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DOE OSTI2022

Real-Time On-Ramp Merging Control of Connected and Automated Vehicles using Pseudospectral Convex Optimization

Highway on-ramp merging can be a challenging task for human drivers due to the complex vehicle negotiations and interactions in limited time and space. Connected and automated vehicles (CAVs) have great potential to address the problem and offer many benefits in terms of safety, traffic efficiency, and fuel economy. However, real-time optimal control of CAVs still faces many challenges, including nonlinear dynamics, complex inter-vehicle interactions, and a highly dynamic and uncertain traffic environment. To address these challenges, we develop a novel control approach that balances the solution optimality and computational efficiency to determine optimal merging speed profiles in real time. Specifically, by employing a pseudospectral method and a sequential convex programming approach, two algorithms are proposed and implemented within the model predictive control (MPC) framework to enable real-time generation of optimal solutions for potential on-vehicle applications. The convergence and optimality of the proposed algorithms are validated by comparing with a general-purpose solver under different traffic scenarios.

Shi, Yang↗

NASA NTRS1982

Shock-fitted Euler solutions to shock vortex interactions

The interaction of a planar shock wave with one or more vortexes is computed using a pseudospectral method and a finite difference method. The development of the spectral method is emphasized. In both methods the shock wave is fitted as a boundary of the computational domain. The results show good agreement between both computational methods. The spectral method is, however, restricted to smaller time steps and requires use of filtering techniques.

Salas, M. D.↗

NASA NTRS1982

Shock-fitted Euler solutions to shock-vortex interactions

The interaction of a shock wave with a hot spot, a single vortex and a vortex street is studied within the framework of the two dimensional compressible Euler equations. The numerical results obtained by the pseudospectral method and the finite difference MacCormack method are compared. In both the methods the shock wave is fitted as a boundary of the computational domain.

Salas, M. E.↗

NASA NTRS1983

Pseudospectral solution of two-dimensional gas-dynamic problems

Chebyshev pseudospectral methods are used to compute two dimensional smooth compressible flows. Grid refinement tests show that spectral accuracy can be obtained. Filtering is not needed if resolution is sufficiently high and if boundary conditions are carefully prescribed.

Kopriva, D. A.↗

NASA NTRS1984

Modeling of unsteady small disturbance transonic flow using parametric differentiation, pseudospectral analysis and finite-differencing

A procedure for solving the nonlinear unsteady small disturbance transonic equation is formulated. This procedure is a synthesis of a pseudospectral method, parametric differentiation, and finite differencing. It is equally applicable to lifting and nonlifting airfoils. The procedure is particularly well suited to aeroelastic stability studies that may require a set of affine solutions.

Brown, M.↗

NASA NTRS1982

Shock-fitted Euler solutions to shock-vortex interactions

Salas, M. D.↗

NASA NTRS1986

Statistical properties and correlation functions for drift waves

The dissipative one-field drift wave equation is solved using the pseudospectral method to generate steady-state fluctuations. The fluctuations are analyzed in terms of space-time correlation functions and modal probability distributions. Nearly Gaussian statistics and exponential decay of the two-time correlation functions occur in the presence of electron dissipation, while in the absence of electron dissipation long-lived vortical structures occur. Formulas from renormalized, Markovianized statistical turbulence theory are given in a local approximation to interpret the dissipative turbulence.

Horton, W.↗

NASA NTRS1986

Direct numerical simulations of a temporally evolving mixing layer subject to forcing

The vortical evolution of mixing layers subject to various types of forcing is numerically simulated using pseudospectral methods. The effect of harmonic forcing and random noise in the initial conditions is examined with some results compared to experimental data. Spanwise forcing is found to enhance streamwise vorticity in a nonlinear process leading to a slow, secondary growth of the shear layer. The effect of forcing on a chemical reaction is favorably compared with experimental data at low Reynolds numbers. Combining harmonic and subharmonic forcing is shown to both augment and later destroy streamwise vorticity.

Claus, Russell W.↗

NASA NTRS1989

Direct numerical simulations of a temporally evolving mixing layer subject to forcing

Claus, R. W.↗

NASA NTRS1989

The secondary flow and its stability for natural convection in a tall vertical enclosure

The multicellular flow between two vertical parallel plates is numerically simulated using a time-splitting pseudospectral method. The steady flow of air and the time-periodic flow of oil are investigated, and descriptions of these flows using both physical and spectral approaches are presented. The time dependence of the flow and temperature fields of oil are shown, and the dynamics of the process is discussed. The spectral transfer of energy among the axial modes comprising the flow is explored. The three-dimensional linear stabiltiy of the multicellular air flow is parametrically studied. The domain of stable two-dimensional cellular motion is found to be constrained by the Eckhaus instability and by two types of monotone instability. The two-dimensional multicellular flow is unstable above a Grashof number of about 8550.

Chait, Arnon↗

NASA NTRS1993

A numerical implementation of MHD in divergence form

Shock computations are presently undertaken by a numerical implementation of fully relativistic MHD in divergence form, as illustrated by pseudospectral-method computations for the coplanar Riemann MHD problem. Compound waves are noted to persist in relativistic MHD. Attention is given to two limiting cases: (1) where the velocities become nonrelativistic, and (2) where the longitudinal magnetic field becomes zero. Comparisons are made with results for both the singular case of zero longitudinal magnetic field, and nonrelativistic MHD.

Van Putten, Maurice H. P. M.↗

NASA NTRS1993

Numerical simulation of three-dimensional self-gravitating flow

The three-dimensional flow of a self-gravitating fluid is numerically simulated using a Fourier pseudospectral method with a logarithmic variable formulation. Two cases with zero total angular momentum are studied in detail, a 323 simulation (Run B). Other than the grid size, the primary difference between the two cases are that Run A modeled atomic hydrogen and had considerably more compressible motion initially than Run B, which modeled molecular hydrogen. The numerical results indicate that gravitational collapse can proceed in a variety of ways. In the Run A, collapse led to an elongated tube-like structure, while in the Run B, collapse led to a flatter, disklike structure.

Shebalin, John V.↗

NASA NTRS1992

Parallel computational fluid dynamics - Implementations and results

The present volume on parallel CFD discusses implementations on parallel machines, numerical algorithms for parallel CFD, and performance evaluation and computer science issues. Attention is given to a parallel algorithm for compressible flows through rotor-stator combinations, a massively parallel Euler solver for unstructured grids, a fast scheme to analyze 3D disk airflow on a parallel computer, and a block implicit multigrid solution of the Euler equations. Topics addressed include a 3D ADI algorithm on distributed memory multiprocessors, clustered element-by-element computations for fluid flow, hypercube FFT and the Fourier pseudospectral method, and an investigation of parallel iterative algorithms for CFD. Also discussed are fluid dynamics using interface methods on parallel processors, sorting for particle flow simulation on the connection machine, a large grain mapping method, and efforts toward a Teraflops capability for CFD.

Simon, Horst D.↗

NASA NTRS1994

Numerical simulation of three-dimensional self-gravitating flow

The three-dimensional flow of a self-gravitating fluid is numerically simulated using a Fourier pseudospectral method with a logarithmic variable formulation. Two cases with zero total angular momentum are studied in detail, a 32(exp 3) simulation (Run A) and a 64(exp 3) simulation (Run B). Other than the grid size, the primary differences between the two cases are that Run A modeled atomic hydrogen and had considerably more compressible motion initially than Run B, which modeled molecular hydrogen. ('Compressible motion' is that part of the velocity which has zero curl, but non-zero divergence). The numerical results indicate that gravitational collapse can proceed in a variety of ways. In Run A, collapse led to an elongated tube-like structure, while in Run B, collapse led to a flatter, disk-like structure.

Shebalin, J. V.↗

NASA NTRS1998

Scaling Properties of Particle Density Fields Formed in Simulated Turbulent Flows

Direct numerical simulations (DNS) of particle concentrations in fully developed 3D turbulence were carried out in order to study the nonuniform structure of the particle density field. Three steady-state turbulent fluid fields with Taylor microscale Reynolds numbers (Re(sub lambda)) of 40, 80 and 140 were generated by solving the Navier-Stokes equations with pseudospectral methods. Large scale forcing was used to drive the turbulence and maintain temporal stationarity. The response of the particles to the fluid was parameterized by the particle Stokes number St, defined as the ratio of the particle's stopping time to the mean period of eddies on the Kolmogorov scale (eta). In this paper, we consider only passive particles optimally coupled to these eddies (St approx. = 1) because of their tendency to concentrate more than particles with lesser or greater St values. The trajectories of up to 70 million particles were tracked in the equilibrated turbulent flows until the particle concentration field reached a statistically stationary state. The nonuniform structure of the concentration fields was characterized by the multifractal singularity spectrum, f(alpha), derived from measures obtained after binning particles into cells ranging from 2(eta) to 15(eta) in size. We observed strong systematic variations of f(alpha) across this scale range in all three simulations and conclude that the particle concentration field is not statistically self similar across the scale range explored. However, spectra obtained at the 2(eta), 4(eta), and 8(eta) scales of each flow case were found to be qualitatively similar. This result suggests that the local structure of the particle concentration field may be flow-Independent. The singularity spectra found for 2n-sized cells were used to predict concentration distributions in good agreement with those obtained directly from the particle data. This Singularity spectrum has a shape similar to the analogous spectrum derived for the inertial-range energy dissipation fields of experimental turbulent flows at Re(sub lambda) = 110 and 1100. Based on this agreement, and the expectation that both dissipation and particle concentration are controlled by the same cascade process, we hypothesize that singularity spectra similar to the ones found in this work provide a good characterization of the spatially averaged statistical properties of preferentially concentrated particles in higher Re(sub lambda) turbulent flows.

Hogan, Robert C.↗

NASA NTRS1992

Direct numerical simulations of a reacting turbulent mixing layer by a pseudospectral-spectral element method

An account is given of the implementation of the spectral-element technique for simulating a chemically reacting, spatially developing turbulent mixing layer. Attention is given to experimental and numerical studies that have investigated the development, evolution, and mixing characteristics of shear flows. A mathematical formulation is presented of the physical configuration of the spatially developing reacting mixing layer, in conjunction with a detailed representation of the spectral-element method's application to the numerical simulation of mixing layers. Results from 2D and 3D calculations of chemically reacting mixing layers are given.

Mcmurtry, Patrick A.↗

NASA NTRS2013

SpF: Enabling Petascale Performance for Pseudospectral Dynamo Models

Pseudospectral (PS) methods possess a number of characteristics (e.g., efficiency, accuracy, natural boundary conditions) that are extremely desirable for dynamo models. Unfortunately, dynamo models based upon PS methods face a number of daunting challenges, which include exposing additional parallelism, leveraging hardware accelerators, exploiting hybrid parallelism, and improving the scalability of global memory transposes. Although these issues are a concern for most models, solutions for PS methods tend to require far more pervasive changes to underlying data and control structures. Further, improvements in performance in one model are difficult to transfer to other models, resulting in significant duplication of effort across the research community.We have developed an extensible software framework for pseudospectral methods called SpF that is intended to enable extreme scalability and optimal performance. High-level abstractions provided by SpF unburden applications of the responsibility of managing domain decomposition and load balance while reducing the changes in code required to adapt to new computing architectures. The key design concept in SpF is that each phase of the numerical calculation is partitioned into disjoint numerical kernels that can be performed entirely in-processor. The granularity of domain-decomposition provided by SpF is only constrained by the data-locality requirements of these kernels. SpF builds on top of optimized vendor libraries for common numerical operations such as transforms, matrix solvers, etc., but can also be configured to use open source alternatives for portability. SpF includes several alternative schemes for global data redistribution and is expected to serve as an ideal testbed for further research into optimal approaches for different network architectures.In this presentation, we will describe the basic architecture of SpF as well as preliminary performance data and experience with adapting legacy dynamo codes. We will conclude with a discussion of planned extensions to SpF that will provide pseudospectral applications with additional flexibility with regard to time integration, linear solvers, and discretization in the radial direction.

Pseudospectral (PS)↗

NASA NTRS2014

Using SpF to Achieve Petascale for Legacy Pseudospectral Applications

Pseudospectral (PS) methods possess a number of characteristics (e.g., efficiency, accuracy, natural boundary conditions) that are extremely desirable for dynamo models. Unfortunately, dynamo models based upon PS methods face a number of daunting challenges, which include exposing additional parallelism, leveraging hardware accelerators, exploiting hybrid parallelism, and improving the scalability of global memory transposes. Although these issues are a concern for most models, solutions for PS methods tend to require far more pervasive changes to underlying data and control structures. Further, improvements in performance in one model are difficult to transfer to other models, resulting in significant duplication of effort across the research community. We have developed an extensible software framework for pseudospectral methods called SpF that is intended to enable extreme scalability and optimal performance. Highlevel abstractions provided by SpF unburden applications of the responsibility of managing domain decomposition and load balance while reducing the changes in code required to adapt to new computing architectures. The key design concept in SpF is that each phase of the numerical calculation is partitioned into disjoint numerical kernels that can be performed entirely inprocessor. The granularity of domain decomposition provided by SpF is only constrained by the datalocality requirements of these kernels. SpF builds on top of optimized vendor libraries for common numerical operations such as transforms, matrix solvers, etc., but can also be configured to use open source alternatives for portability. SpF includes several alternative schemes for global data redistribution and is expected to serve as an ideal testbed for further research into optimal approaches for different network architectures. In this presentation, we will describe our experience in porting legacy pseudospectral models, MoSST and DYNAMO, to use SpF as well as present preliminary performance results provided by the improved scalability.

DYNAMO↗