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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS2006

Model Predictive Optimal Control of a Time-Delay Distributed-Parameter Systems

This paper presents an optimal control method for a class of distributed-parameter systems governed by first order, quasilinear hyperbolic partial differential equations that arise in many physical systems. Such systems are characterized by time delays since information is transported from one state to another by wave propagation. A general closed-loop hyperbolic transport model is controlled by a boundary control embedded in a periodic boundary condition. The boundary control is subject to a nonlinear differential equation constraint that models actuator dynamics of the system. The hyperbolic equation is thus coupled with the ordinary differential equation via the boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to implement a model predictive control design for a wind tunnel to eliminate a transport delay effect that causes a poor Mach number regulation.

Nguyen, Nhan↗
NASA NTRS2021

PatchworkWave: A Multipatch Infrastructure for Multiphysics/Multiscale/Multiframe/Multimethod Simulations at Arbitrary Order

We present an extension of the PatchworkMHD code [1], itself an MHD-capable extension of thePatch-workcode [2], for which several algorithms presented here were co-developed. Its purpose is to create a“multipatch” scheme compatible with numerical simulations of arbitrary equations of motion at any dis-cretization order in space and time. In thePatchworkframework, the global simulation is comprised of anarbitrary number of moving, local meshes, or “patches”, which are free to employ their own resolution, co-ordinate system/topology, physics equations, reference frame, and in our new approach, numerical method.Each local patch exchanges boundary data with a single global patch on which all other patches residethrough a client-router-server parallelization model. In generalizingPatchworkto be compatible witharbitrary order time integration,PatchworkMHDandPatchworkWavehave significantly improved theinterpatch interpolation accuracy by removing an interpolation of interpolated data feedback present in theoriginalPatchworkcode. Furthermore, we extendPatchworkto bemultimethodby allowing multiplestate vectors to be updated simultaneously, with each state vector providing its own interpatch interpolationand transformation procedures. As such, our scheme is compatible with nearly any set of hyperbolic partialdifferential equations. We demonstrate our changes through the implementation of a scalar wave toy-modelthat is evolved on arbitrary, time dependent patch configurations at 4th order accuracy.

Dennis B Bowen↗
NASA NTRS1977

Unsteady supersonic aerodynamic theory by the method of potential gradient

A generalized solution of the hyperbolic wave equation has been derived. The method used has been further developed to relate the velocity components at a field point to the potential gradient distribution in the dependence domain. Singular integrals have been evaluated in closed form, while numerical integration methods are suggested for treating more complex but analytic functions. Idealization of the lifting surfaces by trapezoidal elements with two sides parallel to the streamlines is computationally efficient because line integrations along the other two sides need only be considered. Furthermore, all the integrands vanish on the Mach cone and the need for determining the hyperbolic curves of intersection of the cone with the lifting surface is avoided. Generalized aerodynamic coefficients for three AGARD planforms have been calculated and compared with the available results.

Jones, W. P.↗
DOE OSTI2025

Gradient flow based phase-field modeling using separable neural networks

Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.

42 ENGINEERING↗
DOE OSTI2023

Efficient Multigrid Reduction-in-Time for Method-of-Lines Discretizations of Linear Advection

Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that many of these methods perform quite poorly for advection-dominated problems. In this report we analyze the particular iterative parallel-in-time algorithm of multigrid reduction-in-time (MGRIT) for discretizations of constant-wave-speed linear advection problems. We focus on common method-of-lines discretizations that employ upwind finite differences in space and Runge-Kutta methods in time. Using a convergence framework we developed in previous work, we prove for a subclass of these discretizations that, if using the standard approach of rediscretizing the fine-grid problem on the coarse grid, robust MGRIT convergence with respect to CFL number and coarsening factor is not possible. This poor convergence and non-robustness is caused, at least in part, by an inadequate coarse-grid correction for smooth Fourier modes in space-time known as characteristic components. We propose an alternative coarse-grid operator that provides a better correction of these modes. This coarse-grid operator is related to previous work and uses a semi-Lagrangian discretization combined with an implicitly treated truncation error correction. Theory and numerical experiments show the proposed coarse-grid operator yields fast MGRIT convergence for many of the method-of-lines discretizations considered, including for both implicit and explicit discretizations of high order. Parallel results demonstrate speed-up over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Quasinormal modes of naked singularities in presence of nonlinear scalar fields

We study linear perturbations against static spherically symmetric background configurations of general relativity with a real scalar field (SF), which is minimally coupled with gravity; it is nonlinear due to the presence of the self-action potential. The background solutions have a naked singularity at the center of the configuration. The focus is on the stability of the background and fundamental frequencies of the quasinormal modes (QNM) of the axial perturbations in the Regge-Wheeler gauge. The problem is reduced to one hyperbolic master equation with an effective potential 𝑊eff, which turns out to be positive for a general non-negative SF potential; this ensures the linear stability with respect to this kind of perturbations. For numerical simulations, the SF potential was chosen in the power-law form 𝑉⁡(𝜙) ∼ 𝜙 2⁢𝑛 with 2 < 𝑛 ≤40. We extracted the fundamental frequencies of QNM for different 𝑛 and various sets of the background configuration parameters. The results show that even for a small background SF, there is a significant difference between the fundamental frequencies and ones in case of the Schwarzschild background. Furthermore, the results are also compared with the case of the Fisher-Janis-Newman-Winicour background dealing with a massless linear scalar field.

General relativity↗
DOE OSTI2023

Fast Multigrid Reduction-in-Time for Advection via Modified Semi-Lagrangian Coarse-Grid Operators

Many iterative parallel-in-time algorithms have been shown to be highly efficient for diffusion-dominated partial differential equations (PDEs) but are inefficient or even divergent when applied to advection-dominated PDEs. We consider the application of the multigrid reduction-in-time (MGRIT) algorithm to linear advection PDEs. Here, the key to efficient time integration with this method is using a coarse-grid operator that provides a sufficiently accurate approximation to the so-called ideal coarse-grid operator. For certain classes of semi-Lagrangian discretizations, we present a novel semi-Lagrangian-based coarse-grid operator that leads to fast and scalable multilevel time integration of linear advection PDEs. The coarse-grid operator is composed of a semi-Lagrangian discretization followed by a correction term, with the correction designed so that the leading-order truncation error of the composite operator is approximately equal to that of the ideal coarse-grid operator. Parallel results show substantial speed-ups over sequential time integration for variable-wave-speed advection problems in one and two spatial dimensions, and using high-order discretizations up to order five. The proposed approach establishes the first practical method that provides small and scalable MGRIT iteration counts for advection problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

A method for calculating unsteady turbulent boundary layers in two- and three-dimensional flows.

The governing equations for an unsteady turbulent boundary layer on a swept infinite cylinder, composed of a continuity equation, a pair of momentum equations and a pair of rate equations for the shear stress, based on the turbulent kinetic-energy equation, are solved numerically. These rate equations for the shear-stress express a balance between the convection, production, dissipation and diffusion of the turbulent shear stress components. Due to the physical model of turbulence employed, this system of equations is hyperbolic. An explicit, second-order accurate, conditionally stable difference scheme for this system, together with appropriate boundary and initial conditions, is formulated and developed into a computer program. Calculations for oscillating free stream flows with no pressure gradient show significant unsteady effects on the turbulent boundary layer.

Singleton, R. E.↗
NASA NTRS1974

Theoretical investigations on plasma processes in the Kaufman thruster

An analysis of the sputtering of metal surfaces and grids by ions of medium energies is given and it is shown that an exact, nonlinear, hyperbolic wave equation for the temperature field describes the transient transport of heat in metals. Quantum statistical and perturbation theoretical analysis of surface sputtering by low energy ions are used to develop the same expression for the sputtering rate. A transport model is formulated for the deposition of sputtered atoms on system components. Theoretical efforts in determining the potential distribution and the particle velocity distributions in low pressure discharges are briefly discussed.

Wilhelm, H. E.↗
NASA NTRS1977

Unsteady supersonic aerodynamic theory for interfering surfaces by the method of potential gradient

A generalized solution of the hyperbolic wave equation was further developed to relate the velocity components at a field point to the potential gradient distribution in the dependence domain. Singular integrals were evaluated in closed form, with numerical integration methods for more complex but analytic functions. Idealization of the lifting surfaces by trapezoidal elements with two sides parallel to the streamlines is computationally efficient. Streamwise integrals were performed analytically, and spanwise integrals were neccessary only on element leading and trailing sides. All integrands vanish on the Mach cone. Pressure distribution on a double delta wing and generalized aerodynamic coefficients for three AGARD planforms were calculated and compared with available results.

Jones, W. P.↗
NASA NTRS1976

On the mathematical conditions for the existence of periodic fluctuations in non-uniform media

The assumption that periodic excitations result in periodic responses for the case of waves propagating through nonuniform media is examined by investigating the periodic solutions of linear hyperbolic differential equations whose coefficients vary with position and whose solution must satisfy periodic boundary or source data. It is shown that the nature of the coefficients of undifferentiated terms of the differential system is crucial in determining whether the solution is periodic. Particular attention is paid to the propagation of infinitesimal pressure waves through the nonuniform steady flow of a lossless fluid.

Gunzburger, M. D.↗
NASA NTRS1984

Enthalpy damping for the steady Euler equations

For inviscid steady flow problems where the enthalpy is constant at steady state, it was previously proposed to use the difference between the local enthalpy and the steady state enthalpy as a driving term to accelerate convergence of iterative schemes. This idea is analyzed, both on the level of the partial differential equation and on the level of a particular finite difference scheme. It is shown that for the two-dimensional unsteady Euler equations, a hyperbolic system with eigenvalues on the imaginary axis, there is no enthalpy damping strategy which moves all the eigenvalues into the open left half plane. For the numerical scheme, however, the analysis shows and examples verify that enthalpy damping is potentially effective in accelerating convergence to steady state.

Jespersen, D. C.↗
NASA NTRS1984

On the method of pseudo compressibility for numerically solving incompressible flows

Pseudo compressibility is used for numerically solving incompressible flows to achieve computational efficiency. The use of pseudo compressibility results in a system of hyperbolic-type equations of motion that introduce waves of finite speed. The interactions of the wave propagation and the vorticity spreading are analyzed. A criterion governing the dependence of the pseudo compressiblity on the Reynolds number and the characteristic length of the flow geometry is obtained that allows for a proper convergence. It is demonstrated that the solution does tend to the incompressible limit. External and internal viscous flow test problems are presented to verify the theory.

Chang, J. L. C.↗
NASA NTRS1985

Enthalpy damping for the steady Euler equations

For inviscid steady flow problems where the enthalpy is constant at steady state, it was previously proposed to use the difference between the local enthalpy and the steady state enthalpy as a driving term to accelerate convergence of iterative schemes. This idea is analyzed, both on the level of the partial differential equation and on the level of a particular finite difference scheme. It is shown that for the two-dimensional unsteady Euler equations, a hyperbolic system with eigenvalues on the imaginary axis, there is no enthalpy damping strategy which moves all the eigenvalues into the open left half plane. For the numerical scheme, however, the analysis shows and examples verify that enthalpy damping is potentially effective in accelerating convergence to steady state.

Jespersen, D. C.↗
NASA NTRS1991

Faster Algorithm For Computation Of Incompressible Flow

Improved algorithm yields faster numerical solutions of Navier-Stokes equations of steady or unsteady three-dimensional flow of incompressible fluid. In artificial-compressibility method, unsteady flow treated as incompressible in advancing from one time step to next, but at each time step (or in steady state), fluid treated as having variable compressibility enabling propagation of flow field, and subiterations performed in increments of pseudotime until effects of compressibility subside. Directly couples pressure and velocity fields at same time step and converts elliptic incompressible Navier-Stokes equations to hyperbolic form more amenable to numerical integration.

Rogers, S. E.↗
NASA NTRS1992

On steady field-aligned double-adiabatic flow

The paper summarizes the four general double-adiabatic invariants governing ideal MHD flow in a narrow tube and renders them in a form suitable for the calculation of flow in tubes of nonconstant cross-sectional area. Results for converging-diverging flux tubes are developed and compared to single-adiabatic results which are identical to those for ordinary gasdynamic flow. It is found that in certain parameter regimes the governing equation for the vector potential is elliptic and can be reduced to Laplace's equation by simple stretching of one coordinate. In other regimes the equation is hyperbolic, indicating the presence of wave patterns. The relevance of these results to flow over magnetopause undulations, including flux transfer events, is discussed.

Sonnerup, B. U. O.↗