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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Adaptive Uncertainty Quantification for Stochastic Hyperbolic Conservation Laws

Here, we propose a predictor-corrector adaptive method for the study of hyperbolic partial differential equations (PDEs) under uncertainty. Constructed around the framework of stochastic finite volume (SFV) methods, our approach circumvents sampling schemes or simulation ensembles while also preserving fundamental properties, in particular hyperbolicity of the resulting systems and conservation of the discrete solutions. Furthermore, we augment the existing SFV theory with a priori convergence results for statistical quantities, in particular push-forward densities, which we demonstrate through numerical experiments. By linking refinement indicators to regions of the physical and stochastic spaces, we drive anisotropic refinements of the discretizations, introducing new degrees of freedom where deemed profitable. To illustrate our proposed method, we consider a series of numerical examples for nonlinear hyperbolic PDEs based on Burgers’ and Euler’s equations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

A composite structured/unstructured-mesh Euler method for complex airfoil shapes

A general two-dimensional Euler zonal method has been developed for computing flows about complex airfoil geometries such as multielement and iced airfoils. The method utilizes a composite structured and unstructured grid generated using conformal mapping and Delaunay triangulation, respectively. The finite-volume Euler method is then modified to couple solutions in the zones with structured and unstructured grids. Solutions about an iced airfoil and a multielement airfoil are given as examples of applications of the scheme.

Hefazi, H.↗
DOE OSTI2024

Quantifying local and global mass balance errors in physics-informed neural networks

Physics-informed neural networks (PINN) have recently become attractive for solving partial differential equations (PDEs) that describe physics laws. By including PDE-based loss functions, physics laws such as mass balance are enforced softly in PINN. This paper investigates how mass balance constraints are satisfied when PINN is used to solve the resulting PDEs. We investigate PINN’s ability to solve the 1D saturated groundwater flow equations (diffusion equations) for homogeneous and heterogeneous media and evaluate the local and global mass balance errors. We compare the obtained PINN’s solution and associated mass balance errors against a two-point finite volume numerical method and the corresponding analytical solution. We also evaluate the accuracy of PINN in solving the 1D saturated groundwater flow equation with and without incorporating hydraulic heads as training data. We demonstrate that PINN’s local and global mass balance errors are significant compared to the finite volume approach. Tuning the PINN’s hyperparameters, such as the number of collocation points, training data, hidden layers, nodes, epochs, and learning rate, did not improve the solution accuracy or the mass balance errors compared to the finite volume solution. Mass balance errors could considerably challenge the utility of PINN in applications where ensuring compliance with physical and mathematical properties is crucial.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1989

International Conference on Numerical Methods in Fluid Dynamics, 11th, Williamsburg, VA, June 27-July 1, 1988, Proceedings

Recent advances in computational fluid dynamics (CFD) are discussed in reviews and reports. Topics addressed include CFD models in plasma dynamics, parallel computation for simulation studies, CFD for hypersonic airbreathing aircraft, multigrid methods for the steady incompressible Navier-Stokes equations, upwind differencing techniques, TV stable schemes for shock-interacting flows, Euler models of hypersonic vortex flows, parallel multilevel adaptive methods, and vortex methods for slightly viscous three-dimensional flows. Consideration is given to the accuracy of node-based solutions on irregular meshes, multigrid calculations for cascades, a finite-volume-element method for planar cavity flow, parallel heterogeneous mesh refinement for advection-diffusion equations, the convergence of the spectral-viscosity method for nonlinear conservation laws, and numerical simulations of Taylor vortices in a spherical gap.

Dwoyer, D. L.↗
NASA NTRS1986

Upwind relaxation algorithms for Euler/Navier-Stokes equations

A description of and results from a solution algorithm for the compressible Navier-Stokes equations are presented. The main features of the algorithm are second or third order accurate upwind discretization of the convection and pressure derivatives and a relaxation scheme for the unfactored implicit backward Euler time method, implemented in a finite-volume formulation. Upwind methods were successfully used to obtain solutions to the Euler equations for flows with strong shock waves. The particular upwind method being used is based on the flux vector splitting technique developed by Van Leer and both second and third order accurate discretizations were developed. Currently, the most widely used implicit solution technique for the Navier-Stokes equations use approximate factorization (AF) methods to treat multidimensional problems. The time integration scheme being used in the present algorithm corresponds to a line Gauss-Seidel relaxation method. This method produces good convergence rates for steady-state flows, and most of the algorithm was vectorized on the NASA Langley VPS 32 computer. The Navier-Stokes algorithm was tested for several two-dimensional flow problems. Solutions for the problems gave excellent results. The presented effort is directed toward the extension of the scheme to the full three-dimensional Navier-Stokes equations.

Thomas, J. L.↗
NASA NTRSDate not supplied

Edge-Based Viscous Method for Mixed-Element Node-Centered Finite-Volume Solvers

A novel, efficient, edge-based viscous (EBV) discretization method has been recently developed, implemented in a practical, unstructured-grid, node-centered, finite-volume flow solver, and applied to viscous-kernel computations that include evaluations of meanflow viscous fluxes, turbulence-model and chemistry-model diffusion terms, and the corresponding Jacobian contributions. Initially, the EBV method had been implemented for tetrahedral grids and demonstrated multifold acceleration of all viscous-kernel computations. This paper presents an extension of the EBV method for mixed-element grids. In addition to the primal edges of a given mixed-element grid, virtual edges are introduced to connect cell nodes that are not connected by a primal edge. The EBV method uses an efficient loop over all (primal and virtual) edges and features a compact discretization stencil based on the nearest neighbors. This study verifies the EBV method and assesses its efficiency on mixed-element grids by comparing the EBV solution accuracy and iterative convergence with those of well-established solutions obtained using a cell-based viscous (CBV) discretization method. The EBV solver’s memory footprint is optimized and often smaller than the memory footprint of the CBV solver. A multifold speedup is demonstrated for all viscous-kernel computations resulting in significant reduction of the time to solutions for several benchmark mixed-element-grid computations, including simulations of a flow around NASA’s juncture-flow model and a hypersonic, chemically reacting flow around a blunt body.

CFD↗
NASA NTRS1995

Methodology for simulation of unsteady flows to determine the time-dependent interference between stationary and moving boundaries

A new methodology is developed to simulate unsteady flows about prescribed and aerodynamically determined moving boundary problems. The method couples the fluid dynamics and rigid-body dynamics equations to capture the time-dependent interference between stationary and moving boundaries. The unsteady, compressible, inviscid (Euler) equations are solved on dynamic, unstructured grids by an explicit, finite-volume, upwind method. For efficiency, the grid adaptation is performed within a window around the moving object. The Eulerian equations of the rigid-body dynamics are solved by a Runge-Kutta method in a non-inertial frame of reference. The two-dimensional flow solver is validated by computing the flow past a sinusoidally-pitching airfoil and comparing these results with the experimental data. The overall methodology is used for two two-dimensional examples: the flow past an airfoil which is performing a three-degrees-of-freedom motion in a transonic freestream, and the free-fall of a store after separation from a wing-section. Then the unstructured mesh methodology is extended to three-dimensions to simulate unsteady flow past bodies in relative motion, where the trajectory is determined from the instantaneous aerodynamics. The flow solver and the adaptation scheme in three dimensions are validated by simulating the transonic, unsteady flow around a wing undergoing a forced, periodic, pitching motion, and comparing the results with the experimental data. To validate the trajectory code, the six-degrees-of-freedom motion of a store separating from a wing was computed using the experimentally determined force and moment fields, then comparing with an independently generated trajectory. Finally, the overall methodology was demonstrated by simulating the unsteady flowfield and the trajectory of a store dropped from a wing. The methodology, its computational cost notwithstanding, has proven to be accurate, automated, easy for dynamic gridding, and relatively efficient for the required man-hours.

Singh, Kamakhya Prasad↗
DOE OSTI2022

The Schwarz Alternating Method for the Seamless Coupling of Nonlinear Reduced Order Models and Full Order Models

Projection-based model order reduction allows for the parsimonious representation of full order models (FOMs), typically obtained through the discretization of a set of partial differential equations (PDEs) using conventional techniques (e.g., finite element, finite volume, finite difference methods) where the discretization may contain a very large number of degrees of freedom. As a result of this more compact representation, the resulting projection-based reduced order models (ROMs) can achieve considerable computational speedups, which are especially useful in real-time or multi-query analyses. One known deficiency of projection-based ROMs is that they can suffer from a lack of robustness, stability and accuracy, especially in the predictive regime, which ultimately limits their useful application. Another research gap that has prevented the widespread adoption of ROMs within the modeling and simulation community is the lack of theoretical and algorithmic foundations necessary for the “plug-and-play” integration of these models into existing multi-scale and multi-physics frameworks. This paper describes a new methodology that has the potential to address both of the aforementioned deficiencies by coupling projection-based ROMs with each other as well as with conventional FOMs by means of the Schwarz alternating method [41]. Leveraging recent work that adapted the Schwarz alternating method to enable consistent and concurrent multiscale coupling of finite element FOMs in solid mechanics [35, 36], we present a new extension of the Schwarz framework that enables FOM-ROM and ROM-ROM coupling, following a domain decomposition of the physical geometry on which a PDE is posed. In order to maintain efficiency and achieve computation speed-ups, we employ hyper-reduction via the Energy-Conserving Sampling and Weighting (ECSW) approach [13]. We evaluate the proposed coupling approach in the reproductive as well as in the predictive regime on a canonical test case that involves the dynamic propagation of a traveling wave in a nonlinear hyper-elastic material.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

Three-dimensional unstructured method for flows past bodies in 6-DOF relative motion

A three dimensional, unstructured-mesh methodology was developed to simulate unsteady flows past bodies in relative motion, where the trajectory was determined from the instantaneous aerodynamics. The method coupled the equations of fluid flow and those of rigid-body dynamics, and captured the time-dependent interference between stationary and moving boundaries. The unsteady, compressible Euler equations were solved on dynamic, unstructured meshes by an explicit, finite-volume, upwind method. The grid adaptation was performed within a window placed around the moving body. The Euler equations of dynamics were solved by a Runge-Kutta integration scheme. The flow solver and the adaptation scheme were validated by simulating the transonic, unsteady flow around a wing undergoing a forced, periodic pitching motion, then comparing the results with the experimental data. To validate the trajectory code, the six-degrees-of-freedom (DOF) motion of a store separating from a wing was computed using the experimentally determined force and moment fields, then comparing with an independently generated trajectory. Finally, the overall methodology was demonstrated by simulating the unsteady flowfield and the trajectory of a store dropped from a wing. The methodology, its computational cost notwithstanding, has proven to be accurate, automated, easy for dynamic gridding, and relatively efficient for the required man-hours.

Singh, K. P.↗
DOE OSTI2024

Complex scaling in finite volume

Quantum resonances, i.e., metastable states with a finite lifetime, play an important role in nuclear physics and other domains. Describing this phenomenon theoretically is generally a challenging task. In this work, we combine two established techniques to address this challenge. Complex scaling makes it possible to calculate resonances with bound-state-like methods. Finite-volume simulations exploit the fact that the infinite-volume properties of quantum systems are encoded in how discrete energy levels change as one varies the size of the volume. Herein we apply complex scaling to systems in finite periodic boxes and derive the volume dependence of states in this scenario, demonstrating with explicit examples how one can use these relations to infer infinite-volume resonance energies and lifetimes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1992

Fractional-Step, Finite-Volume Computation Of Flow

Method of solving Navier-Stokes equations of incompressible flow in general nonorthogonal curvilinear coordinates incorporates fractional-step and finite-volume approaches. Developed in continuing effort to achieve accuracy without need for excessive computation time in numerical simulation of time-dependent, three-dimensional flows bounded by surfaces of complicated shape.

Kwak, Dochan↗
DOE OSTI2023

KiT-RT: An Extendable Framework for Radiative Transfer and Therapy

Here, in this article, we present Kinetic Transport Solver for Radiation Therapy (KiT-RT), an open-source C++-based framework for solving kinetic equations in therapy applications available at https://github.com/CSMMLab/KiT-RT . This software framework aims to provide a collection of classical deterministic solvers for unstructured meshes that allow for easy extendability. Therefore, KiT-RT is a convenient base to test new numerical methods in various applications and compare them against conventional solvers. The implementation includes spherical harmonics, minimal entropy, neural minimal entropy, and discrete ordinates methods. Solution characteristics and efficiency are presented through several test cases ranging from radiation transport to electron radiation therapy. Due to the variety of included numerical methods and easy extendability, the presented open-source code is attractive for both developers, who want a basis to build their numerical solvers, and users or application engineers, who want to gain experimental insights without directly interfering with the codebase.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Hourglass control in staggered-grid hydrodynamics using virtual element stabilization techniques

Numerical simulations using the staggered-grid hydrodynamics (SGH) discretization suffer from hourglass instabilities. In this work, we develop a stabilization method to suppress the hourglass instabilities using techniques from the virtual element method (VEM). The stiffness matrix of the VEM consists of two terms: the consistency matrix which is rank deficient and the stability matrix. Here, we first show that in two dimensions and on general polygons, the stiffness matrix of the SGH is identical to the consistency matrix of the linear VEM for both the diffusion equation and the linear elasticity equation. These analyses explain the origin of the hourglass instabilities of the SGH discretization method, and establish a theoretical foundation for our proposed stabilization method by augmenting the stiffness matrix of the SGH discretization using the VEM stability matrix. Then, we present numerical examples using Lagrangian SGH simulations. The numerical experiments demonstrate that the proposed VEM stabilization method is effective at eliminating hourglass modes in the SGH discretization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Nonlinear convergence in contact mechanics: Immersed boundary finite volume

In this report we present an immersed boundary finite volume (IBM) method for simulating quasistatic contact mechanics of linearly elastic domains at small strains. In IBM, all external boundaries and internal contacts of an object are represented by embedded surfaces inside a Cartesian mesh, which need not conform to the grid lines. The contact constraints consist of the non-penetrability condition and Coulomb’s friction law, which are discretized using special interpolation stencils and enforced via penalty parameters. The resulting nonlinear system depends on displacement unknowns only. To solve it, we use the Newton method but find that it diverges frequently. To understand the divergence pattern, we analyze a simplified 2-cell problem and show that the global convergence of Newton cannot be ensured for any choice of penalty parameters. We thus propose a modified Newton solver, which guarantees convergence for the 2-cell problem and is numerically verified to converge for all the challenging simulations considered herein. While both 1 st - and 2 nd -order variants of IBM, in displacement unknowns, are proposed, the modified Newton solver applies only to the 1 st -order variant.

42 ENGINEERING↗
DOE OSTI2022

Three-dimensional Skyrme Hartree-Fock-Bogoliubov solver in coordinate-space representation

The coordinate-space representation of the Hartree-Fock-Bogoliubov theory is the method of choice to study weakly bound nuclei whose properties are affected by the quasiparticle continuum space. To describe such systems, we developed a three-dimensional Skyrme-Hartree-Fock-Bogoliubov solver HFBFFT based on the existing, highly optimized and parallelized Skyrme-Hartree-Fock code Sky3D. The code does not impose any self-consistent spatial symmetries such as mirror inversions or parity. The underlying equations are solved in HFBFFT directly in the canonical basis using the fast Fourier transform. To remedy the problems with pairing collapse, we implemented the soft energy cutoff and pairing annealing. The convergence of HFB solutions was improved by a sub-iteration method. The Hermiticity violation of differential operators brought by Fourier-transform-based differentiation has also been solved. Furthermore, the accuracy and performance of HFBFFT were tested by benchmarking it against other HFB codes, both spherical and deformed, for a set of nuclei, both well-bound and weakly-bound.

3D coordinate-space representation↗
DOE OSTI2024

Solving the Orszag–Tang vortex magnetohydrodynamics problem with physics-constrained convolutional neural networks

We study the 2D Orszag–Tang vortex magnetohydrodynamics (MHD) problem through the use of physics-constrained convolutional neural networks (PCNNs) for forecasting the density, ρ, and the magnetic field, B, as well as the prediction of B given the velocity field v of the fluid. In addition to translation equivariance from the convolutional architecture, other physics constraints were embedded: absence of magnetic monopoles, non-negativity of ρ, use of only relevant variables, and the periodic boundary conditions of the problem. The use of only relevant variables and the hard constraint of non-negative ρ were found to facilitate learning greatly. The divergenceless condition ∇·B=0 was implemented as a hard constraint up to machine precision through the use of a magnetic potential to define B=∇×A. Residual networks and data augmentation were also used to improve performance. This allowed for some of the residual models to function as surrogate models and provide reasonably accurate simulations. For the prediction task, the PCNNs were evaluated against a physics-informed neural network, which had the ideal MHD induction equation as a soft constraint. Several models were able to generate highly accurate fields, which are visually almost indistinguishable and have low mean squared error. Only methods with built-in hard constraints produced physical fields with ∇·B=0. The use of PCNNs for MHD has the potential to produce physically consistent real-time simulations to serve as virtual diagnostics in cases where inferences must be made with limited observables.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2016

Modeling and Simulation of Radiative Compressible Flows in Aerodynamic Heating Arc-Jet Facility

Numerical simulations of an arc heated flow inside NASA's 20 [MW] Aerodynamics heating facility (AHF) are performed in order to investigate the three-dimensional swirling flow and the current distribution inside the wind tunnel. The plasma is considered in Local Thermodynamics Equilibrium(LTE) and is composed of Air-Argon gas mixture. The governing equations are the Navier-Stokes equations that include source terms corresponding to Joule heating and radiative cooling. The former is obtained by solving an electric potential equation, while the latter is calculated using an innovative massively parallel ray-tracing algorithm. The fully coupled system is closed by the thermodynamics relations and transport properties which are obtained from Chapman-Enskog method. A novel strategy was developed in order to enable the flow solver and the radiation calculation to be preformed independently and simultaneously using a different number of processors. Drastic reduction in the computational cost was achieved using this strategy. Details on the numerical methods used for space discretization, time integration and ray-tracing algorithm will be presented. The effect of the radiative cooling on the dynamics of the flow will be investigated. The complete set of equations were implemented within the COOLFluiD Framework. Fig. 1 shows the geometry of the Anode and part of the constrictor of the Aerodynamics heating facility (AHF). Fig. 2 shows the velocity field distribution along (x-y) plane and the streamline in (z-y) plane.

Pasma flows↗
NASA NTRS1987

Free wake analysis of helicopter rotor blades in hover using a finite volume technique

A fully compressible method for determining helicopter rotor wake effects is described which computes the wake without requiring external specification of the wake, or separate computations for the wake and blade region. The method is a modification of a compressible finite volume Potential Flow technique, and it has been implemented in a program, HELIX I, for computing compressible rotor flow fields in hover with free wakes. Wake positions in substantial agreement with experiment have been calculated for cases including subsonic and transonic flows, high and low aspect ratios, and two- and four-bladed rotors.

Ramachandran, K.↗