Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “high-order time integration”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

Improving Trustworthiness of Data-Driven Power Grid Contingency Analysis With Bayesian Residual Graph Neural Networks

The evolving energy landscape requires novel tools to efficiently perform contingency analysis and reliability assessment of power grids, potentially in real-time. The high computational cost of traditional power flow solvers limits their applicability in practice. Machine learning (ML) surrogates such as deep neural networks (NNs) accelerate power flow solvers computations, enabling high-order contingency analysis and real-time decision-making by learning highly nonlinear functions and integrating grid topology via graph architectures. However, (graph) NNs lack predictive power away from training data and do not provide predictive confidence estimates. Here, we present a Bayesian residual graph NN that integrates knowledge from low-fidelity data via residual training and embeds granular quantification of uncertainties, improving trustworthiness critical for high-consequence decision-making. Applying Bayesian concepts to NNs is challenging due to the high-dimensionality of both the parameter space, complicating derivation of a meaningful prior, and the output space in large grid systems, requiring enhanced techniques to assess the predicted high-dimensional uncertainties. Our contributions include: (1) Deriving a prior for fully connected and graph NNs that leverages low-fidelity data to guide mean predictions and appropriately control prior predictive uncertainty. (2) Integrating this prior within an ensembling with anchoring scheme for efficient approximate posterior inference. (3) Deriving enhanced metrics to assess accuracy of both the mean and uncertainty predictions in high dimensions, appropriately accounting for correlations propagated through graph layers. The resulting Bayesian residual graph NN is tested on a contingency analysis task for 14-bus and 118-bus grids.

24 - POWER TRANSMISSION AND DISTRIBUTION↗

Advanced System Thermal Fluids Solver Development for SAM

This work summarizes a feasibility study on testing numerical algorithms that are suitable and efficient for advanced system analysis code development under the mutli-physics framework, MOOSE. The key is the implementation of a high-order one-dimensional staggered-grid finite volume method (SG-FVM), and its direct interaction with the linear/nonlinear solver, PETSc. Leveraging the existing capabilities of the SAM code, significant code coverages were established in the finite volume method code. This in turn allows for a suite of test problems with different problem sizes and levels of complexity to be used to quantify the performance improvement of the finite volume method code. As evidently shown in this study, the implemented SG-FVM demonstrated superior performance improvement against a direct finite element method implementation through MOOSE for the wide range of selected problems. On two computer systems, the speedup was observed to be significant, with at least one order of magnitude of solving time reduction. In addition, for a complex reactor model, transient simulation was performed using the finite volume method code, the results of which agree very well with the reference results from the finite element method code. Overall, this study demonstrates a successful feasibility study on the proposed numerical algorithms and software structure to support advanced system analysis tool development. In this work, short-term priority development and testing items were identified, and long-term code adoption and integration plans were made for the eventual deployment of the finite volume method in the SAM code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Toward Higher-order Accuracy in Self-gravitating Hydrodynamics

High-order algorithms have emerged in numerical astrophysics as a promising avenue to reduce truncation error (proportional to a power of the linear resolution Δ x ) with only a moderate increase to computational expense. Significant effort has been placed in the development of finite-volume algorithms for (magneto)hydrodynamics; however, state-of-the-art astrophysical simulations tightly couple a plenitude of physics, additionally including gravity, photon transport, cosmic-ray transport, chemistry, and/or diffusion, to name a few. Algorithms frequently operator-split this additional physics (often a first-order error in time) and/or adopt a model wherein their evaluation is limited to second-order accuracy in space. In this work, we present a fourth-order-accurate finite-volume scheme for self-gravitating hydrodynamics on a uniform Cartesian grid. The method supplies source terms for the gravitational acceleration ( ρ g ) and gravitational energy release ( ρ v · g ) associated with fourth-order-accurate solutions to the Poisson equation. Our scheme (1) guarantees the conservation of total linear momentum while (2) decreasing (in proportion to Δ x 4 ) the effects of spurious heating and/or cooling associated with truncation error in the gravity. We demonstrate expected convergence rates for the algorithm by measuring errors in test problems evolving self-gravity modified linear waves and 3D polytropic equilibria. We test robustness of the algorithm by integrating an induced “inside-out” adiabatic collapse. We also discuss a method to smoothly downgrade the solution to second-order spatial accuracy to avoid spurious overshoots near steep density and/or pressure gradients.

79 ASTRONOMY AND ASTROPHYSICS↗

On the improvement of deconvolution with digitized data using a Runge-Kutta integration scheme

A relatively simple change in the treatment of the input function in numerical integration of high-order differential equations by Runge-Kutta methods provides substantial improvements in accuracy, particularly when the forcing function is in digitized form. The Runge-Kutta-Gill coefficients are modified to incorporate the changes; with pulse-type excitations, improvements on the order of 2 to 50 times greater accuracy are demonstrated.

Houghton, J. R.↗

Numerical Simulation of a High Mach Number Jet Flow

The recent efforts to develop accurate numerical schemes for transition and turbulent flows are motivated, among other factors, by the need for accurate prediction of flow noise. The success of developing high speed civil transport plane (HSCT) is contingent upon our understanding and suppression of the jet exhaust noise. The radiated sound can be directly obtained by solving the full (time-dependent) compressible Navier-Stokes equations. However, this requires computational storage that is beyond currently available machines. This difficulty can be overcome by limiting the solution domain to the near field where the jet is nonlinear and then use acoustic analogy (e.g., Lighthill) to relate the far-field noise to the near-field sources. The later requires obtaining the time-dependent flow field. The other difficulty in aeroacoustics computations is that at high Reynolds numbers the turbulent flow has a large range of scales. Direct numerical simulations (DNS) cannot obtain all the scales of motion at high Reynolds number of technological interest. However, it is believed that the large scale structure is more efficient than the small-scale structure in radiating noise. Thus, one can model the small scales and calculate the acoustically active scales. The large scale structure in the noise-producing initial region of the jet can be viewed as a wavelike nature, the net radiated sound is the net cancellation after integration over space. As such, aeroacoustics computations are highly sensitive to errors in computing the sound sources. It is therefore essential to use a high-order numerical scheme to predict the flow field. The present paper presents the first step in a ongoing effort to predict jet noise. The emphasis here is in accurate prediction of the unsteady flow field. We solve the full time-dependent Navier-Stokes equations by a high order finite difference method. Time accurate spatial simulations of both plane and axisymmetric jet are presented. Jet Mach numbers of 1.5 and 2.1 are considered. Reynolds number in the simulations was about a million. Our numerical model is based on the 2-4 scheme by Gottlieb & Turkel. Bayliss et al. applied the 2-4 scheme in boundary layer computations. This scheme was also used by Ragab and Sheen to study the nonlinear development of supersonic instability waves in a mixing layer. In this study, we present two dimensional direct simulation results for both plane and axisymmetric jets. These results are compared with linear theory predictions. These computations were made for near nozzle exit region and velocity in spanwise/azimuthal direction was assumed to be zero.

Hayder, M. Ehtesham↗

Effects of spatial order of accuracy on the computation of vortical flowfields

The effect of the order-of-accuracy, used for the spatial discretization, on the resolution of the leading edge vortices over sharp-edged delta wings is investigated. The flowfield is computed using a viscous/inviscid zonal approach. The viscous flow in the vicinity of the wing is computed using the conservative formulation of the compressible, thin-layer Navier-Stokes equations. The leeward-side vortical flowfield and the other flow regions away from the surface are computed as inviscid. The time integration is performed with both an explicit fourth-order Runge-Kutta scheme and an implicit, factorized, iterative scheme. High-order-accurate inviscid fluxes are computed using both a conservative and a non-conservative (primitive variable) formulation. The nonlinear, inviscid terms of the primitive variable form of the governing equations are evaluated with a finite-difference numerical scheme based on the sign of the eigenvalues. High-order, upwind-biased, finite difference formulas are used to evaluate the derivatives of the nonlinear convective terms. Computed results are compared with available experimental data, and comparisons of the flowfield in the vicinity of the vortex cores are presented.

Ekaterinaris, J. A.↗

An Application of the Quadrature-Free Discontinuous Galerkin Method

The process of generating a block-structured mesh with the smoothness required for high-accuracy schemes is still a time-consuming process often measured in weeks or months. Unstructured grids about complex geometries are more easily generated, and for this reason, methods using unstructured grids have gained favor for aerodynamic analyses. The discontinuous Galerkin (DG) method is a compact finite-element projection method that provides a practical framework for the development of a high-order method using unstructured grids. Higher-order accuracy is obtained by representing the solution as a high-degree polynomial whose time evolution is governed by a local Galerkin projection. The traditional implementation of the discontinuous Galerkin uses quadrature for the evaluation of the integral projections and is prohibitively expensive. Atkins and Shu introduced the quadrature-free formulation in which the integrals are evaluated a-priori and exactly for a similarity element. The approach has been demonstrated to possess the accuracy required for acoustics even in cases where the grid is not smooth. Other issues such as boundary conditions and the treatment of non-linear fluxes have also been studied in earlier work This paper describes the application of the quadrature-free discontinuous Galerkin method to a two-dimensional shear layer problem. First, a brief description of the method is given. Next, the problem is described and the solution is presented. Finally, the resources required to perform the calculations are given.

Lockard, David P.↗

Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence

A stable high-order numerical scheme for direct numerical simulation (DNS) of shock-free compressible turbulence is presented. The method is applicable to general geometries. It contains no upwinding, artificial dissipation, or filtering. Instead the method relies on the stabilizing mechanisms of an appropriate conditioning of the governing equations and the use of compatible spatial difference operators for the interior points (interior scheme) as well as the boundary points (boundary scheme). An entropy-splitting approach splits the inviscid flux derivatives into conservative and nonconservative portions. The spatial difference operators satisfy a summation-by-parts condition, leading to a stable scheme (combined interior and boundary schemes) for the initial boundary value problem using a generalized energy estimate. A Laplacian formulation of the viscous and heat conduction terms on the right hand side of the Navier–Stokes equations is used to ensure that any tendency to odd–even decoupling associated with central schemes can be countered by the fluid viscosity. The resulting methods are able to minimize the spurious high-frequency oscillations associated with pure central schemes, especially for long time integration applications such as DNS. For validation purposes, the methods are tested in a DNS of compressible turbulent plane channel flow at low values of friction Mach number, where reference turbulence data bases exist. It is demonstrated that the methods are robust in terms of grid resolution, and in good agreement with published channel data. Accurate turbulence statistics can be obtained with moderate grid sizes. Stability limits on the range of the splitting parameter are determined from numerical tests.

N.D. Sandham↗

Traveling-Wave Tube Amplifier Model to Predict High-Order Modulation Intersymbol Interference

Demands for increased data rates in satellite communications necessitate higher order modulation schemes, larger system bandwidth, and minimum distortion of the modulated signal as it is passed through the traveling wave tube amplifier (TWTA). One type of distortion that the TWTA contributes to is intersymbol interference (ISI), and this becomes particularly disruptive with wide-band, complex modulation schemes. It is suspected that in addition to the dispersion of the TWT, frequency dependent reflections due to mismatches within the TWT are a significant contributor to ISI. To experimentally investigate the effect of these mismatches within the physical TWT on ISI would be prohibitively expensive, as it would require manufacturing numerous amplifiers in addition to the acquisition of the required digital hardware. In an attempt to develop a more accurate model to correlate IS1 with the TWTA and the operational signal, a fully three-dimensional (3D), time-dependent, TWT interaction model has been developed using the electromagnetic particle-in-cell (PIC) code MAFIA (solution of Maxwell's equations by the Finite-Integration-Algorithm). The model includes a user defined slow-wave circuit with a spatially tapered region of loss to implement a sever, and spatially varied geometry (such as helical pitch) to implement a phase velocity taper. The model also includes user defined input/output coupling and an electron beam contained by solenoidal, electrostatic, or periodic permanent magnet (PPM) focusing allowing standard or novel TWTs to be investigated. This model comprehensively takes into account the effects of frequency dependent nonlinear distortions (MAM and AMPM); gain ripple due to frequency dependent reflections at the input/output coupling, severs, and mismatches from dynamic pitch variations; drive induced oscillations; harmonic generation; intermodulation products; and backward waves.

Kory, Carol L.↗

Aeroelastic System Development Using Proper Orthogonal Decomposition and Volterra Theory

This research combines Volterra theory and proper orthogonal decomposition (POD) into a hybrid methodology for reduced-order modeling of aeroelastic systems. The out-come of the method is a set of linear ordinary differential equations (ODEs) describing the modal amplitudes associated with both the structural modes and the POD basis functions for the uid. For this research, the structural modes are sine waves of varying frequency, and the Volterra-POD approach is applied to the fluid dynamics equations. The structural modes are treated as forcing terms which are impulsed as part of the uid model realization. Using this approach, structural and uid operators are coupled into a single aeroelastic operator. This coupling converts a free boundary uid problem into an initial value problem, while preserving the parameter (or parameters) of interest for sensitivity analysis. The approach is applied to an elastic panel in supersonic cross ow. The hybrid Volterra-POD approach provides a low-order uid model in state-space form. The linear uid model is tightly coupled with a nonlinear panel model using an implicit integration scheme. The resulting aeroelastic model provides correct limit-cycle oscillation prediction over a wide range of panel dynamic pressure values. Time integration of the reduced-order aeroelastic model is four orders of magnitude faster than the high-order solution procedure developed for this research using traditional uid and structural solvers.

Lucia, David J.↗

Simultaneous FUSE, HST, and Chandra Observations or Intrinsic Absorbers in NGC 7469 and MRK 279

We obtained FUSE observations of NGC 7469 on 2002 Dec 13 & 14. The two exposures totaled only 7 ks. The observations only have good data in one channel, LiF1, due to channel alignment problems. These observations were obtained simultaneously with high-quality HST/STIS and Chandra HETG spectra. The previously known O VI absorption lines in the FUSE spectrum are detected at good signal to noise ratio, and a wide array of other intrinsic absorption lines are visible in the X-ray spectrum and in the STIS spectrum. Compared to prior FUSE observations, the continuum flux for this observation was 50% lower. We see the effects of this in the lowest-velocity O VI absorber, which we associate with the X-ray absorbing gas also detected in this object. This O VI absorber has only a 50% covering fraction, consistent with its covering only the continuum in this source, and its strength and inferred column density increased as the continuum flux of NGC 7469 decreased. This is consistent with the recombination expected from photoionization models of the highly ionized gas. We obtained FUSE observations of Mrk 279 on 2002 May 18. As for NGC 7469, channel alignment problems led to good data being present only in LiFl. While we obtained a much longer integration on the target than planned (47.4 ks vs. 31 ks requested), the UV flux was down a factor of 10 or more from previous HST and FUSE observations, and our wavelength coverage was restricted due to the channel alignment problems. These data still cover the important O VI emission line and absorption lines in Mrk 279. The FUSE flux also agrees well with the simultaneous HST STIS data, which have good signal to noise. We have also analyzed FUSE observations made at three earlier epochs. We detect the Fe K-alpha emission line in the Chandra spectrum, and its flux is consistent with the low X-ray continuum flux level of Mrk 279 at the time of the observation. Because of low signal-to-noise ratios (S/N) in the Chandra spectrum, no O VII or O VIII absorption features are observable in the Chandra data, but the UV spectra reveal strong and complex absorption from H I and high-ionization species such as O VI, N V, and C IV, as well as from low-ionization species such as C III, N III, C II, and N II in some velocity components. The far-UV spectral coverage of the FUSE data provides information on high-order Lyman series absorption, which we use to calculate the optical depths and line and continuum covering fractions in the intrinsic H I absorbing gas in a self-consistent fashion. Based on the velocities, profile shapes, covering fractions and variability of the UV absorption, we conclude that some of the absorption components, particularly those showing prominent low-ionization lines, are likely associated with the host galaxy of Mrk 279, and possibly with its interaction with a close companion galaxy, while the remainder arises in a nuclear outflow.

Sonneborn, George↗

The Legacy of Space Shuttle Flight Software

The initial goals of the Space Shuttle Program required that the avionics and software systems blaze new trails in advancing avionics system technology. Many of the requirements placed on avionics and software were accomplished for the first time on this program. Examples include comprehensive digital fly-by-wire technology, use of a digital databus for flight critical functions, fail operational/fail safe requirements, complex automated redundancy management, and the use of a high-order software language for flight software development. In order to meet the operational and safety goals of the program, the Space Shuttle software had to be extremely high quality, reliable, robust, reconfigurable and maintainable. To achieve this, the software development team evolved a software process focused on continuous process improvement and defect elimination that consistently produced highly predictable and top quality results, providing software managers the confidence needed to sign each Certificate of Flight Readiness (COFR). This process, which has been appraised at Capability Maturity Model (CMM)/Capability Maturity Model Integration (CMMI) Level 5, has resulted in one of the lowest software defect rates in the industry. This paper will present an overview of the evolution of the Primary Avionics Software System (PASS) project and processes over thirty years, an argument for strong statistical control of software processes with examples, an overview of the success story for identifying and driving out errors before flight, a case study of the few significant software issues and how they were either identified before flight or slipped through the process onto a flight vehicle, and identification of the valuable lessons learned over the life of the project.

Hickey, Christopher J.↗

Parallel Subconvolution Filtering Architectures

These architectures are based on methods of vector processing and the discrete-Fourier-transform/inverse-discrete- Fourier-transform (DFT-IDFT) overlap-and-save method, combined with time-block separation of digital filters into frequency-domain subfilters implemented by use of sub-convolutions. The parallel-processing method implemented in these architectures enables the use of relatively small DFT-IDFT pairs, while filter tap lengths are theoretically unlimited. The size of a DFT-IDFT pair is determined by the desired reduction in processing rate, rather than on the order of the filter that one seeks to implement. The emphasis in this report is on those aspects of the underlying theory and design rules that promote computational efficiency, parallel processing at reduced data rates, and simplification of the designs of very-large-scale integrated (VLSI) circuits needed to implement high-order filters and correlators.

Gray, Andrew A.↗

Planar Superconducting Millimeter-Wave/Terahertz Channelizing Filter

This innovation is a compact, superconducting, channelizing bandpass filter on a single-crystal (0.45 m thick) silicon substrate, which operates from 300 to 600 GHz. This device consists of four channels with center frequencies of 310, 380, 460, and 550 GHz, with approximately 50-GHz bandwidth per channel. The filter concept is inspired by the mammalian cochlea, which is a channelizing filter that covers three decades of bandwidth and 3,000 channels in a very small physical space. By using a simplified physical cochlear model, and its electrical analog of a channelizing filter covering multiple octaves bandwidth, a large number of output channels with high inter-channel isolation and high-order upper stopband response can be designed. A channelizing filter is a critical component used in spectrometer instruments that measure the intensity of light at various frequencies. This embodiment was designed for MicroSpec in order to increase the resolution of the instrument (with four channels, the resolution will be increased by a factor of four). MicroSpec is a revolutionary wafer-scale spectrometer that is intended for the SPICA (Space Infrared Telescope for Cosmology and Astrophysics) Mission. In addition to being a vital component of MicroSpec, the channelizing filter itself is a low-resolution spectrometer when integrated with only an antenna at its input, and a detector at each channel s output. During the design process for this filter, the available characteristic impedances, possible lumped element ranges, and fabrication tolerances were identified for design on a very thin silicon substrate. Iterations between full-wave and lumped-element circuit simulations were performed. Each channel s circuit was designed based on the availability of characteristic impedances and lumped element ranges. This design was based on a tabular type bandpass filter with no spurious harmonic response. Extensive electromagnetic modeling for each channel was performed. Four channels, with 50-GHz bandwidth, were designed, each using multiple transmission line media such as microstrip, coplanar waveguide, and quasi-lumped components on 0.45- m thick silicon. In the design process, modeling issues had to be overcome. Due to the extremely high frequencies, very thin Si substrate, and the superconducting metal layers, most commercially available software fails in various ways. These issues were mitigated by using alternative software that was capable of handling them at the expense of greater simulation time. The design of on-chip components for the filter characterization, such as a broadband antenna, Wilkinson power dividers, attenuators, detectors, and transitions has been completed.

Ehsan, Negar↗

High-Order Implicit-Explicit Multi-Block Time-stepping Method for Hyperbolic PDEs

This work seeks to explore and improve the current time-stepping schemes used in computational fluid dynamics (CFD) in order to reduce overall computational time. A high-order scheme has been developed using a combination of implicit and explicit (IMEX) time-stepping Runge-Kutta (RK) schemes which increases numerical stability with respect to the time step size, resulting in decreased computational time. The IMEX scheme alone does not yield the desired increase in numerical stability, but when used in conjunction with an overlapping partitioned (multi-block) domain significant increase in stability is observed. To show this, the Overlapping-Partition IMEX (OP IMEX) scheme is applied to both one-dimensional (1D) and two-dimensional (2D) problems, the nonlinear viscous Burger's equation and 2D advection equation, respectively. The method uses two different summation by parts (SBP) derivative approximations, second-order and fourth-order accurate. The Dirichlet boundary conditions are imposed using the Simultaneous Approximation Term (SAT) penalty method. The 6-stage additive Runge-Kutta IMEX time integration schemes are fourth-order accurate in time. An increase in numerical stability 65 times greater than the fully explicit scheme is demonstrated to be achievable with the OP IMEX method applied to 1D Burger's equation. Results from the 2D, purely convective, advection equation show stability increases on the order of 10 times the explicit scheme using the OP IMEX method. Also, the domain partitioning method in this work shows potential for breaking the computational domain into manageable sizes such that implicit solutions for full three-dimensional CFD simulations can be computed using direct solving methods rather than the standard iterative methods currently used.

Nielsen, Tanner B.↗

High-Order Finite-Difference Nonlinear Filter Methods for Subsonic Turbulence Simulation with Stochastic Forcing

Numerical stability of high-order filter schemes developed by Yee & Sjogreen is tested on three-dimensional turbulence simulations with stochastic forcing and their performance is compared with that of TVD and WENO schemes. The best­ performing filter method employs an eighth-order central base scheme with the Kennedy & Gruber skew-symmetric splitting of the inviscid flux derivative, a wavelet-based local flow sensor, a nonlinear filter utilizing the dissipative portion of seventh-order \VENO scheme, and an explicit third - or fourth-order Runge­-Kutta time integration. We show that the filter scheme is more computational]y efficient and provides a wider spectral bandwidth compared to the seventh-order WENO scheme. The method also demonstrates robust long-time integration for moderately compressible turbulence. In contrast, the fifth- and seventh­ order WENO schemes show non-trivial evolution of the velocity and density power spectra. over a. few dozen dynamical times, where both TVD and filter schemes recover a so lid statistically stationary turbulent state

Kritsuk, Alexei G.↗

Explicit Discontinuous Galerkin Methods for Conservation Laws

The two explicit DG methods in this study are based on a ‘predictor-corrector’ formulation, the first introduced by Lörcher, Gassner, and Munz (2007, 2008) called space–time expansion discontinuous Galerkin or STE-DG scheme, and the second, introduced independently by the author (Huynh 2006, 2013) called the upwind moment scheme. The predictor step of the two methods is essentially identical using a Cauchy-Kovalevsky (CK) procedure, which involves no interaction of the data among neighboring cells. The corrector step also shares the same space-time integration formulation and is where interaction of the data among neighboring cells takes place; the difference, however, is in how the resulting space-time volume integral is estimated. As a consequence of the different estimates, for the case of advection in one spatial dimension (1D), the moment scheme has a CFL (Courant-Friedrichs-Lewy) condition of 1 for all p and is accurate to order 2p+1, i.e., it possesses the super accuracy property, whereas the STE-DG method has a more restrictive CFL condition and is accurate to the expected order of p+1. For 1D advection, compared with the CFL conditions of 1/(2p+1) of standard RK-DG (Runge-Kutta) scheme where space and time discretization are of the same order, the moment scheme allows a significantly larger time step size. It also turns out that the scheme yields a result identical to Van Leer’s scheme III (1977), which amounts to shifting the data a distance of advection corresponding to the time step and projecting the result onto the space of polynomial solutions. Contrary to Van Leer’s approach, however, the space-time ‘predictor-corrector’ formulation facilitates extensions to the case of systems of equations. Concerning 2D extensions, in the case of advection, when the flow is along the diagonal direction, the CFL conditions for the moment schemes become restrictive as will be shown by Fourier (Von Neumann) stability and accuracy analyses. Since the moment scheme employs the right Radau points as collocation points in time, the method is closely related to the implicit Radau IIA scheme, which is stable for any time step size. The role of Radau IIA in relieving stability restriction for these explicit DG schemes remains to be explored

Discontinuous Galerkin↗

Scale-Resolving Simulations of a Supersonic Retro-Propulsion Concept For Mars Entry, Descent, and Landing

Supersonic retro-propulsion (SRP) is a deceleration technology that could enable largerpayloads and potentially humans to be brought from space to the surface of Mars safely.Accurate and reliable CFD predictions are needed to help design future Mars entry, descent,and landing (EDL) vehicles due to the cost and limitations of wind tunnel tests. TypicalCFD approaches struggle at points along the Mars EDL trajectory with high enough altitude(low enough ambient pressure) that the SRP motor plumes are over-expanded. This workdemonstrates how high-order scale-resolving simulations on Cartesian AMR grids can provideaccurate and reliable time-averaged aerodynamic loads on the vehicle for this challengingflow regime. Greater than second order convergence in the time-averaged integrated axialforce𝐶𝐴is obtained across the three finest mesh resolutions simulated, and the estimateduncertainty is smaller than the unsteady standard deviation – demonstrating the accuracy andreliability of the method. Although costly, this approach can yield higher confidence in𝐶𝐴thanpreviously obtained in a reasonable turnaround time and is within reach for a few points in thetrajectory (i.e. Mach 2.4, 2.52, and 2.78). Further computational performance and numericalmethods improvements are needed to reduce the cost enough to bring this method into the EDLengineering design cycle.

S&M↗