as it has an overwhelmingly large number of operations. Meanwhile, AVQDS and VarQTE can be executed at the hardware level. These algorithms present a new paradigm for computational transport phenomena on quantum computers.

Alipanah, Hirad [Univ. of Pittsburgh, PA (United S↗