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At least 163 records · Page 9

Stability of viscous flow past a circular cylinder

A spectral method which employs trigonometric functions and Chebyshev polynomials is used to compute the steady, incompressible laminar flow past a circular cylinder. Linear stability methods are used to formulate a pair of decoupled generalized eigenvalue problems for the growth of symmetric and asymmetric (about the dividing streamline) perturbations. It is shown that, while the symmetric disturbances are stable, the asymmetric perturbations become unstable at a Reynolds number about 40 with a Strouhal number about 0.12. The critical conditions are found to depend on the size of the computational domain in a manner similar to that observed in the laboratory.

Zebib, A.↗

Accuracy Assessment of Response Surface Approximations for Supersonic Turbine Design

There is a growing trend to employ CFD tools to supply the necessary information for design optimization of fluid dynamics components/systems. Such results are prone to uncertainties due to reasons including discretization. errors, incomplete convergence of computational procedures, and errors associated with physical models such as turbulence closures. Based on this type of information, gradient-based optimization algorithms often suffer from the noisy calculations, which can seriously compromise the outcome. Similar problems arise from the experimental measurements. Global optimization techniques, such as those based on the response surface (RS) concept are becoming popular in part because they can overcome some of these barriers. However, there are also fundamental issues related to such global optimization technique such as RS. For example, in high dimensional design spaces, typically only a small number of function evaluations are available due to computational and experimental costs. On the other hand, complex features of the design variables do not allow one to model the global characteristics of the design space with simple quadratic polynomials. Consequently a main challenge is to reduce the size of the region where we fit the RS, or make it more accurate in the regions where the optimum is likely to reside. Response Surface techniques using either polynomials or and Neural Network (NN) methods offer designers alternatives to conduct design optimization. The RS technique employs statistical and numerical techniques to establish the relationship between design variables and objective/constraint functions, typically using polynomials. In this study, we aim at addressing issues related to the following questions: (1) How to identify outliers associated with a given RS representation and improve the RS model via appropriate treatments? (2) How to focus on selected design data so that RS can give better performance in regions critical to design optimization? (3) How to combine NN and polynomial techniques for improving the accuracy of the RS model?

Papila, Nilay↗

The constraint method: A new finite element technique

An approch to the finite element method which utilizes families of conforming finite elements based on complete polynomials is presented. Finite element approximations based on this method converge with respect to progressively reduced element sizes as well as with respect to progressively increasing orders of approximation. Numerical results of static and dynamic applications of plates are presented to demonstrate the efficiency of the method. Comparisons are made with plate elements in NASTRAN and the high-precision plate element developed by Cowper and his co-workers. Some considerations are given to implementation of the constraint method into general purpose computer programs such as NASTRAN.

Tsai, C.↗

Deterministic Quantum Trajectory via Imaginary Time Evolution

Stochastic quantum trajectories, such as pure state evolutions under unitary dynamics and random measurements, offer a crucial ensemble description of many-body open system dynamics. Recent studies have highlighted that individual quantum trajectories also encode essential physical information. Prominent examples include measurement-induced phase transitions, where a pure quantum state corresponding to fixed measurement outcomes (trajectories) exhibits distinct entanglement phases, depending on the measurement rate. However, direct observation of this effect is hindered by an exponential postselection barrier, whereby the probability of realizing a specific trajectory is exponentially small. We propose a deterministic method to efficiently prepare quantum trajectories in polynomial time using imaginary time evolution and, thus, overcome this fundamental challenge. Here, we demonstrate that our method applies to a certain class of quantum states, and argue that universal approaches do not exist for any quantum trajectories. Our result paves the way for experimentally exploring the physics of individual quantum trajectories at scale and enables direct observation of certain postselection-dependent phenomena.

Mittal, Shivan [Los Alamos National Laboratory (LA↗

Interpolation of compound semiconductor alloy parameters from those of their constituents

Several methods have been proposed for interpolation of the value of physical parameters of quaternary alloys from those of their constituent ternary and binary sub-alloys. These expressions agree when non-linear bowing terms are not required; they differ in how the bowing terms of the bounding ternaries should be utilized. Common interpolation expressions for quaternaries can be generalized into two groups: (1) those that use a linear interpolation of the nearest ternary parameter values and (2) those that interpolate over binary values with a bowing term derived from the bounding ternaries. The second group of methods is equivalent to a polynomial expansion over the alloy’s interpolation space. For compound semiconductor alloys, the geometry of the composition space is the direct sum of the group-III and group-V mixture sub-spaces. The mixture sub-spaces are best described using barycentric coordinates on a regular simplex. A general polynomial expansion of the value of an alloy parameter using barycentric coordinates for the group-III and group-V simplex spaces is described along with an algorithm to generate interpolation expressions for alloys with arbitrary numbers of elements, including quinary and senary alloys. It is shown that a polynomial expansion produces values in closer agreement with the direct gap of quaternaries lattice-matched to common substrates than do approaches using an interpolation of the ternary values, despite a prominent recommendation to the contrary. Finally, a quaternary correction term is described that improves the predicted direct bandgap energies of GaInAsSb for compositions near those lattice matched to InP, InAs, and GaSb.

Olesberg, Jonathon T. [Sandia National Laboratorie↗

Computer program to determine roots of polynomials by ratio of successive derivatives

High speed computing finds roots of polynomials with real number coefficients. Ratios of successive polynomial derivatives approach provides accurate roots-of-polynomial computer programs with very high reliability. With derivative ratio method, root analysis can still be done even though the polynomial and its lower order derivatives cannot be evaluated with sufficient accuracy.

Crouse, J. E.↗

Analytical theory for artificial satellites

A theory for generating segmented ephemerides is discussed as a means for fast generation and simple retrieval of nominal orbit data. Over a succession of finite intervals of time, the orbit is represented by a best approximation expressed by Chebyshev polynomials. Storage of coefficients tables for Chebyshev polynomials is seen as a method to reduce data and decrease transmission costs. A general algorithm was constructed and computer programs were designed. The possibility of storing an ephemeris for a few days in the on-board computer, or in microprocessors attached to the data collectors is suggested.

Deprit, A.↗

Note on the eigensolution of a homogeneous equation with semi-infinite domain

The 'variation-iteration' method using Green's functions to find the eigenvalues and the corresponding eigenfunctions of a homogeneous Fredholm integral equation is employed for the stability analysis of fluid hydromechanics problems with a semiinfinite (infinite) domain of application. The objective of the study is to develop a suitable numerical approach to the solution of such equations in order to better understand the full set of equations for 'real-world' flow models. The study involves a search for a suitable value of the length of the domain which is a fair finite approximation to infinity, which makes the eigensolution an approximation dependent on the length of the interval chosen. In the examples investigated y = 1 = a seems to be the best approximation of infinity; for y greater than unity this method fails due to the polynomial nature of Green's functions.

Wadia, A. R.↗

Research on numerical algorithms for large space structures

Numerical algorithms for analysis and design of large space structures are investigated. The sign algorithm and its application to decoupling of differential equations are presented. The generalized sign algorithm is given and its application to several problems discussed. The Laplace transforms of matrix functions and the diagonalization procedure for a finite element equation are discussed. The diagonalization of matrix polynomials is considered. The quadrature method and Laplace transforms is discussed and the identification of linear systems by the quadrature method investigated.

Denman, E. D.↗

Investigation of Antarctic crust and upper mantle using MAGSAT and other geophysical data

Antarctica is the perfect proving ground for testing data reduction procedures which are alternatives to the standard procedure employing polynomial fitting. Unreduced data (observed values minus corefield model theo each pass) were averaged in 3 degree bins. The resulting map was then high pass filtered using a finite Fourier transform filter so that spectral peaks between 4200 km and 5280 km were diminished by 1/3, peaks corresponding to wavelengths greater than or equal to 5280 km were diminished by 1/2, and the d.c. component was set equal to zero. The surface subtracted in this way differs from the polynomials used in the standard method in that it is static over the 5 north data window. The map produced is presented and the effects of the static model are compared to those of the dynamic mode.

Bentley, C. R.↗

Computation of consistent boundary quantities in finite element thermal-fluid solutions

The consistent boundary quantity method for computing derived quantities from finite element nodal variable solutions is investigated. The method calculates consistent, continuous boundary surface quantities such as heat fluxes, flow velocities, and surface tractions from nodal variables such as temperatures, velocity potentials, and displacements. Consistent and lumped coefficient matrix solutions for such problems are compared. The consistent approach may produce more accurate boundary quantities, but spurious oscillations may be produced in the vicinity of discontinuities. The uncoupled computations of the lumped approach provide greater flexibility in dealing with discontinuities and provide increased computational efficiency. The consistent boundary quantity approach can be applied to solution boundaries other than those with Dirichlet boundary conditions, and provides more accurate results than the customary method of differentiation of interpolation polynomials.

Thornton, E. A.↗

Progress Report on Optimizing X-ray Optical Prescriptions for Wide-Field Applications

We report on the present status of our continuing efforts to develop a method for optimizing wide-field nested x-ray telescope mirror prescriptions. Utilizing extensive Monte-Carlo ray trace simulations, we find an analytic form for the root-mean-square dispersion of rays from a Wolter I optic on the surface of a flat focal plane detector as a function of detector tilt away from the nominal focal plane and detector displacement along the optical axis. The configuration minimizing the ray dispersion from a nested array of Wolter I telescopes is found by solving a linear system of equations for tilt and individual mirror pair displacement. Finally we outline our initial efforts at expanding this method to include higher order polynomial terms in the mirror prescriptions.

Elsner, R. F.↗

Optimization of Car Body under Constraints of Noise, Vibration, and Harshness (NVH), and Crash

To be competitive on the today's market, cars have to be as light as possible while meeting the Noise, Vibration, and Harshness (NVH) requirements and conforming to Government-man dated crash survival regulations. The latter are difficult to meet because they involve very compute-intensive, nonlinear analysis, e.g., the code RADIOSS capable of simulation of the dynamics, and the geometrical and material nonlinearities of a thin-walled car structure in crash, would require over 12 days of elapsed time for a single design of a 390K elastic degrees of freedom model, if executed on a single processor of the state-of-the-art SGI Origin2000 computer. Of course, in optimization that crash analysis would have to be invoked many times. Needless to say, that has rendered such optimization intractable until now. The car finite element model is shown. The advent of computers that comprise large numbers of concurrently operating processors has created a new environment wherein the above optimization, and other engineering problems heretofore regarded as intractable may be solved. The procedure, shown, is a piecewise approximation based method and involves using a sensitivity based Taylor series approximation model for NVH and a polynomial response surface model for Crash. In that method the NVH constraints are evaluated using a finite element code (MSC/NASTRAN) that yields the constraint values and their derivatives with respect to design variables. The crash constraints are evaluated using the explicit code RADIOSS on the Origin 2000 operating on 256 processors simultaneously to generate data for a polynomial response surface in the design variable domain. The NVH constraints and their derivatives combined with the response surface for the crash constraints form an approximation to the system analysis (surrogate analysis) that enables a cycle of multidisciplinary optimization within move limits. In the inner loop, the NVH sensitivities are recomputed to update the NVH approximation model while keeping the Crash response surface constant. In every outer loop, the Crash response surface approximation is updated, including a gradual increase in the order of the response surface and the response surface extension in the direction of the search. In this optimization task, the NVH discipline has 30 design variables while the crash discipline has 20 design variables. A subset of these design variables (10) are common to both the NVH and crash disciplines. In order to construct a linear response surface for the Crash discipline constraints, a minimum of 21 design points would have to be analyzed using the RADIOSS code. On a single processor in Origin 2000 that amount of computing would require over 9 months! In this work, these runs were carried out concurrently on the Origin 2000 using multiple processors, ranging from 8 to 16, for each crash (RADIOSS) analysis. Another figure shows the wall time required for a single RADIOSS analysis using varying number of processors, as well as provides a comparison of 2 different common data placement procedures within the allotted memories for each analysis. The initial design is an infeasible design with NVH discipline Static Torsion constraint violations of over 10%. The final optimized design is a feasible design with a weight reduction of 15 kg compared to the initial design. This work demonstrates how advanced methodology for optimization combined with the technology of concurrent processing enables applications that until now were out of reach because of very long time-to-solution.

Kodiyalam, Srinivas↗

Wave-Front Error Measurements and Alignment of CLASP2 Telescope with a Dual-Band Pass Cold Mirror Coated Primary Mirror

"Chromospheric LAyer Spectro-Polarimeter (CLASP2)" is the next sounding rocket experiment of the "Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP)" that succeeded in observing for the first time the linear polarization spectra in the hydrogen Lyman- line (121.6 nm) and is scheduled to be launched in 2019. In CLASP2, we will carry out full Stokes-vector spectropolarimetric observations in the Mg II h & k lines near 280 nm with the spectro-polarimeter (SP), while imaging observations in the Lyman- line will be conducted with the slitjaw optics (SJ). For the wavelength selection of CLASP2, the primary mirror of the telescope uses a new dual-band pass cold mirror coating targeting both at 121.6 nm and 280 nm. Therefore, we have to perform again the alignment of the telescope after the installation of the recoated primary mirror. Before unmounting the primary mirror from the telescope structure, we measured the wave-front error (WFE) of the telescope. The measured WFE map was consistent with what we had before the CLASP flight, clearly indicating that the telescope alignment has been maintained even after the flight. After the re-coated primary mirror was installed the WFE was measured, and coma aberration was found to be larger. Finally, the secondary mirror shim adjustments were carried out based on the WFE measurements. In CLASP2 telescope, we improved a fitting method of WFE map (applying 8th terms circular Zernike polynomial tting instead of 37th terms circular Zernike fitting) and the improved method enables to achieve better performance than CLASP telescope. Indeed, WFE map obtained after the final shim adjustment indicated that the required specification (< 5:5 m RMS spot radius) that is more stringent than CLASP telescope was met.

chromosphere; polarimetry; sounding rocket↗

Efficient multimode Wigner tomography

Abstract Advancements in quantum system lifetimes and control have enabled the creation of increasingly complex quantum states, such as those on multiple bosonic cavity modes. When characterizing these states, traditional tomography scales exponentially with the number of modes in both computational and experimental measurement requirement, which becomes prohibitive as the system size increases. Here, we implement a state reconstruction method whose sampling requirement instead scales polynomially with system size, and thus mode number, for states that can be represented within such a polynomial subspace. We demonstrate this improved scaling with Wigner tomography of multimode entangled W states of up to 4 modes on a 3D circuit quantum electrodynamics (cQED) system. This approach performs similarly in efficiency to existing matrix inversion methods for 2 modes, and demonstrates a noticeable improvement for 3 and 4 modes, with even greater theoretical gains at higher mode numbers.

Science & Technology - Other Topics↗

Development of new flux splitting schemes

Maximizing both accuracy and efficiency has been the primary objective in designing a numerical algorithm for computational fluid dynamics (CFD). This is especially important for solutions of complex three dimensional systems of Navier-Stokes equations which often include turbulence modeling and chemistry effects. Recently, upwind schemes have been well received for their capability in resolving discontinuities. With this in mind, presented are two new flux splitting techniques for upwind differencing. The first method is based on High-Order Polynomial Expansions (HOPE) of the mass flux vector. The second new flux splitting is based on the Advection Upwind Splitting Method (AUSM). The calculation of the hypersonic conical flow demonstrates the accuracy of the splitting in resolving the flow in the presence of strong gradients. A second series of tests involving the two dimensional inviscid flow over a NACA 0012 airfoil demonstrates the ability of the AUSM to resolve the shock discontinuity at transonic speed. A third case calculates a series of supersonic flows over a circular cylinder. Finally, the fourth case deals with tests of a two dimensional shock wave/boundary layer interaction.

Liou, Meng-Sing↗

The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

In this paper, we study the Local Discontinuous Galerkin methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, their high-order formal accuracy, and their easy handling of complicated geometries, for convection dominated problems. It is proven that for scalar equations, the Local Discontinuous Galerkin methods are L(sup 2)-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are k-th order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown.

Cockburn, Bernardo↗

Non-oscillatory spectral Fourier methods for shock wave calculations

A non-oscillatory spectral Fourier method is presented for the solution of hyperbolic partial differential equations. The method is based on adding a nonsmooth function to the trigonometric polynomials which are the usual basis functions for the Fourier method. The high accuracy away from the shock is enhanced by using filters. Numerical results confirm that no oscillations develop in the solution. Also, the accuracy of the spectral solution of the inviscid Burgers equation is shown to be higher than a fixed order.

Cai, Wei↗