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At least 325 records · Page 18

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NASA NTRS1991

Multigrid for hypersonic viscous two- and three-dimensional flows

The use of a multigrid method with central differencing to solve the Navier-Stokes equations for hypersonic flows is considered. The time-dependent form of the equations is integrated with an explicit Runge-Kutta scheme accelerated by local time stepping and implicit residual smoothing. Variable coefficients are developed for the implicit process that remove the diffusion limit on the time step, producing significant improvement in convergence. A numerical dissipation formulation that provides good shock-capturing capability for hypersonic flows is presented. This formulation is shown to be a crucial aspect of the multigrid method. Solutions are given for two-dimensional viscous flow over a NACA 0012 airfoil and three-dimensional viscous flow over a blunt biconic.

Turkel, E.↗

NASA NTRS2001

Integrated Thermal Response Tool for Earth Entry Vehicles

A system is presented for multi-dimensional, fully-coupled thermal response modeling of hypersonic entry vehicles. The system consists of a two-dimensional implicit thermal response, pyrolysis and ablation program (TITAN), a commercial finite-element thermal and mechanical analysis code (MARC), and a high fidelity Navier-Stokes equation solver (GIANTS). The simulations performed by this integrated system include hypersonic flow-field, fluid and solid interaction, ablation, shape change, pyrolysis gas generation and flow, and thermal response of heatshield and structure. The thermal response of the ablating and charring heatshield material is simulated using TITAN, and that of the underlying structural is simulated using MARC. The ablating heatshield is treated as an outer boundary condition of the structure, and continuity conditions of temperature and heat flux are imposed at the interface between TITAN and MARC. Aerothermal environments with fluid and solid interaction are predicted by coupling TITAN and GIANTS through surface energy balance equations. With this integrated system, the aerothermal environments for an entry vehicle and the thermal response of both the heatshield and the structure can be obtained simultaneously. Representative computations for a proposed blunt body earth entry vehicle are presented and discussed in detail.

Chen, Y.-K.↗

DOE OSTI2022

Transient MOC with frequency transform and DSA on unstructured mesh

We present an implementation of the transient method of characteristics (MOC) with isotropic time derivatives, accelerated by diffusion synthetic acceleration (DSA). The fully implicit frequency transform method is used to solve the transient problem with analytic precursor integration. The code works on meshes composed of almost any of the commonly used non-curvilinear finite element types, and can handle the deformation of geometry in time-dependent transport calculations. We present results of a continuous Fourier analysis for the transient multigroup DSA problem, and representative benchmarking results are presented for the C5G7-TD benchmark in 2D showing reasonable performance and agreement compared to other codes. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1993

Virtual-pulse time integral methodology: A new explicit approach for computational dynamics - Theoretical developments for general nonlinear structural dynamics

The present paper describes a new explicit virtual-pulse time integral methodology for nonlinear structural dynamics problems. The purpose of the paper is to provide the theoretical basis of the methodology and to demonstrate applicability of the proposed formulations to nonlinear dynamic structures. Different from the existing numerical methods such as direct time integrations or mode superposition techniques, the proposed methodology offers new perspectives and methodology of development, and possesses several unique and attractive computational characteristics. The methodology is tested and compared with the implicit Newmark method (trapezoidal rule) through a nonlinear softening and hardening spring dynamic models. The numerical results indicate that the proposed explicit virtual-pulse time integral methodology is an excellent alternative for solving general nonlinear dynamic problems.

Chen, Xiaoqin↗

DOE OSTI2019

A computational model for nanosecond pulse laser-plasma interactions

A multi-physics numerical model for laser-induced optical breakdown and laser-plasma interaction in a non-equilibrium gas is presented, accounting for: production of priming electrons via multi-photon ionization, energy absorption, cascade ionization, induced hydrodynamic response, and shock formation and propagation. The gas is governed by the Navier-Stokes equations, with non-equilibrium effects taken into account by means of a two-temperature model. The space-time dependence of the laser beam is modeled with a flux-tube formulation for the Radiative Transfer Equation. The flow governing equations are discretized in space using a second-order finite volume method. The semi-discrete equations are marched in time using an implicit-explicit (IMEX) dual time-stepping strategy, where diffusion and chemistry are solved implicitly, whereas convection is explicit. Application to a 20 ns long 50 mJ pulse laser-induced breakdown in quiescent O 2 shows the advantages of this temporal discretization during and just after the laser pulse, while a less-expensive symmetric Strang splitting (with implicit chemistry) is sufficient for the post-breakdown gas dynamics after ≃ 0.1 μs. The integrated model is shown to reproduce key features of corresponding experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1975

A generalized hyperbolic marching method for chemically reacting 3-D supersonic flow using a splitting technique

A generalized hyperbolic marching method employing a nonorthogonal coordinate system and using a split differencing scheme for calculating steady supersonic flow over aerodynamic shapes is presented. It is a second-order-accurate mixed explicit-implicit procedure that solves the inviscid adiabatic and nondiffusive equations for chemically reacting flow in integral conservation-law form. The relationship between the integral and differential forms of the equations are examined and the relative merits of each discussed. The method admits initial Cauchy data situated on any arbitrary surface and integrates them forward along a general curvilinear coordinate, distorting and deforming the surface as it advances. The chemical kinetics term is split from the convective terms which are themselves dimensionally split, thereby freeing the fluid operators from the restricted step-size imposed by the chemical reactions and increasing the computational efficiency. The accuracy of this splitting technique is analyzed, a sufficient stability criterion is established, and comparisons are made with another method.

Rizzi, A. W.↗

NASA NTRS1976

Second-order closure analysis of turbulent reacting flows

A reacting shear layer program for a complete second-order closure of turbulent reacting flows is developed. The program uses a typical eddy box model and many of the fluid mechanical turbulence models developed in earlier studies. The computer program actually solves a total of 30 equations, where the numerical integration of the equations is performed by a forward-time-centered space quasi-implicit upwind finite-difference scheme. Results for nonreacting and simple isothermal reacting flows are presented along with preliminary results for propane-air flames. It is shown that the program predictions for simple nonreacting flows are in good agreement with available data. The calculations for isothermal reacting flows demonstrate the importance of including a mixedness correlation in finite rate chemistry calculations, where significant errors in the flowfield properties can result from neglect of the interaction between turbulence and the chemistry. Results for propane-air diffusion flames further support this conclusion.

Varma, A. K.↗

NASA NTRS1982

A computer program for the calculation of the flow field including boundary layer effects for mixed-compression inlets at angle of attack

A computer program was developed which is capable of calculating the flow field in the supersonic portion of a mixed compression aircraft inlet operating at angle of attack. The supersonic core flow is computed using a second-order three dimensional method-of-characteristics algorithm. The bow shock and the internal shock train are treated discretely using a three dimensional shock fitting procedure. The boundary layer flows are computed using a second-order implicit finite difference method. The shock wave-boundary layer interaction is computed using an integral formulation. The general structure of the computer program is discussed, and a brief description of each subroutine is given. All program input parameters are defined, and a brief discussion on interpretation of the output is provided. A number of sample cases, complete with data listings, are provided.

Vadyak, J.↗

NASA NTRS1988

Unsteady transonic aerodynamics and aeroelastic calculations at low-supersonic freestreams

A computational procedure is presented to simulate transonic unsteady flows and corresponding aeroelasticity of wings at low-supersonic freestreams. The flow is modeled by using the transonic small-perturbation theory. The structural equations of motions are modeled using modal equations of motion directly coupled with aerodynamics. Supersonic freestreams are simulated by properly accounting for the boundary conditions based on pressure waves along the flow characteristics in streamwise planes. The flow equations are solved using the time-accurate, alternating-direction implicit finite-difference scheme. The coupled aeroelastic equations of motion are solved by an integration procedure based on the time-accurate, linear-acceleration method. The flow modeling is verified by comparing calculations with experiments for both steady and unsteady flows at supersonic freestreams. The unsteady computations are made for oscillating wings. Comparisons of computed results with experiments show good agreement. Aeroelastic responses are computed for a rectangular wing at Mach numbers ranging from subtransonic to upper-transonic (supersonic) freestreams. The extension of the transonic dip into the upper transonic regime is illustrated.

Guruswamy, Guru P.↗

NASA NTRS1991

An effective multigrid method for high-speed flows

The use is considered of a multigrid method with central differencing to solve the Navier-Stokes equations for high speed flows. The time dependent form of the equations is integrated with a Runge-Kutta scheme accelerated by local time stepping and variable coefficient implicit residual smoothing. Of particular importance are the details of the numerical dissipation formulation, especially the switch between the second and fourth difference terms. Solutions are given for 2-D laminar flow over a circular cylinder and a 15 deg compression ramp.

Swanson, R. C.↗

NASA NTRS1992

An effective multigrid method for high-speed flows

Swanson, R. C.↗

NASA NTRS1976

Split Space-Marching Finite-Volume Method for Chemically Reacting Supersonic Flow

A space-marching finite-volume method employing a nonorthogonal coordinate system and using a split differencing scheme for calculating steady supersonic flow over aerodynamic shapes is presented. It is a second-order-accurate mixed explicit-implicit procedure that solves the inviscid adiabatic and nondiffusive equations for chemically reacting flow in integral conservation-law form. The relationship between the finite-volume and differential forms of the equations is examined and the relative merits of each discussed. The method admits initial Cauchy data situated on any arbitrary surface and integrates them forward along a general curvilinear coordinate, distorting and deforming the surface as it advances. The chemical kinetics term is split from the convective terms which are themselves dimensionally split, thereby freeing the fluid operators from the restricted step size imposed by the chemical reactions and increasing the computational efficiency. The accuracy of this splitting technique is analyzed, a sufficient stability criterion is established, a representative flow computation is discussed, and some comparisons are made with another method.

Rizzi, Arthur W.↗

NASA NTRS2022

Chapter 7: Integrative Science

A key part of DOE's mission is addressing energy and environmental problems through transformative science and technology, which includes discovering and developing new energy systems and understanding and predicting their consequences at local to global scales. Enabling these advances are the fundamental scientific discoveries and tools delivered by the Office of Science. Implicit in DOE's mission is the need to understand the complex, multiscale interactions between energy systems and the environment. Attaining this knowledge requires an integrated research portfolio that promotes understanding and discovery across different subsystems of the overall energy system and enables sustainable prosperity through a vibrant bioeconomy.

Biological and Environmental Research Advisory Com↗

DOE OSTI2024

Implementation and (Inverse Modified) Error Analysis for Implicitly Templated ODE-Nets

We focus on learning unknown dynamics from data using ODE-nets templated on implicit numerical initial value problem solvers. First, we perform inverse modified error analysis of the ODE-nets using unrolled implicit schemes for ease of interpretation. It is shown that training an ODE-net using an unrolled implicit scheme returns a close approximation of an inverse modified differential equation (IMDE). In addition, we establish a theoretical basis for hyperparameter selection when training such ODE-nets, whereas current strategies usually treat numerical integration of ODE-nets as a black box. We thus formulate an adaptive algorithm which monitors the level of error and adapts the number of (unrolled) implicit solution iterations during the training process, so that the error of the unrolled approximation is less than the current learning loss. This helps accelerate training while maintaining accuracy. Several numerical experiments are performed to demonstrate the advantages of the proposed algorithm compared to nonadaptive unrollings and validate the theoretical analysis. Here, we also note that this approach naturally allows for incorporating partially known physical terms in the equations, giving rise to what is termed “gray box” identification.

ODE-nets↗

NASA NTRS1986

Implicit methods for computing chemically reacting flow

The backward Euler scheme was used to solve a large system of inviscid flow and chemical rate equations in three spatial coordinates. The flow equations were integrated simultaneously in time by a conventional ADI factorization technique, then the species equations were solved by either simultaneous or successive techniques. The methods were evaluated in their efficiency and robustness for a hypersonic flow problem involving an aerobrake configuration. It was found that both implicit methods can effectively reduce the stiffness associated with the chemical production term and that the successive solution for the species was as stable as the simultaneous solution. The latter method is more economical because the computation time varies linearly with the number of species.

Li, C. P.↗

DOE OSTI2023

An implicit, conservative and asymptotic-preserving electrostatic particle-in-cell algorithm for arbitrarily magnetized plasmas in uniform magnetic fields

Here, we introduce a new electrostatic particle-in-cell algorithm capable of using large timesteps compared to particle gyro-period under a uniform external magnetic field. The algorithm extends earlier electrostatic fully implicit PIC implementations with a new asymptotic-preserving particle-push scheme that allows timesteps much larger than particle gyroperiods. In the large-timestep limit, the integrator preserves all particle drifts, while recovering the full orbit for small timesteps. The scheme allows for a seamless, efficient treatment of particles with coexisting magnetized and unmagnetized species, and conserves energy and charge exactly without spoiling implicit solver performance. We demonstrate by numerical experiment with several problems of variable species magnetization (diocotron instability, modified two-stream instability, and drift instability) that orders of magnitude wall-clock-time speedups vs. the standard fully implicit electrostatic PIC algorithm are possible without sacrificing solution accuracy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1988

An unconditionally stable Runge-Kutta method for unsteady flows

A quasi-three dimensional analysis was developed for unsteady rotor-stator interaction in turbomachinery. The analysis solves the unsteady Euler or thin-layer Navier-Stokes equations in a body fitted coordinate system. It accounts for the effects of rotation, radius change, and stream surface thickness. The Baldwin-Lomax eddy viscosity model is used for turbulent flows. The equations are integrated in time using a four stage Runge-Kutta scheme with a constant time step. Implicit residual smoothing was employed to accelerate the solution of the time accurate computations. The scheme is described and accuracy analyses are given. Results are shown for a supersonic through-flow fan designed for NASA Lewis. The rotor:stator blade ratio was taken as 1:1. Results are also shown for the first stage of the Space Shuttle Main Engine high pressure fuel turbopump. Here the blade ratio is 2:3. Implicit residual smoothing was used to increase the time step limit of the unsmoothed scheme by a factor of six with negligible differences in the unsteady results. It is felt that the implicitly smoothed Runge-Kutta scheme is easily competitive with implicit schemes for unsteady flows while retaining the simplicity of an explicit scheme.

Jorgenson, Philip C. E.↗

NASA NTRS1988

Analytical study of the liquid phase transient behavior of a high temperature heat pipe

The transient operation of the liquid phase of a high temperature heat pipe is studied. The study was conducted in support of advanced heat pipe applications that require reliable transport of high temperature drops and significant distances under a broad spectrum of operating conditions. The heat pipe configuration studied consists of a sealed cylindrical enclosure containing a capillary wick structure and sodium working fluid. The wick is an annular flow channel configuration formed between the enclosure interior wall and a concentric cylindrical tube of fine pore screen. The study approach is analytical through the solution of the governing equations. The energy equation is solved over the pipe wall and liquid region using the finite difference Peaceman-Rachford alternating direction implicit numerical method. The continuity and momentum equations are solved over the liquid region by the integral method. The energy equation and liquid dynamics equation are tightly coupled due to the phase change process at the liquid-vapor interface. A kinetic theory model is used to define the phase change process in terms of the temperature jump between the liquid-vapor surface and the bulk vapor. Extensive auxiliary relations, including sodium properties as functions of temperature, are used to close the analytical system. The solution procedure is implemented in a FORTRAN algorithm with some optimization features to take advantage of the IBM System/370 Model 3090 vectorization facility. The code was intended for coupling to a vapor phase algorithm so that the entire heat pipe problem could be solved. As a test of code capabilities, the vapor phase was approximated in a simple manner.

Roche, Gregory Lawrence↗