A Parallel Symmetric Successive Overrelaxation Method for OVERFLOW
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Computational Fluid Dynamics↗
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Aerothermodynamic Measurements in Hypersonic Non-Equilibrium Flows
High enthalpy arc-jets are unique facilities particularly suited for simulating complex flows in the aerospace field, such as the aerothermodynamics of a re-entry vehicle. Arc-jets are often used to evaluate important design factors such as heat shield materials and vehicle design. Characterization of these facilities is important, as studies often match specific in-flight environments during experiments. Due to the complex environment produced by an arc-jet, with effects such as thermodynamic and chemical non-equilibrium occurring in the flow, characterization experiments are significantly more difficult than in traditional blow-down wind tunnels. The current work aims to characterize an arc-jet facility in terms of flow temperature, velocity and unsteadiness, in a spatially-resolved analysis. To achieve this goal, a non-intrusive imaging technique called “planar laser-induced fluorescence” was performed in the NASA Langley Hypersonic Materials Environ-mental Test System arc-jet facility. The experimental data was analyzed to produce the quantitative measurements in multiple regions of the flow around a blunt body sample. A quasi-1D low fidelity solver was created to numerically simulate the flow to investigate non-equilibrium effects occur-ring outside the imaging region in the arc-jet nozzle. Unsteadiness in the test section was minimized by analyzing a subset of data assessing the gas injection location. Radial velocity, rotational temperature and translational temperature measurements are provided that can be used to validate future high-fidelity computational studies. The temperature measurements revealed rotational non-equilibrium potentially occurring in the flow. This work provides a methodology for characterizing arc-jet facilities, identifying and correcting sources of systematic error, and estimating the uncertainty associated with the quantitative measurements.
laser induced fluorescence↗
Application of computational aeroacoustic methodologies to advanced propeller configurations - A review
Current research in the area of advanced propeller configurations for performance and acoustics are briefly reviewed. Particular attention is given to the techniques of Lock and Theodorsen modified for use in the design of counterrotating propeller configurations; a numerical method known as SSTAGE, which is a Euler solver for the unducted fan concept; the NASPROP-E numerical analysis also based on a Euler solver and used to study the near acoustic fields for the SR series propfan configurations; and a counterrotating propeller test rig designed to obtain an experimental performance/acoustic data base for various propeller configurations.
Korkan, Kenneth D.↗
Neutronic-Thermal Hydraulic Benchmark using the SKINATH Point Kinetics Model
The SKINATH point kinetics program, whose name comes from: A Computer Program for Solving the Reactor Point Kinetics Equations with Simple Thermal Hydraulic-Feedback, had its origins at ORNL. The authors were interested in investigating low-level criticality events such as might occur in a waste repository of 55 gallon drums. We assume a relatively realistic thermal feedback for fissionable material in a container (called a reactor here), either critical or subcritical, with the potential to undergo a further excursion. The system is a homogeneous fissile fluid (mostly water), increasing in temperature as it absorbs all heat from the excursion. An ideal gas eternally cools the reactor at constant temperature T{sub c}. The SKINATH numerical concept in 1984 was to use an off-the-shelf Livermore ODE solver LSODE to solve the kinetic equations, much as one does today with MATLAB{sup TM}. Here, we develop a novel solver that uses the simplest of numerical methods including convergence acceleration. This work represents the initiation of a Multiphysics benchmark effort at INL. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Advances in Application of Fast Semidirect Computational Methods in Transonic Flow
This paper is intended as a review and summary of the advances made in a recently developed approach for rapid numerical solution of the equations of inviscid transonic aerodynamics. The investigation has been limited to two-dimensional, steady, inviscid flow over airfoils in a subsonic free stream, with emphasis on development of a rapid computational technique, rather than on generality of application. The approach uses finite-difference algorithms called "fast direct elliptic solvers" within an iteration scheme. "Direct" means that the entire computation field is solved at once, rather than in successive traverses over the field as in a point- or line-relaxation method. Such an iterative method is referred to as "semidirect." The iterative convergence can be faster than in other relaxation methods because changes are felt simultaneously at all points in each succeeding iteration. Direct elliptic solvers and semidirect methods have restrictions, but these are gradually being removed. Direct solvers were first developed for solving Poisson's equation on a rectangle without interior boundaries. A method to treat first-order systems, a direct Cauchy-Riemann solver has also been developed. Numerical treatment of part of a system of nonlinear equations by a Poisson solver has been reported. Also Poisson solvers in semidirect methods were used for nonseparable elliptic equations. The semidirect method was extended to the solution of a problem of mixed type, where the improved Murman-Cole transonic small-disturbance difference equations were solved. A slightly supercritical flow over a biconvex airfoil was treated successfully, but the iterations did not converge for more strongly supercritical conditions In another work the addition of terms ot both sides of the difference equations stabilized the iteration for supercritical conditions with large supersonic zones. For this, the Cauchy-Riemann solver was revised to incl,ude the needed terms. Most recently, the evaluation of parameters for rapid convergence and comparisons, with Murman's line-relaxation method was described. The method was extended to full second order accuracy in a fully conservative formulation in another work.
Martin, E. Dale↗
An Interior-Point Solver for Optimal Power Flow Problem Considering Distributed FACTS Devices
In this paper, we propose an AC optimal power flow (ACOPF) model considering distributed flexible AC transmission system (D-FACTS) devices, in which the reactance of D-FACTS equipped lines are introduced as decision variables. This is motivated by increasing interests in using D-FACTS devices to address system operational and cyber-security concerns. First, D-FACTS devices can be incorporated in real-time operations for economic benefits such as managing power congestions and reducing system losses. Second, D-FACTS devices can be utilized by moving target defense (MTD), an emerging concept against cyber-attacks, to prevent attackers from knowing true system configurations. Therefore, system operators can use the proposed ACOPF model to achieve economic benefits and provide the setpoints of D-FACTS devices for MTD at the same time. In addition, we rigorously derive the gradient and Hessian matrices of the objective function and constraints, which are further used to build an interior-point solver of the proposed ACOPF. Numerical results on the IEEE 118-bus transmission system show the validity of the proposed ACOPF model as well as the efficacy of the interior-point solver in minimizing system losses and generation costs.
Liu, Bo↗
Numerical solution of the two-dimensional time-dependent incompressible Euler equations
A numerical method is presented for solving the artificial compressibility form of the 2D time-dependent incompressible Euler equations. The approach is based on using an approximate Riemann solver for the cell face numerical flux of a finite volume discretization. Characteristic variable boundary conditions are developed and presented for all boundaries and in-flow out-flow situations. The system of algebraic equations is solved using the discretized Newton-relaxation (DNR) implicit method. Numerical results are presented for both steady and unsteady flow.
Whitfield, David L.↗
Development of a Performance Portable Non-Equilibrium Plasma Fluid Solver on Adaptive Grids
This presentation will describe the numerical techniques, programming paradigms, verification, and performance of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures. Our plasma fluid model solves the conservation equations for self-consistent electrostatic Poisson, electron and heavy species transport, and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive mesh management library, AMReX (Zhang et al., JOSS, 4 (37) 1370, 2019), and can be built and run on widely available vendor specific GPU architectures (NVIDIA/AMD/Intel). We utilize a non-subcycled second order semi-implicit time-stepping method where all adaptive mesh refinement (AMR) levels are advanced with the same time step. The composite multi-level multigrid solver from within AMReX is used for each of the governing equations that are cast into a Helmholtz equation form. We have also developed a python based chemical mechanism parser framework that uses a similar format as CANTERA (Goodwin et al., Zenodo, 2018) yaml files as input. Our custom parser reads the yaml file and provides C++ files with transport and production rate functions that can be executed on both host (CPU) and device (GPU). We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on low-pressure capacitive and high-pressure streamer discharges. Our initial performance studies indicate 10X speed-up using 20 NVIDIA GPUs versus 200 CPUs for an atmospheric streamer discharge problem solved on a 512 x 1024 x 512 grid.
graphics processing units↗
Parallel Solver for H(div) Problems Using Hybridization and AMG
In this paper, a scalable parallel solver is proposed for H(div) problems discretized by arbitrary order finite elements on general unstructured meshes. The solver is based on hybridization and algebraic multigrid (AMG). Unlike some previously studied H(div) solvers, the hybridization solver does not require discrete curl and gradient operators as additional input from the user. Instead, only some element information is needed in the construction of the solver. The hybridization results in a H1-equivalent symmetric positive definite system, which is then rescaled and solved by AMG solvers designed for H1 problems. Weak and strong scaling of the method are examined through several numerical tests. Our numerical results show that the proposed solver provides a promising alternative to ADS, a state-of-the-art solver [12], for H(div) problems. In fact, it outperforms ADS for higher order elements.
97 MATHEMATICS AND COMPUTING↗
Three-dimensional Finite Element Formulation and Scalable Domain Decomposition for High Fidelity Rotor Dynamic Analysis
This paper has two objectives. The first objective is to formulate a 3-dimensional Finite Element Model for the dynamic analysis of helicopter rotor blades. The second objective is to implement and analyze a dual-primal iterative substructuring based Krylov solver, that is parallel and scalable, for the solution of the 3-D FEM analysis. The numerical and parallel scalability of the solver is studied using two prototype problems - one for ideal hover (symmetric) and one for a transient forward flight (non-symmetric) - both carried out on up to 48 processors. In both hover and forward flight conditions, a perfect linear speed-up is observed, for a given problem size, up to the point of substructure optimality. Substructure optimality and the linear parallel speed-up range are both shown to depend on the problem size as well as on the selection of the coarse problem. With a larger problem size, linear speed-up is restored up to the new substructure optimality. The solver also scales with problem size - even though this conclusion is premature given the small prototype grids considered in this study.
Datta, Anubhav↗
Overcoming timestep limitations in boosted-frame particle-in-cell simulations of plasma-based acceleration
Explicit electromagnetic Particle-In-Cell (PIC) codes are typically limited by the Courant- Friedrichs-Lewy (CFL) condition, which implies that the timestep multiplied by the speed of light must be smaller than the smallest cell size. In the case of boosted-frame PIC simulations of plasma-based acceleration, this limitation can be a major hinderance as the cells are often very elongated along the longitudinal direction and the timestep is thus limited by the small, transverse cell size. This entails many small-timestep PIC iterations, and can limit the potential speed-up of the boosted-frame technique. Here, by using a CFL-free analytical spectral solver, and by mitigating additional numerical instabilities that arise at large timestep, we show that it is possible to overcome traditional limitations on the timestep and thereby realize the full potential of the boosted-frame technique over a much wider range of parameters.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Effect of high current electron beam in a 30 MeV radio frequency linac for neutron-time-of-flight applications
A high power pulsed radio frequency electron linac is designed by BARC, India to accelerate 30 MeV, 10 A, 10 ns beam for neutron-time-of-flight applications. It will be used as a neutron generator and will produce ∼10{sup 12}–10{sup 13} n/s. It is essential to reduce the beam instability caused by space charge effect and the beam cavity interaction. In this paper, the wakefield losses in the accelerating section due to bunch of RMS (Root mean square) length 2 mm (at the gun exit) is analysed. Loss and kick factors are numerically calculated using CST wakefield solver. Both the longitudinal and transverse wake potentials are incorporated in beam dynamics code ELEGANT to find the transverse emittance growth of the beam propagating through the linac. Beam loading effect is examined by means of numerical computation carried out in ASTRA code. Beam break up start current has been estimated at the end of the linac which arises due to deflecting modes excited by the high current beam. At the end, transverse beam dynamics of such high current beam has been analysed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Assessment of Hybrid RANS/LES Turbulence Models for Aeroacoustics Applications
Predicting the noise from aircraft with exposed landing gear remains a challenging problem for the aeroacoustics community. Although computational fluid dynamics (CFD) has shown promise as a technique that could produce high-fidelity flow solutions, generating grids that can resolve the pertinent physics around complex configurations can be very challenging. Structured grids are often impractical for such configurations. Unstructured grids offer a path forward for simulating complex configurations. However, few unstructured grid codes have been thoroughly tested for unsteady flow problems in the manner needed for aeroacoustic prediction. A widely used unstructured grid code, FUN3D, is examined for resolving the near field in unsteady flow problems. Although the ultimate goal is to compute the flow around complex geometries such as the landing gear, simpler problems that include some of the relevant physics, and are easily amenable to the structured grid approaches are used for testing the unstructured grid approach. The test cases chosen for this study correspond to the experimental work on single and tandem cylinders conducted in the Basic Aerodynamic Research Tunnel (BART) and the Quiet Flow Facility (QFF) at NASA Langley Research Center. These configurations offer an excellent opportunity to assess the performance of hybrid RANS/LES turbulence models that transition from RANS in unresolved regions near solid bodies to LES in the outer flow field. Several of these models have been implemented and tested in both structured and unstructured grid codes to evaluate their dependence on the solver and mesh type. Comparison of FUN3D solutions with experimental data and numerical solutions from a structured grid flow solver are found to be encouraging.
Vatsa, Veer N.↗
Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes
In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.
97 MATHEMATICS AND COMPUTING↗
Low thrust viscous nozzle flow field predictions
The low thrust viscous nozzle flows have been studied numerically by using the steady-state Reynolds-averaged Navier-Stokes equations in conservative form. A new Lower-Upper factorization scheme in the axisymmetric coordinate system has been developed and is analyzed in this paper. This new Navier-Stokes solver has shown that the numerical analog is accurate and stable for the convergent and divergent nozzle flowfield calculation. The range of the chamber pressure is (1.85-29.4)psi with the chamber temperature equal to 600 F. The results are compared with the data collected in the NASA/MSFC vacuum chamber, and they are in very reasonable agreement.
Chou, L. C.↗
PeleLMeX [SWR-22-48]
PeleLMeX is a solver for high fidelity reactive flow simulations, namely direct numerical simulation (DNS) and large eddy simulation (LES). The solver combines a low Mach number approach, adaptive mesh refinement (AMR), embedded boundary (EB) geometry treatment and high performance computing (HPC) to provide a flexible tool to address research questions on platforms ranging from small workstations to the world's largest GPU-accelerated supercomputers. PeleLMeX has been used to study complex flame/turbulence interactions in RCCI engines and hydrogen combustion or the effect of sustainable aviation fuel on gas turbine combustion. PeleLMeX is part of the Pele combustion Suite (https://amrex-combustion.github.io/)
Day, Marcus↗
Courant Number and Mach Number Insensitive CE/SE Euler Solvers
It has been known that the space-time CE/SE method can be used to obtain ID, 2D, and 3D steady and unsteady flow solutions with Mach numbers ranging from 0.0028 to 10. However, it is also known that a CE/SE solution may become overly dissipative when the Mach number is very small. As an initial attempt to remedy this weakness, new 1D Courant number and Mach number insensitive CE/SE Euler solvers are developed using several key concepts underlying the recent successful development of Courant number insensitive CE/SE schemes. Numerical results indicate that the new solvers are capable of resolving crisply a contact discontinuity embedded in a flow with the maximum Mach number = 0.01.
Chang, Sin-Chung↗
Numerical Modeling of the Chilldown of Cryogenic Transfer Lines Using a Sinda/GFSSP Integrated Solver
An important first step in cryogenic propellant loading is the chilldown of transfer lines. During the chilldown of the transfer line, the flow is two-phase and unsteady, with solid to fluid heat transfer and therefore a coupled thermo-fluid analysis is necessary to model the system. This paper describes a numerical model of pipe chilldown that utilizes the Sinda/GFSSP Conjugate Integrator (SGCI). SGCI is a new analysis tool developed at NASA's Marshall Space Flight Center (MSFC). SGCI facilitates the solution of thermofluid problems in interconnected solid-fluid systems. The solid component of the system is modeled in MSC Patran and translated into an MSC Sinda thermal network model. The fluid component is modeled in GFSSP, the Generalized Fluid System Simulation Program. GFSSP is a general network flow solver developed at NASA/MSFC. GFSSP uses a finite-volume approach to model fluid systems that can include phase change, multiple species, fluid transients, and heat transfer to simple solid networks. SGCI combines the GFSSP Fortran code with the Sinda input file and compiles the integrated model. Sinda solves for the temperatures of the solid network, while GFSSP simultaneously solves the fluid network for pressure, temperature, and flow rate. The two networks are coupled by convection heat transfer from the solid wall to the cryogenic fluid. The model presented here is based on a series of experiments conducted in 1966 by the National Bureau of Standards (NBS). A vacuum-jacketed, 200 ft copper transfer line was chilled by liquid nitrogen and liquid hydrogen. The predictions of transient temperature profiles and chilldown time of the integrated Sinda/GFSSP model will be compared to the experimental measurements.
LeClair, Andre↗