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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS2007

GRMHD and GRPIC Simulations

We have developed a new three-dimensional general relativistic magnetohydrodynamic (GRMHD) code by using a conservative, high-resolution shock-capturing scheme. The numerical fluxes are calculated using the HLL approximate Riemann solver scheme. The flux-interpolated constrained transport scheme is used to maintain a divergence-free magnetic field. We have performed various 1-dimensional test problems in both special and general relativity by using several reconstruction methods and found that the new 3D GRMHD code shows substantial improvements over our previous code. The simulation results show the jet formations from a geometrically thin accretion disk near a nonrotating and a rotating black hole. We will discuss the jet properties depended on the rotation of a black hole and the magnetic field configuration including issues for future research. A General Relativistic Particle-in-Cell Code (GRPIC) has been developed using the Kerr-Schild metric. The code includes kinetic effects, and is in accordance with GRMHD code. Since the gravitational force acting on particles is extreme near black holes, there are some difficulties in numerically describing these processes. The preliminary code consists of an accretion disk and free-falling corona. Results indicate that particles are ejected from the black hole. These results are consistent with other GRMHD simulations. The GRPIC simulation results will be presented, along with some remarks and future improvements. The emission is calculated from relativistic flows in black hole systems using a fully general relativistic radiative transfer formulation, with flow structures obtained by GRMHD simulations considering thermal free-free emission and thermal synchrotron emission. Bright filament-like features protrude (visually) from the accretion disk surface, which are enhancements of synchrotron emission where the magnetic field roughly aligns with the line-of-sight in the co-moving frame. The features move back and forth as the accretion flow evolves, but their visibility and morphology are robust. We would like to extend this research using GRPIC simulations and examine a possible new mechanism for certain X-ray quasi-periodic oscillations (QPOs) observed in blackhole X-ray binaries.

Nishikawa, K.-I.↗
NASA NTRS2008

High-Order Energy Stable WENO Schemes

A new third-order Energy Stable Weighted Essentially NonOscillatory (ESWENO) finite difference scheme for scalar and vector linear hyperbolic equations with piecewise continuous initial conditions is developed. The new scheme is proven to be stable in the energy norm for both continuous and discontinuous solutions. In contrast to the existing high-resolution shock-capturing schemes, no assumption that the reconstruction should be total variation bounded (TVB) is explicitly required to prove stability of the new scheme. A rigorous truncation error analysis is presented showing that the accuracy of the 3rd-order ESWENO scheme is drastically improved if the tuning parameters of the weight functions satisfy certain criteria. Numerical results show that the new ESWENO scheme is stable and significantly outperforms the conventional third-order WENO finite difference scheme of Jiang and Shu in terms of accuracy, while providing essentially nonoscillatory solutions near strong discontinuities.

Yamaleev, Nail K.↗
NASA NTRS2009

Implementation of Radiation, Ablation, and Free Energy Minimization Modules for Coupled Simulations of Hypersonic Flow

A description of models and boundary conditions required for coupling radiation and ablation physics to a hypersonic flow simulation is provided. Chemical equilibrium routines for varying elemental mass fraction are required in the flow solver to integrate with the equilibrium chemistry assumption employed in the ablation models. The capability also enables an equilibrium catalytic wall boundary condition in the non-ablating case. The paper focuses on numerical implementation issues using FIRE II, Mars return, and Apollo 4 applications to provide context for discussion. Variable relaxation factors applied to the Jacobian elements of partial equilibrium relations required for convergence are defined. Challenges of strong radiation coupling in a shock capturing algorithm are addressed. Results are presented to show how the current suite of models responds to a wide variety of conditions involving coupled radiation and ablation.

Gnoffo, Peter A.↗
NASA NTRS2009

CFD Simulation on the J-2X Engine Exhaust in the Center-Body Diffuser and Spray Chamber at the B-2 Facility

A computational fluid dynamic (CFD) code is used to simulate the J-2X engine exhaust in the center-body diffuser and spray chamber at the Spacecraft Propulsion Facility (B-2). The CFD code is named as the space-time conservation element and solution element (CESE) Euler solver and is very robust at shock capturing. The CESE results are compared with independent analysis results obtained by using the National Combustion Code (NCC) and show excellent agreement.

Wang, Xiao-Yen↗
NASA NTRS2010

Updates to Multi-Dimensional Flux Reconstruction for Hypersonic Simulations on Tetrahedral Grids

The quality of simulated hypersonic stagnation region heating with tetrahedral meshes is investigated by using an updated three-dimensional, upwind reconstruction algorithm for the inviscid flux vector. An earlier implementation of this algorithm provided improved symmetry characteristics on tetrahedral grids compared to conventional reconstruction methods. The original formulation however displayed quantitative differences in heating and shear that were as large as 25% compared to a benchmark, structured-grid solution. The primary cause of this discrepancy is found to be an inherent inconsistency in the formulation of the flux limiter. The inconsistency is removed by employing a Green-Gauss formulation of primitive gradients at nodes to replace the previous Gram-Schmidt algorithm. Current results are now in good agreement with benchmark solutions for two challenge problems: (1) hypersonic flow over a three-dimensional cylindrical section with special attention to the uniformity of the solution in the spanwise direction and (2) hypersonic flow over a three-dimensional sphere. The tetrahedral cells used in the simulation are derived from a structured grid where cell faces are bisected across the diagonal resulting in a consistent pattern of diagonals running in a biased direction across the otherwise symmetric domain. This grid is known to accentuate problems in both shock capturing and stagnation region heating encountered with conventional, quasi-one-dimensional inviscid flux reconstruction algorithms. Therefore the test problems provide a sensitive indicator for algorithmic effects on heating. Additional simulations on a sharp, double cone and the shuttle orbiter are then presented to demonstrate the capabilities of the new algorithm on more geometrically complex flows with tetrahedral grids. These results provide the first indication that pure tetrahedral elements utilizing the updated, three-dimensional, upwind reconstruction algorithm may be used for the simulation of heating and shear in hypersonic flows in upwind, finite volume formulations.

Gnoffo, Peter A.↗
NASA NTRS2011

Numerical Dissipation and Wrong Propagation Speed of Discontinuities for Stiff Source Terms

In compressible turbulent combustion/nonequilibrium flows, the constructions of numerical schemes for (a) stable and accurate simulation of turbulence with strong shocks, and (b) obtaining correct propagation speed of discontinuities for stiff reacting terms on coarse grids share one important ingredient - minimization of numerical dissipation while maintaining numerical stability. Here coarse grids means standard mesh density requirement for accurate simulation of typical non-reacting flows. This dual requirement to achieve both numerical stability and accuracy with zero or minimal use of numerical dissipation is most often conflicting for existing schemes that were designed for non-reacting flows. The goal of this paper is to relate numerical dissipations that are inherited in a selected set of high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities for two representative stiff detonation wave problems.

Yee, H. C.↗
NASA NTRS2012

In-Flight Boundary-Layer Transition on a Large Flat Plate at Supersonic Speeds

A flight experiment was conducted to investigate the pressure distribution, local flow conditions, and boundary-layer transition characteristics on a large flat plate in flight at supersonic speeds up to Mach 2.0. The primary objective of the test was to characterize the local flow field in preparation for future tests of a high Reynolds number natural laminar flow test article. The tests used a F-15B testbed aircraft with a bottom centerline mounted test fixture. A second objective was to determine the boundary-layer transition characteristics on the flat plate and the effectiveness of using a simplified surface coating for future laminar flow flight tests employing infrared thermography. Boundary-layer transition was captured using an onboard infrared imaging system. The infrared imagery was captured in both analog and digital formats. Surface pressures were measured with electronically scanned pressure modules connected to 60 surface-mounted pressure orifices. The local flow field was measured with five 5-hole conical probes mounted near the leading edge of the test fixture. Flow field measurements revealed the local flow characteristics including downwash, sidewash, and local Mach number. Results also indicated that the simplified surface coating did not provide sufficient insulation from the metallic structure, which likely had a substantial effect on boundary-layer transition compared with that of an adiabatic surface. Cold wall conditions were predominant during the acceleration to maximum Mach number, and warm wall conditions were evident during the subsequent deceleration. The infrared imaging system was able to capture shock wave impingement on the surface of the flat plate in addition to indicating laminar-to-turbulent boundary-layer transition.

Banks, Daniel W.↗
NASA NTRS2012

Numerical Dissipation and Wrong Propagation Speed of Discontinuities for Stiff Source Terms

In compressible turbulent combustion/nonequilibrium flows, the constructions of numerical schemes for (a) stable and accurate simulation of turbulence with strong shocks, and (b) obtaining correct propagation speed of discontinuities for stiff reacting terms on coarse grids share one important ingredient - minimization of numerical dissipation while maintaining numerical stability. Here coarse grids means standard mesh density requirement for accurate simulation of typical non-reacting flows. This dual requirement to achieve both numerical stability and accuracy with zero or minimal use of numerical dissipation is most often conflicting for existing schemes that were designed for non-reacting flows. The goal of this paper is to relate numerical dissipations that are inherited in a selected set of high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities as a function of stiffness of the source term and the grid spacing.

Yee, H. C.↗
NASA NTRS2011

Multidisciplinary Modeling Software for Analysis, Design, and Optimization of HRRLS Vehicles

The concept for Highly Reliable Reusable Launch Systems (HRRLS) under the NASA Hypersonics project is a two-stage-to-orbit, horizontal-take-off / horizontal-landing, (HTHL) architecture with an air-breathing first stage. The first stage vehicle is a slender body with an air-breathing propulsion system that is highly integrated with the airframe. The light weight slender body will deflect significantly during flight. This global deflection affects the flow over the vehicle and into the engine and thus the loads and moments on the vehicle. High-fidelity multi-disciplinary analyses that accounts for these fluid-structures-thermal interactions are required to accurately predict the vehicle loads and resultant response. These predictions of vehicle response to multi physics loads, calculated with fluid-structural-thermal interaction, are required in order to optimize the vehicle design over its full operating range. This contract with ResearchSouth addresses one of the primary objectives of the Vehicle Technology Integration (VTI) discipline: the development of high-fidelity multi-disciplinary analysis and optimization methods and tools for HRRLS vehicles. The primary goal of this effort is the development of an integrated software system that can be used for full-vehicle optimization. This goal was accomplished by: 1) integrating the master code, FEMAP, into the multidiscipline software network to direct the coupling to assure accurate fluid-structure-thermal interaction solutions; 2) loosely-coupling the Euler flow solver FEFLO to the available and proven aeroelasticity and large deformation (FEAP) code; 3) providing a coupled Euler-boundary layer capability for rapid viscous flow simulation; 4) developing and implementing improved Euler/RANS algorithms into the FEFLO CFD code to provide accurate shock capturing, skin friction, and heat-transfer predictions for HRRLS vehicles in hypersonic flow, 5) performing a Reynolds-averaged Navier-Stokes computation on an HRRLS configuration; 6) integrating the RANS solver with the FEAP code for coupled fluid-structure-thermal capability; and 7) integrating the existing NASA SRGULL propulsion flow path prediction software with the FEFLO software for quasi-3D propulsion flow path predictions, 8) improving and integrating into the network, an existing adjoint-based design optimization code.

Spradley, Lawrence W.↗
NASA NTRS2013

On Spurious Numerics in Solving Reactive Equations

The objective of this study is to gain a deeper understanding of the behavior of high order shock-capturing schemes for problems with stiff source terms and discontinuities and on corresponding numerical prediction strategies. The studies by Yee et al. (2012) and Wang et al. (2012) focus only on solving the reactive system by the fractional step method using the Strang splitting (Strang 1968). It is a common practice by developers in computational physics and engineering simulations to include a cut off safeguard if densities are outside the permissible range. Here we compare the spurious behavior of the same schemes by solving the fully coupled reactive system without the Strang splitting vs. using the Strang splitting. Comparison between the two procedures and the effects of a cut off safeguard is the focus the present study. The comparison of the performance of these schemes is largely based on the degree to which each method captures the correct location of the reaction front for coarse grids. Here "coarse grids" means standard mesh density requirement for accurate simulation of typical non-reacting flows of similar problem setup. It is remarked that, in order to resolve the sharp reaction front, local refinement beyond standard mesh density is still needed.

Numerics↗
NASA NTRS2017

Stabilized Finite Elements in FUN3D

A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.

Anderson, W. Kyle↗
NASA NTRS2019

WRLES: Wave Resolving Large-Eddy Simulation Code, Theory and Usage

A computational fluid dynamics code has been developed for large-eddy simulations (LES) of turbulent flow. The code uses high-order of accuracy and high-resolution numerical methods to minimize solution error and maximize the resolution of the turbulent structures. Spatial discretization is performed using explicit central differencing. The central differencing schemes in the code include 2nd- to 12th-order standard central difference methods as well as 7-, 9-, 11- and 13-point dispersion relation preserving schemes. Solution filtering and high-order shock capturing are included for stability. Time discretization is performed using multistage Runge-Kutta methods that are up to 4th order accurate. Several options are available to model turbulence including: Baldwin-Lomax and Spalart-Allmaras Reynolds-averaged Navier-Stokes turbulence models, and Smagorinsky, Dynamic Smagorinsky and Vreman sub-grid scale models for LES. This report presents the theory behind the numerical and physical models used in the code and provides a user's manual to the operation of the code.

High-Order↗
NASA NTRS2010

TPSAS-NF1676L-10658-DND

The systematic methodology for constructing fourth-order finite domain Energy Stable WENO schemes is developed. We prove that for hyperbolic systems, the finite domain ESWENO scheme is stable in the energy norm for both continuous and discontinuous solutions. The eigenvalues of the finite domain ESWENO dissipation operator are located in the left-half plane. Based on the rigorous truncation error analysis, the new weight functions are developed, which drastically improve the accuracy of the ESWENO scheme and provide excellent shock-capturing capabilities. Numerical experiments show that the new finite domain ESWENO scheme with the new weights outperform the conventional WENO schemes in terms of accuracy.

Travis Fisher↗
NASA NTRSDate not supplied

OVERFLOW Analysis of Supersonic Retropropulsion Testingon the CobraMRV Mars Entry Vehicle Concept

The CFD solver OVERFLOW was used to simulate the CobraMRV undergoing supersonic retropropulsion (SRP) in the Langley Unitary Plan Wind Tunnel as part of a pre-test study. Aerodynamics of the CobraMRV are summarized and the sensitivity of vehicle loads to CFD parameters at a subset of operating conditions are investigated. Specific numerical methods, boundary conditions, and turbulence modeling options have been selected after considering the complex phenomena in SRP flows. Proper shock-capturing methods and dynamic grid adaption are necessary to correctly capture vehicle loads and dynamics. Present data indicates that at particular conditions, upstream asymmetries originating from the tunnel inflow plane contribute to measurable asymmetries on the CobraMRV heatshield.

OVERFLOW↗
NASA NTRSDate not supplied

Uncertainty Quantification of CFD Model Assumptions Against Sonic Boom Noise Prediction of a Commercial Supersonic Transport

This paper presents the results of uncertainty modeling of sonic boom noise generation from commercial supersonic transport considering the Spalart-Allmaras (SA) turbulence modeling parameters as well as Mach number, angle of attack and altitude. Sample generation and analysis for this uncertainty model was performed by UQPCE, which is a software package developed at the NASA Langley Research Center. To build the uncertainty model, 42 cases of sonic boom noise calculation were performed. Computation of the ground noise can be briefly summarized in two steps. First, the near field pressure waveforms are sampled from CFD calculation using the NASA Langley’s FUN3D solver. Second, this information is passed to an atmospheric propagation code, sBOOM, which solves an augmented Burger’s equation and simulates how the near field waveforms will change while passing through the atmosphere. The ground signature is further processed to obtain the perceived loudness, PLdB. Having a high spatial resolution near the shockwave in the CFD calculation is critical in sonic boom noise prediction. Because the variation in the input parameters for the current uncertainty quantification (UQ) study is likely to lead to change in shock location, angle and strength, the grid adaptation for shock capturing is independently applied for each condition. The final mesh used in the CFD calculation consists of approximately 420 million cells. The pressure signatures are sampled at three, four and five body lengths away from the aircraft to make sure the three dimensional effects around the aircraft are resolved. The results of the UQ analysis shows that within the three aleatory variables, the angle of attack had the most impact against ground noise, followed by the altitude and the Mach number. Between the two SA model parameters, the Kármán constant (𝜅) was significantly more important than the turbulent Prandtl number (𝜎), but these two parameters were only marginally significant in the overall prediction variance in ground noise. The UQ procedure explained in this paper can be widely applied to other model parameters.

Uncertainty Quantification↗
NASA NTRSDate not supplied

Uncertainty Quantification of CFD Model Assumptions Against Sonic Boom Noise Prediction of a Commercial Supersonic Transport

This paper presents the results of uncertainty modeling of sonic boom noise generation from commercial supersonic transport considering the Spalart-Allmaras (SA) turbulence modeling parameters as well as Mach number, angle of attack and altitude. Sample generation and analysis for this uncertainty model was performed by UQPCE, which is a software package developed at the NASA Langley Research Center. To build the uncertainty model, 42 cases of sonic boom noise calculation were performed. Computation of the ground noise can be briefly summarized in two steps. First, the near field pressure waveforms are sampled from CFD calculation using the NASA Langley’s FUN3D solver. Second, this information is passed to an atmospheric propagation code, sBOOM, which solves an augmented Burger’s equation and simulates how the near field waveforms will change while passing through the atmosphere. The ground signature is further processed to obtain the perceived loudness, PLdB. Having a high spatial resolution near the shock wave in the CFD calculation is critical in sonic boom noise prediction. Because the variation in the input parameters for the current uncertainty quantification (UQ) study is likely to lead to change in shock location, angle and strength, the grid adaptation for shock capturing is independently applied for each condition. The final mesh used in the CFD calculation consists of approximately 420 million cells. The pressure signatures are sampled at three, four and five body lengths away from the aircraft to make sure the three dimensional effects around the aircraft are resolved. The results of the UQ analysis shows that within the three aleatory variables, the angle of attack had the most impact against ground noise, followed by the altitude and the Mach number. Between the two SA model parameters, the Kármán constant (𝜅) was significantly more important than the turbulent Prandtl number (𝜎), but these two parameters were only marginally significant in the overall prediction variance in ground noise. The UQ procedure explained in this paper can be widely applied to other model parameters.

Uncertainty Quantifications↗
NASA NTRS2023

Chemical Thermodynamics and the Mathematical Integration of Reaction Kinetics

Key advances in the development of numerical methods for non-reacting compressible flows have been enabled by translating physical requirements into concrete numerical guidelines, such as the satisfaction of entropy inequalities for shock-capturing techniques [Lax, Contributions to Nonlinear Functional Analysis (1971) 603-634]. In the present work, we present nonlinear numerical analysis tools that draw from Chemical Thermodynamics , the branch of Nonequilibrium Thermodynamics that deals with chemical reactions. Through Gibbs formalism, chemical thermodynamics provides a well-known theoretical expression for the chemical equilibrium constant of a reaction in terms of reduced chemical potentials. A less-known, yet extremely valuable result, due to [Krambeck, Arch. Ration. Mech. Anal. , 38 (1970) 317], states that when this expression is implemented, mass-action kinetic models are consistent with the dynamical prescriptions of the 2nd law of thermodynamics. For fixed-temperature ordinary differential equations modeling constant-volume reacting gas mixtures, this leads to a decreasing Helmholtz free energy. If the temperature is allowed to vary in accordance with conservation of energy (1st law), this leads to the statement of increasing entropy. These nonlinear prescriptions can, and should be, used to further develop temporal integration techniques for reaction kinetics. We demonstrate that Krambeck's result holds even when the equilibrium constants are approximated from data. We prove this result by constructing the implicit free energy and the implicit entropy inherent to a given approximation. This is first done for a 5-species, 17-reaction model problem for air. With this structure established, elements of discrete entropy-stability theory [Tadmor, Acta Numer. , 12 (2003) 451] are leveraged to examine the consistency of time-integration schemes with these prescriptions. Using chemical potentials, one can compute the respective contributions of the kinetics model and of the temporal scheme to free energy/entropy variations. We introduce a nonlinear-stable version of the Discontinuous-Galerkin (DG) scheme in time which shows robustness improvements over the standard linearly-stable version. Most notably, the maximum timestep that can be resolved with the nonlinearly-stable variant tends to grow with polynomial order, in contrast to the linearly-stable variant. We generalize our constructions to arbitrary systems of reversible chemical reactions, ultimately showing that the compressible reacting Euler system admits the opposite of the implicitly constructed thermodynamic entropy as a mathematical entropy . This lays important theoretical foundations towards robust scheme development [Harten, J. Comput. Phys. 49 (1983) 151-164].

STMD↗
NASA NTRS2003

Finite Element Method for Capturing Ultra-relativistic Shocks

While finite element methods are used extensively by researchers solving computational fluid dynamics in fields other than astrophysics, their use in astrophysical fluid simulations has been predominantly overlooked. Current simulations using other methods such as finite difference and finite volume (based on finite difference) have shown remarkable results, but these methods are limited by their fundamental properties in aspects that are important for simulations with complex geometries and widely varying spatial and temporal scale differences. We have explored the use of finite element methods for astrophysical fluids in order to establish the validity of using such methods in astrophysical environments. We present our numerical technique applied to solving ultra-relativistic (Lorentz Factor Gamma >> 1) shocks which are prevalent in astrophysical studies including relativistic jets and gamma-ray burst studies. We show our finite element formulation applied to simulations where the Lorentz factor ranges up to 2236 and demonstrate its stability in solving ultra-relativistic flows. Our numerical method is based on the Flowfield Dependent Variation (FDV) Method, unique in that numerical diffusion is derived from physical parameters rather than traditional artificial viscosity methods. Numerical instabilities account for most of the difficulties when capturing shocks in this regime. Our method results in stable solutions and accurate results as compared with other methods.

Richardson, G. A.↗