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At least 127 records · Page 7

Numerical solution of Euler's equation by perturbed functionals

A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.

Dey, S. K.↗

Validation and Verification for INL Modelica-based TEDS models Via Experimental Results

This report provides an overview on the verification and validation (V&V) of the Thermal Energy Distribution System (TEDS) model developed in the Modelica process modeling ecosystem using experimental data. Model development has led to the creation of a dynamic process model of the experimental TEDS facility housed within the Energy Systems Laboratory (ESL) at Idaho National Laboratory (INL). The model was then used during the preconstruction phase of the experimental effort to inform experimental design (e.g., insulation requirements, bypass line placement, expected performance of components) and to test innovative control schemes prior to the initial operation. The TEDS model developed in Modelica includes the primary components of the TEDS experimental unit: a 200kW Chromalox heater; a single-tank packed-bed thermal energy storage system filled with 0.125-inch alumina (Al2O3) beads; an ethylene-glycol-to-Therminol-66 heat exchanger; system piping; five control valves; and all associated temperature, pressure, and volumetric flow sensors. Using the Institute of Electrical and Electronics Engineers (IEEE) V&V methodologies, considered the gold standard in the engineering field, the model was verified using a combination of static analysis, spatial convergence, and regression tests. Then using dynamic time warping (DTW) initial runs to validate and tune the TEDS model versus the experiment were conducted. This tuning method was accomplished using the INL Risk Analysis Virtual ENvironment (RAVEN) software package. Tuning is required to account for physical phenomena that are less understood within the empirical heat transfer correlations. Through the commencement of this work, a systems-level model of TEDS with associated control systems, sensors, piping diameters, and component capabilities has been created. This model was utilized in the pre-experimental phase to inform system design, insulation thicknesses, and potential control schemes to operate the system effectively and safely. Then, initial experimental startup and operational data were used to demonstrate the validation and tuning methodology. This process demonstrates the classical two-step approach of a model informing experimental design followed by the experiment validation and tuning the model.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Refinement of the ICRF

Since the ICRF was generated in 1995, VLBI modeling and estimation, data quality: source position stability analysis, and supporting observational programs have improved markedly. There are developing and potential applications in the areas of space navigation Earth orientation monitoring and optical astrometry from space that would benefit from a refined ICRF with enhanced accuracy, stability and spatial distribution. The convergence of analysis, focused observations, and astrometric needs should drive the production of a new realization in the next few years.

Ma, Chopo↗

A quasi-Newton versus a homotopy method for nonlinear structural analysis

The globally convergent quasi-Newton minimization algorithm and the homotopy algorithms are discussed in detail and their effectiveness in solving certain classes of highly nonlinear problems of structural analysis is demonstrated. The application of the double dogleg strategy controls the directions and step-lengths of the quasi-Newtonian algorithm and overcomes the problem of nonpositive definite Hessians being produced during the iteration process. The algorithms are applied to a centrally loaded clamped beam, the snap-through of a shallow arch, and a shallow reticulated dome.

Kamat, M. P.↗

System Sensitivity Analysis Applied to the Conceptual Design of a Dual-Fuel Rocket SSTO

This paper reports the results of initial efforts to apply the System Sensitivity Analysis (SSA) optimization method to the conceptual design of a single-stage-to-orbit (SSTO) launch vehicle. SSA is an efficient, calculus-based MDO technique for generating sensitivity derivatives in a highly multidisciplinary design environment. The method has been successfully applied to conceptual aircraft design and has been proven to have advantages over traditional direct optimization methods. The method is applied to the optimization of an advanced, piloted SSTO design similar to vehicles currently being analyzed by NASA as possible replacements for the Space Shuttle. Powered by a derivative of the Russian RD-701 rocket engine, the vehicle employs a combination of hydrocarbon, hydrogen, and oxygen propellants. Three primary disciplines are included in the design - propulsion, performance, and weights & sizing. A complete, converged vehicle analysis depends on the use of three standalone conceptual analysis computer codes. Efforts to minimize vehicle dry (empty) weight are reported in this paper. The problem consists of six system-level design variables and one system-level constraint. Using SSA in a 'manual' fashion to generate gradient information, six system-level iterations were performed from each of two different starting points. The results showed a good pattern of convergence for both starting points. A discussion of the advantages and disadvantages of the method, possible areas of improvement, and future work is included.

Olds, John R.↗

Comparative genomic analysis of thermophilic fungi reveals convergent evolutionary adaptations and gene losses

Thermophily is a trait scattered across the fungal tree of life, with its highest prevalence within three fungal families (Chaetomiaceae, Thermoascaceae, and Trichocomaceae), as well as some members of the phylum Mucoromycota. We examined 37 thermophilic and thermotolerant species and 42 mesophilic species for this study and identified thermophily as the ancestral state of all three prominent families of thermophilic fungi. Thermophilic fungal genomes were found to encode various thermostable enzymes, including carbohydrate-active enzymes such as endoxylanases, which are useful for many industrial applications. At the same time, the overall gene counts, especially in gene families responsible for microbial defense such as secondary metabolism, are reduced in thermophiles compared to mesophiles. We also found a reduction in the core genome size of thermophiles in both the Chaetomiaceae family and the Eurotiomycetes class. The Gene Ontology terms lost in thermophilic fungi include primary metabolism, transporters, UV response, and O-methyltransferases. Comparative genomics analysis also revealed higher GC content in the third base of codons (GC3) and a lower effective number of codons in fungal thermophiles than in both thermotolerant and mesophilic fungi. Furthermore, using the Support Vector Machine classifier, we identified several Pfam domains capable of discriminating between genomes of thermophiles and mesophiles with 94% accuracy. Using AlphaFold2 to predict protein structures of endoxylanases (GH10), we built a similarity network based on the structures. We found that the number of disulfide bonds appears important for protein structure, and the network clusters based on protein structures correlate with the optimal activity temperature. Thus, comparative genomics offers new insights into the biology, adaptation, and evolutionary history of thermophilic fungi while providing a parts list for bioengineering applications.

59 BASIC BIOLOGICAL SCIENCES↗

Scaling Analysis of Two–Phase Flow in Fractal Permeability Fields

Fluid mixing in permeable media is essential in many practical applications. The mixing process is a consequence of velocity fluctuations owing to geological heterogeneities and mobility contrast of fluids. Heterogeneities in natural rocks are often spatially correlated, and their properties, such as permeability, may be described using fractal distributions. This work models the fractal characteristics of such permeability fields in which the covariance function is expressed as a power-law function. A generalized scaling relation is derived relating various fractal permeability fields using the magnitude of their fluctuations. Here, this relation reveals the self-similar behavior of two-phase flow in such permeable media. To that end, a recently developed, high-resolution numerical simulator is employed to validate the analytically derived scaling relations. Two flow problems are considered in which flow is governed by 1) a linear, and 2) a nonlinear transport equation. Due to the probabilistic representation of the fractal permeability fields, a sensitivity study is conducted for each flow scenario to determine the number of realizations required for statistical convergence. Scaling analysis is performed using ensemble averages of simulated saturation profiles and their mixing lengths. Results support the validity of the developed scaling relation across the range of investigated flow conditions at intermediate times. The dynamics of linear flow in the asymptotic regime is affected by the correlation structure of heterogeneity. In nonlinear flow, scaling behavior appears to be dominated by the degree of nonlinearity.

58 GEOSCIENCES↗

An inexact semismooth Newton method with application to adaptive randomized sketching for dynamic optimization

In many applications, one can only access the inexact gradients and inexact hessian times vector products. Thus it is essential to consider algorithms that can handle such inexact quantities with a guaranteed convergence to solution. An inexact adaptive and provably convergent semismooth Newton method is considered to solve constrained optimization problems. In particular, dynamic optimization problems, which are known to be highly expensive, are the focus. A memory efficient semismooth Newton algorithm is introduced for these problems. The source of efficiency and inexactness is the randomized matrix sketching. Further, applications to optimization problems constrained by partial differential equations are also considered.

97 MATHEMATICS AND COMPUTING↗

ALESQP: An Augmented Lagrangian Equality-Constrained SQP Method for Optimization with General Constraints

Here we present a new algorithm for infinite-dimensional optimization with general constraints, called ALESQP. In short, ALESQP is an augmented Lagrangian method that penalizes inequality constraints and solves equality-constrained nonlinear optimization subproblems at every iteration. The subproblems are solved using a matrix-free trust-region sequential quadratic programming (SQP) method that takes advantage of iterative, i.e., inexact linear solvers, and is suitable for large-scale applications. A key feature of ALESQP is a constraint decomposition strategy that allows it to exploit problem-specific variable scalings and inner products. We analyze convergence of ALESQP under different assumptions. We show that strong accumulation points are stationary. Consequently, in finite dimensions ALESQP converges to a stationary point. In infinite dimensions we establish that weak accumulation points are feasible in many practical situations. Under additional assumptions we show that weak accumulation points are stationary. We present several infinite-dimensional examples where ALESQP shows remarkable discretization-independent performance in all of its iterative components, requiring a modest number of iterations to meet constraint tolerances at the level of machine precision. Also, we demonstrate a fully matrix-free solution of an infinite-dimensional problem with nonlinear inequality constraints.

97 MATHEMATICS AND COMPUTING↗

Validity test for linear error analysis

To determine whether estimation process simulated by linear error analysis will converge, criterion has been developed based on extension of classical observability. Particular application of technique is with groups of batched navigation data where statistics of estimation errors are derived with classical minimum-variance methods.

Diamant, L. S.↗

Adaptive finite element analysis based on p-convergence

The results of numerical experiments are presented in which a posteriori estimators of error in strain energy were examined on the basis of a typical problem in linear elastic fracture mechanics. Two estimators were found to give close upper and lower bounds for the strain energy error. The potential significance of this is that the same estimators may provide a suitable basis for adaptive redistribution of the degrees of freedom in finite element models.

Szabo, B. A.↗

Prediction of subsonic aircraft flows with jet exhaust interactions

A numerical procedure to calculate the flow fields resulting from the viscous inviscid interactions that occur when a strong jet exhaust and aircraft flow field coupling exists was developed. The approach divides the interaction region into zones which are either predominantly viscous or inviscid. The flow in the inviscid zone, which surrounds most of the aircraft, is calculated using an existing potential flow code. The viscous flow zone, which encompasses the jet plume, is modeled using a parabolized Navier-Stokes code. The procedure features the coupling of the zonal solutions such that sufficient information is transferred between the zones to preserve the effects of the interactions. The zonal boundaries overlap and the boundary conditions are the information link between zones. An iteration scheme iterates the coupled analysis until convergence has been obtained.

Roberts, D. W.↗

Flow analysis of nozzle installations with strong airplane flow interactions

A numerical procedure has been developed to calculate the flow fields resulting from the viscous-inviscid interactions that occur when a strong jet exhaust and aircraft flow field coupling exists. The approach used in the current procedure is to divide the interaction region into zones which are either predominantly viscous or inviscid. The flow in the inviscid zone, which surrounds most of the aircraft, is calculated using an existing linearized potential flow code. The viscous flow zone, which encompasses the jet plume, is modeled using a parabolized Navier-Stokes code. The key feature of the present procedure is the coupling of the zonal solutions such that sufficient information is transferred between the zones to preserve the effects of the interactions. The zonal boundaries overlap with the boundary conditions being the information link between zones. An iteraction scheme iterates the coupled analysis until convergence has been obtained. The procedure has been successfully used for several test cases for which the computed results are presented.

Roberts, D. W.↗

A zonal method for modeling 3-D aircraft flow fields with jet plume effects

A coupled zonal method has been developed for modeling flows about aircraft with highly integrated advanced nozzle installations in which the exhaust plume interacts with the aircraft flow field to enhance performance. A cost effective flow analysis is achieved by dividing the flow domain into zones and coupling the zonal solutions. PAN AIR is used to model the flow in the inviscid zone which surrounds the aircraft. The plume zone flow field is solved with a PNS code. The flow in the optional internal nozzle zone is modeled using a full Navier-Stokes code. An automated iterative procedure couples the inviscid and plume zones by passing updated boundary conditions between the zones. The coupled analysis provides converged solutions for the overall flow field. The method is demonstrated for a highly integrated nonaxisymmetric vectored nozzle installed on a swept-wing aircraft.

Roberts, D. W.↗

Applications of a transonic wing design method

A method for designing wings and airfoils at transonic speeds using a predictor/corrector approach was developed. The procedure iterates between an aerodynamic code, which predicts the flow about a given geometry, and the design module, which compares the calculated and target pressure distributions and modifies the geometry using an algorithm that relates differences in pressure to a change in surface curvature. The modular nature of the design method makes it relatively simple to couple it to any analysis method. The iterative approach allows the design process and aerodynamic analysis to converge in parallel, significantly reducing the time required to reach a final design. Viscous and static aeroelastic effects can also be accounted for during the design or as a post-design correction. Results from several pilot design codes indicated that the method accurately reproduced pressure distributions as well as the coordinates of a given airfoil or wing by modifying an initial contour. The codes were applied to supercritical as well as conventional airfoils, forward- and aft-swept transport wings, and moderate-to-highly swept fighter wings. The design method was found to be robust and efficient, even for cases having fairly strong shocks.

Campbell, Richard L.↗

The arbitrary-order virtual element method for linear elastodynamics models. Convergence, stability and dispersion-dissipation analysis.

We design the conforming virtual element method for the numerical approximation of the two dimensional elastodynamics problem. We prove stability and convergence of the semi-discrete approximation and derive optimal error estimates under $\textit{h}$-refinement in both the energy and the $L^2$ norms, and optimal error estimates under $\textit{p}$-refinement in the energy norm. The performance of the proposed virtual element method is assessed on a set of different computational meshes, including non-convex cells up to order four in the h-refinement setting. Exponential convergence is also experimentally observed under p-refinement. Finally, we present a dispersion-dissipation analysis for both the semi-discrete and fully-discrete schemes, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion-dissipation properties.

97 MATHEMATICS AND COMPUTING↗

An Overview of the Null-Field Method. II: Convergence and Numerical Stability

In this paper we provide an analysis of the convergence and numerical stability of the null-field method with discrete sources. We show that (i) if the null-field scheme is numerically stable then we can decide whether or not convergence can be achieved; (ii) if the null-field scheme is numerically unstable then we cannot draw any conclusion about the convergence issue; and (iii) the numerical stability is closely related to the property of a tangential system of radiating discrete sources to form a Riesz basis. Our numerical analysis indicates that for prolate spheroids and localized vector spherical wave functions, the null-field scheme is numerically unstable (this system of vector functions does not form a Riesz basis), while for distributed vector spherical wave functions, the numerical instability is not so pronounced (this system of discrete sources almost possesses the property of being a Riesz basis). We also describe an analytical method for computing the surface integrals in the framework of the conventional null-field method with localized vector spherical wave functions which increases the stability of the numerical scheme.

Null-field method↗

Evaluating route to impact convergence of the harmonic balance method for piecewise-smooth systems

Here in this work, we investigate the applicability of the harmonic balance method (HBM) to predict periodic solutions of a single degree-of-freedom forced Duffing oscillator with freeplay nonlinearity. By studying the route to impact, which refers to a parametric study as the contact stiffness increases from soft to hard, the convergence behavior of the HBM can be understood in terms of the strength of the non-smooth forcing term. HBM results are compared to time-integration results to facilitate an evaluation of the accuracy of nonlinear periodic responses. An additional contribution of this study is to perform convergence and stability analysis specifically for isolas generated by the non-smooth nonlinearity. Residual error analysis is used to determine the approximate number of harmonics required to get results accurate to a given error tolerance. Hill’s method and Floquet theory are employed to compute the stability of periodic solutions and identify the types of bifurcations in the system.

42 ENGINEERING↗