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Results for “Conservation equations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,441 records · Page 80
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Bidirectional Reflectance of a Macroscopically Flat, High-Albedo Particulate Surface: An Efficient Radiative Transfer Solution and Applications to Regoliths

Many remote sensing applications rely on accurate knowledge of the bidirectional reflection function (BRF) of surfaces composed of discrete, randomly positioned scattering particles. Theoretical computations of BRFs for plane-parallel particulate layers are usually reduced to solving the radiative transfer equation (RTE) using one of existing exact or approximate techniques. Since semi-empirical approximate approaches are notorious for their low accuracy, violation of the energy conservation law, and ability to produce unphysical results, the use of numerically exact solutions of RTE has gained justified popularity. For example, the computation of BRFs for macroscopically flat particulate surfaces in many geophysical publications is based on the adding-doubling (AD) and discrete ordinate (DO) methods. A further saving of computer resources can be achieved by using a more efficient technique to solve the plane-parallel RTE than the AD and DO methods. Since many natural particulate surfaces can be well represented by the model of an optically semi-infinite, homogeneous scattering layer, one can find the BRF directly by solving the Ambartsumian's nonlinear integral equation using a simple iterative technique. In this way, the computation of the internal radiation field is avoided and the computer code becomes highly efficient and very accurate and compact. Furthermore, the BRF thus obtained fully obeys the fundamental physical laws of energy conservation and reciprocity. In this paper, we discuss numerical aspects and the computer implementation of this technique, examine the applicability of the Henyey-Greenstein phase function and the sigma-Eddington approximation in BRF and flux calculations, and describe sample applications demonstrating the potential effect of particle shape on the bidirectional reflectance of flat regolith surfaces. Although the effects of packing density and coherent backscattering are currently neglected, they can also be incorporated. The FORTRAN implementation of the technique is available on the World Wide Web, and can be applied to a wide range of remote sensing problems. BRF computations for undulated (macroscopically rough) surfaces are more complicated and often rely on time consuming Monte Carlo procedures. This approach is especially inefficient for optically thick, weakly absorbing media (e.g., snow and desert surfaces at visible wavelengths since a photon may undergo many internal scattering events before it exists the medium or is absorbed. However, undulated surfaces can often be represented as collections of locally flat tilted facets characterized by the BRF found from the traditional plane parallel RTE. In this way the MOnte Carlo procedure could be used only to evaluate the effects of surface shadowing and multiple surface reflections, thereby bypassing the time-consuming ray tracing inside the medium and providing a great savings of CPU time.

Mishchenko, Michael I.↗
DOE OSTI2023

Embedding hard physical constraints in neural network coarse-graining of three-dimensional turbulence

In recent years, deep learning approaches have shown much promise in modeling complex systems in the physical sciences. A major challenge in deep learning of partial differential equations is enforcing physical constraints and boundary conditions. In this work, we propose a general framework to directly embed the notion of an incompressible fluid into convolutional neural networks, and apply this to coarse-graining of turbulent flow. These physics-embedded neural networks leverage interpretable strategies from numerical methods and computational fluid dynamics to enforce physical laws and boundary conditions by taking advantage the mathematical properties of the underlying equations. Here, we demonstrate results on three-dimensional fully developed turbulence, showing that this technique drastically improves local conservation of mass, without sacrificing performance according to several other metrics characterizing the fluid flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Xyce(™) Parallel Electronic Simulator v.7.5

The Xyce Parallel Electronic Simulator simulates electronic circuit behavior in DC, AC, HB, MPDE and transient mode using standard analog (DAE) and/or device (PDE) device models including several age and radiation aware devices. It supports a variety of computing platforms (both serial and parallel) computers. Lastly, it uses a variety of modern solution algorithms dynamic parallel load-balancing and iterative solvers.! ! Xyce is primarily used to simulate the voltage and current behavior of a circuit network (a network of electronic devices connected via a conductive network). As a tool, it is mainly used for the design and analysis of electronic circuits.! ! Kirchoff's conservation laws are enforced over a network using modified nodal analysis. This results in a set of differential algebraic equations (DAEs). The resulting nonlinear problem is solved iteratively using a fully coupled Newton method, which in turn results in a linear system that is solved by either a standard sparse-direct solver or iteratively using Trilinos linear solver packages, also developed at Sandia National Laboratories.

Source record↗
NASA NTRS1977

Combustion response modeling for composite solid propellants

A computerized mathematical model of the combustion response function of composite solid propellants was developed with particular attention to the contributions of the solid phase heterogeneity. The one-dimensional model treats the solid phase as alternating layers of ammonium perchlorate and binder, with an exothermic melt layer at the surface. Solution of the Fourier heat equation in the solid provides temperature and heat flux distributions with space and time. The problem is solved by conserving the heat flux at the surface from that produced by a suitable model of the gas phase. An approximation of the BDP flame model is utilized to represent the gas phase. By the use of several reasonable assumptions, it is found that a significant portion of the problem can be solved in closed form. A method is presented by which the model can be applied to tetramodal particle size distributions. A computerized steady-state version of the model was completed, which served to validate the various approximations and lay a foundation for the combustion response modeling. The combustion response modeling was completed in a form which does not require an iterative solution, and some preliminary results were acquired.

Source record↗
NASA NTRS1980

Gas bearings

The present work deals with the fundamentals of gas lubrication theory, which forms the foundation of all analytical design tools for gas bearings. Most of the hard lessons learned in the past are outlined with reference to dry contact, debris ingestion, sliding speed, and chemical stability of lubricant. The mathematical theory of gas lubrication is described for scaling rules in thin-film viscous flow, momentum conservation, mass conservation, energy conservation, isothermal gas bearing theory, coupling effects, and global bearing characteristics. Particular attention is given to the governing differential equations for common bearing configurations. Also discussed are representative solutions of self-acting gas bearings, externally pressurized bearings, and time-dependent effects.

Pan, C. H. T.↗
NASA NTRS1985

Computation of supersonic flows over three-dimensional configurations

An aerodynamic prediction technique based on the steady form of the full-potential equation has been applied to a variety of three-dimensional supersonic flow problems exhibiting embedded subsonic regions. A conservative switching scheme is employed to transition from the supersonic relaxation algorithm, and vice versa. Numerical solutions are obtained for a number of complex configurations, including advanced tactical fighter, Langley canard-wing fighter configuration, isolated shuttle orbiter, and mated shuttle orbiter configuration with external tank. The computed results are in good agreement with available experimental data.

Szema, K.-Y.↗
NASA NTRS1987

Effect of shaft frequency on cavitation in a journal bearing for noncentered circular whirl

The effect of shaft frequency on the performance of a submerged journal undergoing noncentered circular whirl is examined. The main emphasis of the paper is on the behavior of the vapor cavitation bubble and its effect on the bearing performance as a function of frequency. A cavitation algorithm due to Elrod was implemented in a computer program which solves a time-dependent Reynolds equation. This algorithm automatically handles the boundary conditions by using a switch function and a control volume approach which conserves mass throughout the entire flow. The shaft frequencies in this investigation ranged from 0 rad/s (squeeze-film damper) to -104 rad/s (a case in which oil-whip condition was produced momentarily). For the particular vibration amplitude chosen in this investigation it was observed that vapor cavitation had an effect on the load components for the full range of shaft frequencies investigated.

Brewe, David E.↗
NASA NTRS1989

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

Baker, A. J.↗
NASA NTRS1993

Analysis of hypersonic arcjet flow fields and surface heating of blunt bodies

A Gauss-Seidel implicit aerothermodynamic Navier-Stokes computational CFD code with thermochemical surface conditions (GIANTS) and with appropriate boundary conditions was developed for the analysis of hypersonic arcjet flows over large angle blunt bodies. Two-dimensional axisymmetric multicomponent full Navier-Stokes equations were solved, together with boundary conditions, to account for the surface slip, surface catalysis, and energy and mass conservation at the body surface. It is shown that the predictions for isothermal, noncatalytic, and no-slip surface conditions which are made using the GIANTS code with simple boundary conditions agree with those of the LAURA code, and the predicted normalized heating distributions over the forebody surface with boundary conditions for various cone angles are consistent with the trends of data from arcjet experiments.

Chen, Y.-K.↗
NASA NTRS1993

Finite element procedures for coupled linear analysis of heat transfer, fluid and solid mechanics

Coupled finite element formulations for fluid mechanics, heat transfer, and solid mechanics are derived from the conservation laws for energy, mass, and momentum. To model the physics of interactions among the participating disciplines, the linearized equations are coupled by combining domain and boundary coupling procedures. Iterative numerical solution strategy is presented to solve the equations, with the partitioning of temporal discretization implemented.

Sutjahjo, Edhi↗
NASA NTRSDate not supplied

Assessment of UMUSCL Scheme for DNS of Turbulent Flows

Direct Numerical Simulations (DNS) are performed using the FUN3D code ( https://fun3d.larc.nasa.gov) for three validation cases: (1) flow through a plane channel, (2) flow through a channel with a constriction, and (3) flow over a flat plate. FUN3D is a node-centered finite-volume code developed at the NASA Langley Research Center that solves the three-dimensional compressible Navier-Stokes equations on unstructured computational grids. The simulations are performed employing the 2nd-order unstructured monotonic upstream scheme for conservation laws (UMUSCL). The results are compared with available experimental and numerical data. The effect of the UMUSCL reconstruction parameter (κ) is assessed, and the results indicate that κ = 0.9 yields satisfactory results in terms of accuracy and robustness compared to available data. Further analyses of the results, along with additional test cases and grids will be presented in the final manuscript.

Direct Numerical Simulation↗
DOE OSTI2024

Dyn$\mathrm{AMO}$: Multi-agent reinforcement learning for dynamic anticipatory mesh optimization with applications to hyperbolic conservation laws

Here we introduce DynAMO, a reinforcement learning paradigm for Dynamic Anticipatory Mesh Optimization. Adaptive mesh refinement is an effective tool for optimizing computational cost and solution accuracy in numerical methods for partial differential equations. However, traditional adaptive mesh refinement approaches for time-dependent problems typically rely only on instantaneous error indicators to guide adaptivity. As a result, standard strategies often require frequent remeshing to maintain accuracy. In the DynAMO approach, multi-agent reinforcement learning is used to discover new local refinement policies that can anticipate and respond to future solution states by producing meshes that deliver more accurate solutions for longer time intervals. By applying DynAMO to discontinuous Galerkin methods for the linear advection and compressible Euler equations in two dimensions, we demonstrate that this new mesh refinement paradigm can outperform conventional threshold-based strategies while also generalizing to different mesh sizes, remeshing and simulation times, and initial conditions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A fully implicit, scalable, conservative nonlinear relativistic Fokker–Planck 0D-2P solver for runaway electrons

Upon application of a sufficiently strong electric field, electrons break away from thermal equilibrium and approach relativistic speeds. These highly energetic ‘runaway’ electrons (~ MeV) play a significant role in tokamak disruption physics, and therefore their accurate understanding is essential to develop reliable mitigation strategies. As such, we have developed a fully implicit solver for the 0D-2P (i.e., including two momenta coordinates) relativistic nonlinear Fokker–Planck equation (rFP). As in earlier implicit rFP studies (NORSE, CQL3D), electron–ion interactions are modeled using the Lorentz operator, and synchrotron damping using the Abraham–Lorentz–Dirac reaction term. However, our implementation improves on these earlier studies by (1) ensuring exact conservation properties for electron collisions, (2) strictly preserving positivity, and (3) being scalable algorithmically and in parallel. Key to our proposed approach is an efficient multigrid preconditioner for the linearized rFP equation, a multigrid elliptic solver for the Braams–Karney potentials, and a novel adaptive technique to determine the associated boundary values. We verify the accuracy and efficiency of the proposed scheme with numerical results ranging from small electric-field electrical conductivity measurements to the accurate reproduction of runaway tail dynamics when strong electric fields are applied.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Conservative DG method for the micro-macro decomposition of the Vlasov–Poisson–Lenard–Bernstein model

The micro-macro (mM) decomposition approach is considered for the numerical solution of the Vlasov– Poisson–Lenard–Bernstein (VPLB) system, which is relevant for plasma physics applications. In the mM approach, the kinetic distribution function is decomposed as $f$ = $\mathscr{E}$[$ρ_f$] + g , where $\mathscr{E}$ is a local equilibrium distribution, depending on the macroscopic moments $ρ_f$ = $∫_{\mathbb{R}}$ $efdv$ = $\langle$$ef$$\rangle$$_{\mathbb{R}}$, where e = (1, $v$, $\frac{1}{2}$ $v^2$) T , and $g$, the microscopic distribution, is defined such that $\langle$$eg$$\rangle$$_{\mathbb{R}}$ = 0. We aim to design numerical methods for the mM decomposition of the VPLB system, which consists of coupled equations for $ρ_f$ and $g$. To this end, we use the discontinuous Galerkin (DG) method for phase-space discretization, and implicit-explicit (IMEX) time integration, where the phase-space advection terms are integrated explicitly and the collision operator is integrated implicitly. We give special consideration to ensure that the resulting mM method maintains the $\langle$$eg$$\rangle$$_{\mathbb{R}}$ = 0 constraint, which may be necessary for obtaining (i) satisfactory results in the collision dominated regime with coarse velocity resolution, and (ii) unambiguous conservation properties. The constraint-preserving property is achieved through a consistent discretization of the equations governing the micro and macro components. Here, we present numerical results that demonstrate the performance of the mM method. The mM method is also compared against a corresponding DG-IMEX method solving directly for $f$.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Computational Fluid Dynamics and Heat Transfer Modeling of a Dimpled Heat Exchanger

Multiphysics and analytical calculations were conducted for a heat exchanger with passive, natural circulation flow. A glycol/water working fluid convects the heat to a dimpled heat exchanger shell, which subsequently transfers the heat to the soil, which acts as the ultimate heat sink. Because the system is fully-passive, it is not subject to the expenses, maintenance, and mechanical breakdowns associated with moving parts. Density, heat capacity, and thermal conductivity material properties were measured for various soil samples, and subsequently included as input for the soil heat conduction model. The soil model was coupled to a computational fluid dynamics (CFD) heat exchanger model that included the dynamic Smagorinsky large eddy simulation and k- omega turbulence models. The analysis showed that the fluid dynamics and heat transfer models worked properly, albeit at a slow pace. Nevertheless, the coupled CFD/heat conduction simulation ran long enough to determine a key parameter—the amount of heat conducted from the heat exchanger to the ground. This unique performance value, along with experimental data, was used as input for stand-alone, fast-running CFD models, as well as boundaries to obtain solutions to partial differential equations for soil heat conduction.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS2003

A Reduced-Order Model for Efficient Simulation of Synthetic Jet Actuators

A new reduced-order model of multidimensional synthetic jet actuators that combines the accuracy and conservation properties of full numerical simulation methods with the efficiency of simplified zero-order models is proposed. The multidimensional actuator is simulated by solving the time-dependent compressible quasi-1-D Euler equations, while the diaphragm is modeled as a moving boundary. The governing equations are approximated with a fourth-order finite difference scheme on a moving mesh such that one of the mesh boundaries coincides with the diaphragm. The reduced-order model of the actuator has several advantages. In contrast to the 3-D models, this approach provides conservation of mass, momentum, and energy. Furthermore, the new method is computationally much more efficient than the multidimensional Navier-Stokes simulation of the actuator cavity flow, while providing practically the same accuracy in the exterior flowfield. The most distinctive feature of the present model is its ability to predict the resonance characteristics of synthetic jet actuators; this is not practical when using the 3-D models because of the computational cost involved. Numerical results demonstrating the accuracy of the new reduced-order model and its limitations are presented.

Yamaleev, Nail K.↗