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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.

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At least 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Time-periodic steady-state solution of fluid-structure interaction and cardiac flow problems through multigrid-reduction-in-time

In this study, a time-periodic MGRIT algorithm is proposed as a means to reduce the time-to-solution of numerical algorithms by exploiting the time periodicity inherent to many applications in science and engineering. The time-periodic MGRIT algorithm is applied to a variety of linear and nonlinear single- and multiphysics problems that are periodic-in-time. It is demonstrated that the proposed parallel-in-time algorithm can obtain the same time-periodic steady-state solution as sequential time-stepping. It is shown that the required number of MGRIT iterations can be estimated a priori and that the new MGRIT variant can significantly and consistently reduce the time-to-solution compared to sequential time-stepping, irrespective of the number of dimensions, linear or nonlinear PDE models, single-physics or coupled problems and the employed computing resources. The numerical experiments demonstrate that the time-periodic MGRIT algorithm enables a greater level of parallelism yielding faster turnaround, and thus, facilitating more complex and more realistic problems to be solved.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

thornado+FLASH-X: A Hybrid Discontinuous Galerkin–Implicit-explicit and Finite-volume Framework for Neutrino-radiation Hydrodynamics in Core-collapse Supernovae

We present neutrino-transport algorithms implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado) and their coupling to self-gravitating hydrodynamics within the adaptive mesh refinement–based multiphysics simulation framework FLASH-X. thornado, developed primarily for simulations of core-collapse supernovae (CCSNe), employs a spectral, six-species two-moment formulation with algebraic closure and special-relativistic observer corrections accurate to $\mathcal{O}(v/c)$, and uses discontinuous Galerkin (DG) methods for phase-space discretization combined with implicit-explicit time stepping. A key development is a nonlinear neutrino–matter coupling algorithm based on nested fixed-point iteration with Anderson acceleration, enabling fully implicit treatment of collisional processes, including energy-coupling interactions such as neutrino–electron scattering and pair production. Coupling to finite-volume (FV) hydrodynamics is achieved through a hybrid DG-FV representation of the fluid variables and operator-split evolution within FLASH-X. The implementation is verified using basic transport tests with idealized opacities and relaxation and deleptonization problems with tabulated microphysics. Spherically symmetric CCSN simulations demonstrate accuracy and robustness of the coupled scheme, including close agreement with the CCSN simulation code Chimera. An axisymmetric CCSN simulation further demonstrates the viability of DG-based neutrino transport for multidimensional supernova modeling within FLASH-X. thornado’s neutrino-transport solver is GPU-enabled using OpenMP offloading or OpenACC, and all CCSN applications included in this work use the GPU implementation. Together, these results establish a foundation for future enhancements in physics fidelity, numerical algorithms, and computational performance, for increasingly realistic large-scale CCSN simulations.

Endeve, Eirik [Oak Ridge National Laboratory (ORNL↗
DOE OSTI2023

Pseudospectral convex optimization for on-ramp merging control of connected vehicles

It can be a daunting task for human drivers to merge into highways because of the intricate vehicle negotiations and potential risk within limited time and space. Connected vehicle (CV) technologies could be a solution to this problem and offer many benefits to the road safety, traffic mobility, and energy efficiency. However, real-time optimal control of CVs is still an open challenge, due to the nonlinear vehicle dynamics, non-convex fuel consumption model, and highly dynamic uncertain inter-vehicle interactions. To tackle these issues, a novel real-time optimal control approach that balances the computational efficiency and solution optimality is proposed for the purpose of onboard application. To this end, the pseudospectral collocation method is integrated with a sequential convex programming approach to develop two new optimization algorithms, which are implemented within a model predictive control (MPC) framework to allow for real-time generation of optimal merging speed profiles. One algorithm leverages the line search technique to improve convergence, and the other benefits from the trust region method for better computational efficiency. The optimality and convergence process of both proposed algorithms are investigated by comparing their solutions with a popular non-linear solver. Furthermore, simulation results show that the proposed methods outperform the benchmark in terms of computational cost, fuel consumption, and traffic efficiency. In particular, the proposed fuel-economy merging rule can save 57.1% fuel consumption on average on four different traffic volumes. Meanwhile, the proposed optimal control algorithms can reduce 2.2% travel time on average comparing to the “first-in-first-out” merging rule.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

Exploiting Power Flow Manifold to Solve AC Optimal Power Flow

AC optimal power flow has proven difficult to solve with interior point methods on GPUs. This is largely due to challenging linear algebra problems that current state of the art massively parallel linear solvers struggle with. However, the advent of Riemannian optimization techniques and the fact that the power flow equations form a smooth manifold present an alternative approach. In this talk, we present the basics of Riemannian optimization techniques in which optimization is done directly on a manifold. Then we present computational results showing that Riemannian techniques are capable of producing solutions of comparable quality as interior point methods.

AC optimal power flow↗
NASA NTRS1995

The coupling of fluids, dynamics, and controls on advanced architecture computers

This grant provided for the demonstration of coupled controls, body dynamics, and fluids computations in a workstation cluster environment; and an investigation of the impact of peer-peer communication on flow solver performance and robustness. The findings of these investigations were documented in the conference articles.The attached publication, 'Towards Distributed Fluids/Controls Simulations', documents the solution and scaling of the coupled Navier-Stokes, Euler rigid-body dynamics, and state feedback control equations for a two-dimensional canard-wing. The poor scaling shown was due to serialized grid connectivity computation and Ethernet bandwidth limits. The scaling of a peer-to-peer communication flow code on an IBM SP-2 was also shown. The scaling of the code on the switched fabric-linked nodes was good, with a 2.4 percent loss due to communication of intergrid boundary point information. The code performance on 30 worker nodes was 1.7 (mu)s/point/iteration, or a factor of three over a Cray C-90 head. The attached paper, 'Nonlinear Fluid Computations in a Distributed Environment', documents the effect of several computational rate enhancing methods on convergence. For the cases shown, the highest throughput was achieved using boundary updates at each step, with the manager process performing communication tasks only. Constrained domain decomposition of the implicit fluid equations did not degrade the convergence rate or final solution. The scaling of a coupled body/fluid dynamics problem on an Ethernet-linked cluster was also shown.

Atwood, Christopher↗
NASA NTRS2003

Fast-Running Aeroelastic Code Based on Unsteady Linearized Aerodynamic Solver Developed

The NASA Glenn Research Center has been developing aeroelastic analyses for turbomachines for use by NASA and industry. An aeroelastic analysis consists of a structural dynamic model, an unsteady aerodynamic model, and a procedure to couple the two models. The structural models are well developed. Hence, most of the development for the aeroelastic analysis of turbomachines has involved adapting and using unsteady aerodynamic models. Two methods are used in developing unsteady aerodynamic analysis procedures for the flutter and forced response of turbomachines: (1) the time domain method and (2) the frequency domain method. Codes based on time domain methods require considerable computational time and, hence, cannot be used during the design process. Frequency domain methods eliminate the time dependence by assuming harmonic motion and, hence, require less computational time. Early frequency domain analyses methods neglected the important physics of steady loading on the analyses for simplicity. A fast-running unsteady aerodynamic code, LINFLUX, which includes steady loading and is based on the frequency domain method, has been modified for flutter and response calculations. LINFLUX, solves unsteady linearized Euler equations for calculating the unsteady aerodynamic forces on the blades, starting from a steady nonlinear aerodynamic solution. First, we obtained a steady aerodynamic solution for a given flow condition using the nonlinear unsteady aerodynamic code TURBO. A blade vibration analysis was done to determine the frequencies and mode shapes of the vibrating blades, and an interface code was used to convert the steady aerodynamic solution to a form required by LINFLUX. A preprocessor was used to interpolate the mode shapes from the structural dynamic mesh onto the computational dynamics mesh. Then, we used LINFLUX to calculate the unsteady aerodynamic forces for a given mode, frequency, and phase angle. A postprocessor read these unsteady pressures and calculated the generalized aerodynamic forces, eigenvalues, and response amplitudes. The eigenvalues determine the flutter frequency and damping. As a test case, the flutter of a helical fan was calculated with LINFLUX and compared with calculations from TURBO-AE, a nonlinear time domain code, and from ASTROP2, a code based on linear unsteady aerodynamics.

Reddy, T. S. R.↗
NASA NTRSDate not supplied

Reduced-Order Aerodynamic Modeling Based on CFD Frequency Responses from Multisine Inputs

A system identification analysis was performed to determine a reduced-order model (ROM) of a computational fluid dynamics (CFD) solver in support of linear aeroservoelastic model development and feedback control design. The approach was applied to the FUN3D code for the half-span wind tunnel test article used in the NASA-Boeing collaboration called the Integrated Adaptive Wing Technology Maturation (IAWTM) project. In a transonic flow condition, multiple inputs (11 structural mode displacements and 3 control surface deflections) were simultaneously excited with orthogonal phase-optimized multisines while multiple outputs (the corresponding 14 generalized aerodynamic forces) were recorded. From these recorded times series, the matrix of frequency responses was computed and subsequently fit using rational function approximations (RFAs). It was found that the entire (14 x 14) matrix of frequency responses could be determined from a single CFD run and that results generally followed trends predicted using other methods. Differences were attributed to the modeling fidelity and nonlinearities from structural mode and control surface interactions at higher reduced frequencies. More accurate fits of the RFAs to the frequency response data were obtained by making two CFD runs, one with only structural mode excitations and one with only control surface excitations, which reduced the degree of nonlinearity in the modeling data.

Aeroservoelasticity↗
NASA NTRS2016

Assessment of Preconditioner for a USM3D Hierarchical Adaptive Nonlinear Method (HANIM) (Invited)

Enhancements to the previously reported mixed-element USM3D Hierarchical Adaptive Nonlinear Iteration Method (HANIM) framework have been made to further improve robustness, efficiency, and accuracy of computational fluid dynamic simulations. The key enhancements include a multi-color line-implicit preconditioner, a discretely consistent symmetry boundary condition, and a line-mapping method for the turbulence source term discretization. The USM3D iterative convergence for the turbulent flows is assessed on four configurations. The configurations include a two-dimensional (2D) bump-in-channel, the 2D NACA 0012 airfoil, a three-dimensional (3D) bump-in-channel, and a 3D hemisphere cylinder. The Reynolds Averaged Navier Stokes (RANS) solutions have been obtained using a Spalart-Allmaras turbulence model and families of uniformly refined nested grids. Two types of HANIM solutions using line- and point-implicit preconditioners have been computed. Additional solutions using the point-implicit preconditioner alone (PA) method that broadly represents the baseline solver technology have also been computed. The line-implicit HANIM shows superior iterative convergence in most cases with progressively increasing benefits on finer grids.

Pandya, Mohagna J.↗
DOE OSTI2021

Encoder–decoder neural network for solving the nonlinear Fokker–Planck–Landau collision operator in XGC

An encoder–decoder neural network has been used to examine the possibility for acceleration of a partial integro-differential equation, the Fokker–Planck–Landau collision operator. This is part of the governing equation in the massively parallel particle-in-cell code XGC, which is used to study turbulence in fusion energy devices. The neural network emphasizes physics-inspired learning, where it is taught to respect physical conservation constraints of the collision operator by including them in the training loss, along with the ℓ 2 loss. In particular, network architectures used for the computer vision task of semantic segmentation have been used for training. A penalization method is used to enforce the ‘soft’ constraints of the system and integrate error in the conservation properties into the loss function. During training, quantities representing the particle density, momentum and energy for all species of the system are calculated at each configuration vertex, mirroring the procedure in XGC. This simple training has produced a median relative loss, across configuration space, of the order of 10 –4 , which is low enough if the error is of random nature, but not if it is of drift nature in time steps. The run time for the current Picard iterative solver of the operator is O(n 2 ), where n is the number of plasma species. As the XGC1 code begins to attack problems including a larger number of species, the collision operator will become expensive computationally, making the neural network solver even more important, especially since its training only scales as O(n). Here, a wide enough range of collisionality has been considered in the training data to ensure the full domain of collision physics is captured. An advanced technique to decrease the losses further will be subject of a subsequent report. Eventual work will include expansion of the network to include multiple plasma species.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Quantum algorithm for the linear Vlasov equation with collisions

The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability. In this paper, we present a quantum algorithm that simulates the linearized Vlasov equation with and without collisions, in the one-dimensional electrostatic limit. Rather than solving this equation in its native spatial and velocity phase space, we adopt an efficient representation in the dual space yielded by a Fourier-Hermite expansion. For a given simulation time, the Fourier-Hermite representation is exponentially more compact, thus yielding a classical algorithm that can match the performance of a previously proposed quantum algorithm for this problem. Further, this representation results in a system of linear ordinary differential equations (ODEs) which can be solved with well-developed quantum algorithms: a Hamiltonian simulation in the collisionless case, and quantum ODE solvers in the collisional case. In particular, we demonstrate that a quadratic speedup in system size is attainable.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Multi-variance replica exchange SGMCMC for inverse and forward problems via Bayesian PINN

Physics-informed neural network (PINN) has been successfully applied in solving a variety of nonlinear non-convex forward and inverse problems. However, the training is challenging because of the non-convex loss functions and the multiple optima in the Bayesian inverse problem. In this work, we propose a multi-variance replica exchange stochastic gradient Langevin dynamics method to tackle the challenge of the multiple local optima in the optimization and the challenge of the multiple modal posterior distribution in the inverse problem. Replica exchange methods are capable of escaping from the local traps and accelerating the convergence; two chains with different temperatures are designed where the low temperature chain aims for the local convergence, and the target of the high temperature chain is to travel globally and explore the whole loss function entropy landscape. However, it may not be efficient to solve mathematical inversion problems by using the vanilla replica method directly since the method doubles the computational cost in evaluating the forward solvers (likelihood functions) in the two chains. To address this issue, we propose to make different assumptions on the energy function estimation and this facilities one to use solvers of different fidelities in the likelihood function evaluation. More precisely, one can use a solver with low fidelity in the high temperature chain while using a solver with high fidelity in the low temperature chain. Our proposed method significantly lowers the computational cost in the high temperature chain, meanwhile preserving the accuracy and converging very fast. Here we give an unbiased estimate of the swapping rate and give an estimation of the discretization error of the scheme. To verify our idea, we design and solve four inverse problems which have multiple modes. The proposed method is also employed to train the Bayesian PINN to solve the forward and inverse problems; faster and more accurate convergence has been observed when compared to the stochastic gradient Langevin dynamics (SGLD) method and vanilla replica exchange methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A geospatial model for the analysis of time-dependent land subsidence induced by reservoir depletion

Land subsidence due to fluid depletion is an outcome of physical processes operating across a wide range of time and length scales. Although geomechanical models are crucial to simulate reservoir compaction and predict its long-term fate, their use across large regions often bears prohibitive computational costs. To overcome this obstacle, this paper proposes a simplified modelling framework consisting of (i) a near-field numerical solver simulating the coupling between fluid flow and rock deformation with reference to a simplified one-dimensional geometry and (ii) a far-field geospatial algorithm mapping ground settlements across a region through the superposition of poroelastic computations at multiple wells. The model computes the delay between depletion history and reservoir compaction in proximity of a producing well by assuming basal depletion of a fluid-saturated deformable disk, while the Geertsma solution of nucleus of strain is used to extrapolate the impact of such time-varying reservoir compaction around the well. This approach has been used to back-analyze the spatio-temporal progression of subsidence at the Groningen gas field. The results are compared against measurements collected over 50 year of production at 25 benchmark locations scattered over an area of 900 km 2 . It is shown that coupled simulations based on average values of rock compressibility and permeability lead to nonlinear trends of subsidence evolution in good agreement with field measurements, while uncoupled analyses overpredict settlements by more than 70%. Lastly, synthetic forecasts based on different rates of depletion were provided. The results suggest that slower depletion rates lead to lower subsidence at a given time, and that residual subsidence may continue to develop for several decades after interruption of production activities.

58 GEOSCIENCES↗
DOE OSTI2025

Computational Algorithms for Unit Commitment with AC Power Flows (Final Report)

Security-constrained unit commitment (SCUC) is a key component in power system operations. When AC power flow constraints are considered in the SCUC model (AC-SCUC), the problem becomes extremely difficult due to its discrete and non-convex nature, as described in “Grid Optimization Competition Challenge 3 Problem Formulation (GOCC)”. There are four main challenges: (i) Discrete decisions regarding unit online/offline status and start-up/shut-down procedures for every single unit. The number of discrete decision variables increases considerably when a system integrates multiple generators; (ii) Configuration-based combined-cycle formulations, and multi-commodity models that include ramping products, spin/non-spin products, and regulation up/down products. The combined-cycle units introduce additional discrete decision variables and auxiliary service products further complicate the model by connecting multi-commodity products’ continuous and discrete variables; (iii) SCUC models with AC power flow constraints are far more complex due to massive bilinear terms in the large-scale nonlinear power balance equations. The nonlinear power balance equations are further complicated by the discrete step control variables of shunts; (iv) N − 1 contingency analysis. The size of the model increases linearly with the number of contingencies considered, greatly increasing the size of the optimization model. Accordingly, there is an emergent need to develop a robust algorithm capable of deriving a high-quality solution in a short time and passing through contingency tests simultaneously. In this project, we explore innovative techniques to address this challenging problem by integrating advanced polyhedral theory, approximation methods, relaxation strategies, decomposition techniques, and parallel computing. Each technique approaches the problem from a different perspective, leveraging its specific strengths to tackle distinct challenges. Each individual method has demonstrated its effectiveness in the PI’s previous research. Their integration is expected to significantly reduce the computational time required to solve the proposed complex problem. Successful completion of this project has the potential to transform the industry by enhancing optimization solvers capable of handling large-scale day-ahead energy market clearing models within strict time constraints, while incorporating AC power flow constraints. This advancement will lead to reduced overall generation costs and, consequently, increased social welfare.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRS1991

Prediction of unsteady aerodynamic loads in cascades using the linearized Euler equations on deforming grids

A linearized Euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and blade motion is presented. Using the linearized Euler technique, one decomposes the flow into a mean (or steady) flow plus an unsteady, harmonically varying, small disturbance flow. Linear variable coefficient equations describe the small disturbance behavior of the flow, and are solved using a pseudo-time marching Lax-Wendroff scheme. For the blade motion problem, a harmonically deforming computational rid that conforms to the motion of vibrating blades eliminates large error producing mean flow gradient terms that would otherwise appear in the unsteady flow tangency boundary condition. The paper also presents a new, numerically exact, nonreflecting far-field boundary condition based on an eigenanalysis of the discretized equations. Computed flow solutions demonstrate the computational accuracy and efficiency of the present method. The solution of the linearized Euler equations requires one to two orders of magnitude less computer time than solution of the nonlinear Euler equations using traditional time-accurate time-marching techniques. In addition, the deformable grid significantly improves the accuracy of the solution.

Hall, Kenneth C.↗
DOE OSTI2023

New Developments and Capabilities Within WEC-Sim

WEC-Sim is an open-source software for simulating wave energy converters and has been actively developed and applied since its initial release in 2014 to simulate a wide variety of device archetypes. WEC-Sim is developed jointly by the National Renewable Energy Laboratory and Sandia National Laboratories within the MATLAB/SIMULINK environment. A general wave-to-wire model begins with a deployment site resource characterization, which is used to complete the hydrodynamic simulation of wave energy converters (WEC), with the power generation profile imported to a grid simulator to understand the influence on the local electrical network. While modeling the entire wave-to-wire is difficult and encompasses multiple time scales and physics, WEC-Sim is focused on the hydrodynamics simulation to predict, analyze, and optimize WEC dynamics and power performance. WEC-Sim simulations are performed in the time domain based on the radiation and diffraction method using hydrodynamics coefficients derived from boundary element method (BEM)-based frequency-domain potential flow solvers (e.g., WAMIT, NEMOH, Capytaine, or ANSYS-AQWA). With this level of modeling fidelity, WEC-Sim can handle floating body hydrodynamics, mechanical and electrical power generation methods, advanced control implementation, mooring systems, and other unique applications such as desalination. Additional WEC-Sim functionalities include pre-built Simulink blocks and MATLAB scripts that can simulate a wide range of floating systems and the corresponding auxiliary subsystems. The developers of WEC-Sim continue to release new versions of the software, at least annually, with the latest release in September 2022. These releases include bug fixes, updates to software documentation, as well as new features to expand WEC-Sim's capabilities to model a wide range of WEC concepts. This publication will highlight the new features added to WEC-Sim between versions 4.1.0 to 5.0.1, which spans a 2-year period from June 2020 to September 2022. New features described here include topics such as continuous integration checks, revised Morison Element and nonlinear hydro implementations, run directly from Simulink (required for hardware-in-the-loop execution), BEMIO updates to import Capytaine BEM hydrodynamics, addition of cable blocks, and new wave visualization features.

TIDAL AND WAVE POWER↗
DOE OSTI2023

New Developments and Capabilities Within WEC-Sim: Preprint

WEC-Sim is an open-source software for simulating wave energy converters, which has been actively developed and applied since its initial release in 2014 to simulate a wide variety of device archetypes. WEC-Sim is developed jointly by the National Renewable Energy Laboratory (NREL) and Sandia National Laboratories (Sandia) within the MATLAB/SIMULINK environment. A general wave-to-wire model begins with a deployment site resource characterization, which is used to complete the hydrodynamic simulation of wave energy converters (WEC), with the power generation profile imported to a grid simulator to understand the influence on the local electrical network. While modeling the entire wave-to-wire is difficult and encompasses multiple time scales and physics, WEC-Sim is focused on the hydrodynamics simulation to predict, analyze, and optimize WEC dynamics and power performance. WEC-Sim simulations are performed in the time domain based on the radiation and diffraction method using hydrodynamics coefficients derived from boundary element method (BEM)-based frequency-domain potential flow solvers (e.g., WAMIT, NEMOH, Capytaine, or ANSYS-AQWA). With this level of modeling fidelity, WEC-Sim can handle floating body hydrodynamics, mechanical and electrical power generation methods, advanced control implementation, mooring systems, and other unique applications such as desalination. Additional WEC-Sim functionalities include pre-built Simulink blocks and MATLAB scripts that can simulate a wide range of floating systems and the corresponding auxiliary subsystems. The developers of WEC-Sim continue to release new versions of the software, at least annually, with our latest release in September 2022. These releases include bug fixes, updates to software documentation, as well as new features to expand WEC-Sim's capabilities to model a wide range of WEC concepts. This publication will highlight the new features added to WEC-Sim between versions 4.1.0 to 5.0.1 which spans over a two year period from June 2020 to September 2022. New features to be described will include topics such as continuous integration checks, revised Morison Element and nonlinear hydro implementations, run directly from Simulink (required for hardware-in-the-loop execution), BEMIO updates to import Capytaine BEM hydrodynamics, addition of cable blocks, and new wave visualization features.

TIDAL AND WAVE POWER↗
DOE OSTI2026

Identifying Differential Equations in Fourier Domain (FourierIdent)

We investigate identifying differential equations in the frequency domain. Fourier analysis is an important tool in theoretical analysis and numerical solvers of differential equations, yet there is limited work in exploring this connection in the identification of differential equations. This paper aims to identify the underlying differential equation in the frequency domain, from a given single realization of the differential equation perturbed by noise. Such setting imposes difficulties which are different from other identification methods where computation is carried out in the physical domain. We propose several ways to mitigate the challenges arising from noise in data and large differences in the magnitudes of frequency responses. The main takeaways are that identifying differential equations solely in the frequency domain is challenging, the method we propose is based on a form of domain partitions in the frequency domain, and this method shows benefits for complex data even with high level of noise. We introduce a Fourier feature denoising, and define the meaningful data region and the core regions of features to reduce the effect of noise in the frequency domain and to enhance the accuracy in coefficient identification. The proposed method is tested on various differential equations with linear, nonlinear, and high-order derivative feature terms, and shows advantages on complex data with many frequency modes, even under high level of noise.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Relationship between the contact force strength and numerical inaccuracies in piecewise-smooth systems

This work studies the different types of behavior and inaccuracies that can occur when contact is not adequately accounted for in a dynamical system with freeplay, as the strength of the contact stiffness increases. The MATLAB® ode45 time integration solver, with the built-in Event Location capability, is first validated using past experimental data from a forced Duffing oscillator with freeplay. Next, numerical results utilizing event location are compared to results neglecting event location in order to highlight possible numerical errors and effects on multistable dynamical responses. Inaccuracies tend to occur in two different ways. First, neglecting event location can affect the boundaries between basins of attraction. Second, neglecting event location has little effect on the behaviors of the attractor solutions themselves besides merely resembling poorly converged solutions. Errors are less pronounced at the limits of soft or hard contact stiffness. Finally, this study shows the importance of accurately solving piecewise-smooth systems and the existing correlation between the strength of the contact force and possible numerical inaccuracies.

42 ENGINEERING↗