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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 1,279 records · Page 71
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow

High order essentially non-oscillatory (ENO) schemes, originally designed for compressible flow and in general for hyperbolic conservation laws, are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions. The projection to divergence-free velocity fields is achieved by fourth order central differences through Fast Fourier Transforms (FFT) and a mild high-order filtering. The objective of this work is to assess the resolution of ENO schemes for large scale features of the flow when a coarse grid is used and small scale features of the flow, such as shears and roll-ups, are not fully resolved. It is found that high-order ENO schemes remain stable under such situations and quantities related to large-scale features, such as the total circulation around the roll-up region, are adequately resolved.

Weinan, E.↗
NASA NTRS1993

The prediction of nozzle performance and heat transfer in hydrogen/oxygen rocket engines with transpiration cooling, film cooling, and high area ratios

An advanced engineering computational model has been developed to aid in the analysis and design of hydrogen/oxygen chemical rocket engines. The complete multi-species, chemically reacting and diffusing Navier-Stokes equations are modelled, finite difference approach that is tailored to be conservative in an axisymmetric coordinate system for both the inviscid and viscous terms. Demonstration cases are presented for a 1030:1 area ratio nozzle, a 25 lbf film cooled nozzle, and transpiration cooled plug-and-spool rocket engine. The results indicate that the thrust coefficient predictions of the 1030:1 nozzle and the film cooled nozzle are within 0.2 to 0.5 percent, respectively, of experimental measurements when all of the chemical reaction and diffusion terms are considered. Further, the model's predictions agree very well with the heat transfer measurements made in all of the nozzle test cases. The Soret thermal diffusion term is demonstrated to have a significant effect on the predicted mass fraction of hydrogen along the wall of the nozzle in both the laminar flow 1030:1 nozzle and the turbulent plug-and-spool rocket engine analysis cases performed. Further, the Soret term was shown to represent a significant fraction of the diffusion fluxes occurring in the transpiration cooled rocket engine.

Kacynski, Kenneth J.↗
NASA NTRS1994

A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow

High order essentially non-oscillatory (ENO) schemes, originally designed for compressible flow and in general for hyperbolic conservation laws, are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions. The projection to divergence-free velocity fields is achieved by fourth-order central differences through fast Fourier transforms (FFT) and a mild high-order filtering. The objective of this work is to assess the resolution of ENO schemes for large scale features of the flow when a coarse grid is used and small scale features of the flow, such as shears and roll-ups, are not fully resolved. It is found that high-order ENO schemes remain stable under such situations and quantities related to large scale features, such as the total circulation around the roll-up region, are adequately resolved.

Weinan, E.↗
NASA NTRS2006

Time-Accurate, Unstructured-Mesh Navier-Stokes Computations with the Space-Time CESE Method

Application of the newly emerged space-time conservation element solution element (CESE) method to compressible Navier-Stokes equations is studied. In contrast to Euler equations solvers, several issues such as boundary conditions, numerical dissipation, and grid stiffness warrant systematic investigations and validations. Non-reflecting boundary conditions applied at the truncated boundary are also investigated from the stand point of acoustic wave propagation. Validations of the numerical solutions are performed by comparing with exact solutions for steady-state as well as time-accurate viscous flow problems. The test cases cover a broad speed regime for problems ranging from acoustic wave propagation to 3D hypersonic configurations. Model problems pertinent to hypersonic configurations demonstrate the effectiveness of the CESE method in treating flows with shocks, unsteady waves, and separations. Good agreement with exact solutions suggests that the space-time CESE method provides a viable alternative for time-accurate Navier-Stokes calculations of a broad range of problems.

Chang, Chau-Lyan↗
NASA NTRS2008

The a(3) Scheme--A Fourth-Order Space-Time Flux-Conserving and Neutrally Stable CESE Solver

The CESE development is driven by a belief that a solver should (i) enforce conservation laws in both space and time, and (ii) be built from a non-dissipative (i.e., neutrally stable) core scheme so that the numerical dissipation can be controlled effectively. To initiate a systematic CESE development of high order schemes, in this paper we provide a thorough discussion on the structure, consistency, stability, phase error, and accuracy of a new 4th-order space-time flux-conserving and neutrally stable CESE solver of an 1D scalar advection equation. The space-time stencil of this two-level explicit scheme is formed by one point at the upper time level and three points at the lower time level. Because it is associated with three independent mesh variables (the numerical analogues of the dependent variable and its 1st-order and 2ndorder spatial derivatives, respectively) and three equations per mesh point, the new scheme is referred to as the a(3) scheme. Through the von Neumann analysis, it is shown that the a(3) scheme is stable if and only if the Courant number is less than 0.5. Moreover, it is established numerically that the a(3) scheme is 4th-order accurate.

Chang, Sin-Chung↗
NASA NTRS1985

Numerical solution of the unsteady Navier-Stokes equation

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws are discussed. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most first-order accuracy, in the sense of truncation error, at extrema of the solution. In this paper a uniformly second-order approximation is constructed, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Osher, Stanley J.↗
NASA NTRS1998

A Stable and Conservative Interface Treatment of Arbitrary Spatial Accuracy

Stable and accurate interface conditions are derived for the linear advection-diffusion equation. The conditions are functionally independent of the spatial order of accuracy and rely only on the form of the discrete operator. We focus on high-order finite-difference operators that satisfy the summation-by-parts (SBP) property. We prove that stability is a natural consequence of the SBP operators used in conjunction with the new boundary conditions. In addition, we show that the interface treatments are conservative. New finite-difference operators of spatial accuracy up to sixth order are constructed: these operators satisfy the SBP property. Finite-difference operators are shown to admit design accuracy (p(sup th)-order global accuracy) when (p - 1)(sup th)-order stencil closures are used near the boundaries if the physical boundary conditions are implemented to at least p(sup th)-order accuracy. Stability and accuracy are demonstrated on the nonlinear Burgers' equation for an twelve-subdomain problem with randomly distributed interfaces.

Carpenter, Mark H.↗
NASA NTRS1998

EOS Interdisciplinary Investigation: Observational and Modeling Studies of Radiative, Chemical, and Dynamical Interactions in the Earth's Atmosphere

A 3-dimensional model of atmospheric dynamics and photochemistry has been developed from the primitive equations in isentropic coordinates. The model extends from the upper troposphere through the middle atmosphere and is driven by observed dynamical and chemical structure in the troposphere. The model's formulation is entirely spectral: Horizontal structure is represented in terms of vector Hough functions, which explicitly partition the motion into its rotational and divergent components. This formulation enables the model's computational performance to be increased dramatically by filtering high-frequency gravity waves, which do not affect PV conservation. Vertical structure is represented in terms of eigenfunctions that follow from the primitive equations in isentropic coordinates. The model's fully spectral formulation enables scale-selective dissipation, necessary for numerical stability, to be applied at 6th order-in all 3 coordinate directions. This feature leaves all but the shortest vertical scales undamped and, consequently, allows potential vorticity and chemical tracers to be conserved quite accurately, distinctly better than in the model's layered counterpart. These dynamical features are complemented by a basic but fairly complete treatment of gas phase photochemistry, which accounts for some 48 chemical species, diurnally-varying SW absorption by O2 and O3, and LW cooling calculated via a detailed band calculation of radiative transfer. Driven by observed tropospheric structure, the 3D model reproduces observed structure in the middle atmosphere, inclusive of transport by the Brewer-Dobson circulation and accompanying chemical variations. Calculated residual motion is consistent with diabatic cooling rates, poleward transport, and descent in the polar night derived from satellite measurements of chemical tracers made from LIMS, SAGE, and UARS. The model also reproduces the observed structure of chemical species like O3, HNO3, and ClO. At the same time, it provides a respectable 3D simulation of the wintertime increase of midlatitude total ozone, as well as its geographical structure observed by Nimbus-7 TOMS. The 3D model has been used to explore the origin of diabatic upwelling in the tropical lower stratosphere, which has been related to planetary wave absorption in the winter- time stratosphere, as well as to influences from tropospheric convection at the tropical tropopause.

Salby, Murry L.↗
DOE OSTI2026

Transport-based initial conditions for heavy-ion collisions at finite densities

Here, we employ the SMASH transport model to provide event-by-event initial conditions for the energy-momentum tensor and conserved charge currents in hydrodynamic simulations of relativistic heavy-ion collisions. We study the fluctuations and dynamical evolution of three conserved charge currents (net baryon, net electric charges, and net strangeness) with a four-dimensional lattice-QCD-based equation of state, NEOS-4D, in the hydrodynamic phase. Out-of-equilibrium corrections at the particlization are generalized to finite densities to ensure the conservation of energy, momentum, and the three types of charges. These theoretical developments are integrated within the X-SCAPE code as a unified framework for studying the nuclear matter properties in the Beam Energy Scan program.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1995

Convergence properties of finite-difference hydrodynamics schemes in the presence of shocks

We investigate the asymptotic convergence of finite-difference schemes for the Euler equations when the limiting solution contains shocks. The Lax-Wendroff theorem guarantees that certain conservative schemes converge to correct, physically valid solutions. We focus on two one-dimensional operator-split schemes with explicit artificial-viscosity terms. One, an internal-energy scheme, does not satisfy the assumptions of Lax-Wendroff; the other, a conservative total-energy scheme, does. With viscous lengths chosen proportional to the grid size, we find that both schemes converge to their zero-grid-size limits at the theoretically expected rate, but only the conversative scheme converges toward correct solutions of the inviscid fluid equations. We show that the difference in their behaviors results directly from the presence of shocks in the limiting solution. Empirically, we find that when the viscous lenghts tend toward zero more slowly than the grid size, however the nonconservative scheme also converges toward correct solutions. We characterize the asymptotic behavior of the total-energy scheme in a particular problem in which a shock forms. As the grid is refined, a Cauchy error approaches the expected rate of change slowly. We show that the changes in the artificial viscosity alter the diffusion of small-amplitude waves. The differences associated with such waves make the dominant contribution to the Cauchy error. We formulate an analytic model to relate the rate of approach to the effect of varying diffusion in waves and find quantitative agreement with our numerical results.

Kimoto, Paul A.↗
NASA NTRS1976

Hamilton, Ritz, and elastodynamics

The theory of Ritz is applied to the equation that Hamilton called the 'Law of Varying Action.' Direct analytical solutions are obtained for the transient motion of beams, both conservative and nonconservative. The results achieved are compared to exact solutions obtained by the use of rigorously exact free-vibration modes in the differential equations of Lagrange and to an approximate solution obtained through the application of Gurtin's principles for linear elastodynamics. A brief discussion of Hamilton's law and Hamilton's principle is followed by examples of results for both free-free and cantilever beams with various loadings.

Bailey, C. D.↗
NASA NTRS1976

Hamilton, Ritz, and elastodynamics

The theory of Ritz is applied to the equation that Hamilton called the 'Law of Varying Action'. Direct analytical solutions are obtained for the transient motion of beams, both conservative and nonconservative. The results obtained are compared to exact solutions obtained by the use of rigorously exact free-vibration modes in the differential equations of Lagrange and to an approximate solution obtained through the application of Gurtin's principles for linear elastodynamics. A brief discussion of Hamilton's law and Hamilton's principle is followed by examples of results for both free-free and cantilever beams with various loadings.

Bailey, C. D.↗
DOE OSTI2023

On the design of stable, consistent, and conservative high-order methods for multi-material hydrodynamics

Obtaining stable and high-order numerical solutions for multi-material hydrodynamics is an open challenge. Although slope limiters are widely used to maintain monotonicity near discontinuities, typical limiting procedures violate closure laws at the discrete level when applied to multi-material hydrodynamics equations. Due to this, the high-order expansions of quantities related by the closure laws are no longer consistent. The commonly observed symptom of this consistency-violation is that the numerical method fails to maintain constant pressure and velocity across material interfaces. This leads to sub-optimal convergence rates for smooth multi-material problems as well. Specialized limiting procedures that satisfy consistency while maintaining conservation need to be developed for such equations. A novel procedure that re-instates consistency into slope-limited high-order discretizations applied to the multi-material hydrodynamics equations is presented here. Using simple examples, it is demonstrated that the presented method satisfies closure laws at the discrete level, while maintaining conservative properties of the high-order method. Furthermore, this procedure involves a projection step which relies on the compact basis of the underlying spatial discretization, i.e. for discontinuous schemes (viz. DG and FV) the projection is local, and does not involve global matrix solves. Comparisons with conventional approaches emphasizes the necessity of the consistent closure-law preserving limiting approach, in order to maintain design order of accuracy for smooth multi-material problems.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Reconciling and Improving Formulations for Thermodynamics and Conservation Principles in Earth System Models (ESMs)

Abstract This paper provides a comprehensive derivation of the total energy equations for the atmospheric components of Earth System Models (ESMs). The assumptions and approximations made in this derivation are motivated and discussed. In particular, it is emphasized that closing the energy budget is conceptually challenging and hard to achieve in practice without resorting to ad hoc fixers. As a concrete example, the energy budget terms are diagnosed in a realistic climate simulation using a global atmosphere model. The largest total energy errors in this example are spurious dynamical core energy dissipation, thermodynamic inconsistencies (e.g., coupling parameterizations with the host model) and missing processes/terms associated with falling precipitation and evaporation (e.g., enthalpy flux between components). The latter two errors are not, in general, reduced by increasing horizontal resolution. They are due to incomplete thermodynamic and dynamic formulations. Future research directions are proposed to reconcile and improve thermodynamics formulations and conservation principles.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1989

Numerical solution of unsteady incompressible viscous flows in generalized moving coordinate systems

A solution method of the time-accurate, incompressible Navier-Stokes equations in generalized curvilinear moving coordinate systems is presented in this paper. Accuracy is achieved by a conservative finite-volume discretization which satisfies the geometric conservation laws in generalized moving coordinate systems. The solution method is second-order accurate in space and first-order accurate in time. A fractional step solution method is used to efficiently solve the discrete equations. The unknowns, namely the pressure and the volume-fluxes, are chosen to facilitate the formulation of a consistent Poisson equation and to obtain a robust Poisson solver with favorable convergence properties. The method is validated by comparisons to other numerical and experimental solutions. The comparisons show good agreement.

Rosenfeld, Moshe↗
DOE OSTI2026

ECLEIRS: Exact conservation law embedded identification of reduced states for parameterized nonlinear conservation laws from sparse and noisy data

Multi-query applications such as parameter estimation, uncertainty quantification and design optimization for parameterized partial differential equation (PDE) systems are expensive. While reduced/latent state dynamics approaches for parameterized PDEs offer a viable alternative, these approaches rely on high-quality data and struggle with highly sparse spatiotemporal noisy measurements typically obtained from experiments. Furthermore, there is no guarantee that these models satisfy governing physical conservation laws. In this article, we propose a reduced state dynamics approach, referred to as ECLEIRS, that embeds exact conservation in the solution and flux representation by utilizing a space-time divergence-free neural network formulation. We compare ECLEIRS with other reduced state dynamics approaches, those that do not enforce any physical constraints and those with physics-informed loss functions, for three shock-propagation problems: 1-D advection, 1-D Burgers and 2-D Euler equations. In conclusion, the numerical experiments conducted in this study demonstrate that ECLEIRS provides the most accurate prediction of dynamics for unseen parameters even in the presence of highly sparse and noisy data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

SODAs: sparse optimization for the discovery of differential and algebraic equations

Differential-algebraic equations (DAEs) integrate ordinary differential equations (ODEs) with algebraic constraints, providing a fundamental framework for developing models of dynamical systems characterized by time-scale separation, conservation laws and physical constraints. While sparse optimization has revolutionized model development by allowing data-driven discovery of parsimonious models from a library of possible equations, existing approaches for dynamical systems assume DAEs can be reduced to ODEs by eliminating variables before model discovery. This assumption limits the applicability of such methods for DAE systems with unknown constraints and time scales. We introduce sparse optimization for differential-algebraic systems (SODAs), a data-driven method for the identification of DAEs in their explicit form. By discovering the algebraic and dynamic components sequentially without prior identification of the algebraic variables, this approach leads to a sequence of convex optimization problems. It has the advantage of discovering interpretable models that preserve the structure of the underlying physical system. To this end, SODAs improves since SODAs is singular numerical stability when handling high correlations between library terms, caused by near-perfect algebraic relationships, by iteratively refining the conditioning of the candidate library. We demonstrate the performance of our method on biological, mechanical and electrical systems, showcasing its robustness to noise in both simulated time series and real-time experimental data.

DAE↗
DOE OSTI2024

Anti-symmetric and positivity preserving formulation of a spectral method for Vlasov-Poisson equations

We analyze the anti-symmetric properties of a spectral discretization for the one-dimensional Vlasov-Poisson equations. The discretization is based on a spectral expansion in velocity with the symmetrically weighted Hermite basis functions, central finite differencing in space, and an implicit Runge Kutta integrator in time. The proposed discretization preserves the anti-symmetric structure of the advection operator in the Vlasov equation, resulting in a stable numerical method. We apply such discretization to two formulations: the canonical Vlasov-Poisson equations and their continuously transformed square-root representation. The latter preserves the positivity of the particle distribution function. We derive analytically the conservation properties of both formulations, including particle number, momentum, and energy, which are verified numerically on the following benchmark problems: manufactured solution, linear and nonlinear Landau damping, two-stream instability, bump-on-tail instability, and ion-acoustic wave.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗