Reverberation Modelling Using a Parabolic Equation Method

DTIC Science & Technology

2012-10-01

the limits of their applicability. Results: Transmission loss estimates produced by the PECan parabolic equation acoustic model were used in...environments is possible when used in concert with a parabolic equation passive acoustic model . Future plans: The authors of this report recommend further...technique using other types of acoustic models should be undertaken. Furthermore, as the current method when applied as-is results in estimates that reflect

Identifying the principal coefficient of parabolic equations with non-divergent form

NASA Astrophysics Data System (ADS)

Jiang, L. S.; Bian, B. J.

2005-01-01

We deal with an inverse problem of determining a coefficient a(x, t) of principal part for second order parabolic equations with non-divergent form when the solution is known. Such a problem has important applications in a large fields of applied science. We propose a well-posed approximate algorithm to identify the coefficient. The existence, uniqueness and stability of such solutions a(x, t) are proved. A necessary condition which is a couple system of a parabolic equation and a parabolic variational inequality is deduced. Our numerical simulations show that the coefficient is recovered very well.

Far-Field Turbulent Vortex-Wake/Exhaust Plume Interaction for Subsonic and HSCT Airplanes

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Adam, Ihab; Wong, Tin-Chee

1996-01-01

Computational study of the far-field turbulent vortex-wake/exhaust plume interaction for subsonic and high speed civil transport (HSCT) airplanes is carried out. The Reynolds-averaged Navier-Stokes (NS) equations are solved using the implicit, upwind, Roe-flux-differencing, finite-volume scheme. The two-equation shear stress transport model of Menter is implemented with the NS solver for turbulent-flow calculation. For the far-field study, the computations of vortex-wake interaction with the exhaust plume of a single engine of a Boeing 727 wing in a holding condition and two engines of an HSCT in a cruise condition are carried out using overlapping zonal method for several miles downstream. These results are obtained using the computer code FTNS3D. The results of the subsonic flow of this code are compared with those of a parabolized NS solver known as the UNIWAKE code.

Crank-Nicholson difference scheme for a stochastic parabolic equation with a dependent operator coefficient

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ashyralyev, Allaberen; Okur, Ulker

In the present paper, the Crank-Nicolson difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is considered. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, convergence estimates for the solution of difference schemes for the numerical solution of three mixed problems for parabolic equations are obtained. The numerical results are given.

Langley Stability and Transition Analysis Code (LASTRAC) Version 1.2 User Manual

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan

2004-01-01

LASTRAC is a general-purposed, physics-based transition prediction code released by NASA for Laminar Flow Control studies and transition research. The design and development of the LASTRAC code is aimed at providing an engineering tool that is easy to use and yet capable of dealing with a broad range of transition related issues. It was written from scratch based on the state-of-the-art numerical methods for stability analysis and modern software technologies. At low fidelity, it allows users to perform linear stability analysis and N-factor transition correlation for a broad range of flow regimes and configurations by using either the linear stability theory or linear parabolized stability equations method. At high fidelity, users may use nonlinear PSE to track finite-amplitude disturbances until the skin friction rise. This document describes the governing equations, numerical methods, code development, detailed description of input/output parameters, and case studies for the current release of LASTRAC.

THE PLUTO CODE FOR ADAPTIVE MESH COMPUTATIONS IN ASTROPHYSICAL FLUID DYNAMICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mignone, A.; Tzeferacos, P.; Zanni, C.

We present a description of the adaptive mesh refinement (AMR) implementation of the PLUTO code for solving the equations of classical and special relativistic magnetohydrodynamics (MHD and RMHD). The current release exploits, in addition to the static grid version of the code, the distributed infrastructure of the CHOMBO library for multidimensional parallel computations over block-structured, adaptively refined grids. We employ a conservative finite-volume approach where primary flow quantities are discretized at the cell center in a dimensionally unsplit fashion using the Corner Transport Upwind method. Time stepping relies on a characteristic tracing step where piecewise parabolic method, weighted essentially non-oscillatory,more » or slope-limited linear interpolation schemes can be handily adopted. A characteristic decomposition-free version of the scheme is also illustrated. The solenoidal condition of the magnetic field is enforced by augmenting the equations with a generalized Lagrange multiplier providing propagation and damping of divergence errors through a mixed hyperbolic/parabolic explicit cleaning step. Among the novel features, we describe an extension of the scheme to include non-ideal dissipative processes, such as viscosity, resistivity, and anisotropic thermal conduction without operator splitting. Finally, we illustrate an efficient treatment of point-local, potentially stiff source terms over hierarchical nested grids by taking advantage of the adaptivity in time. Several multidimensional benchmarks and applications to problems of astrophysical relevance assess the potentiality of the AMR version of PLUTO in resolving flow features separated by large spatial and temporal disparities.« less

A model of transverse fuel injection applied to the computation of supersonic combustor flow

NASA Technical Reports Server (NTRS)

Rogers, R. C.

1979-01-01

A two-dimensional, nonreacting flow model of the aerodynamic interaction of a transverse hydrogen jet within a supersonic mainstream has been developed. The model assumes profile shapes of mass flux, pressure, flow angle, and hydrogen concentration and produces downstream profiles of the other flow parameters under the constraints of the integrated conservation equations. These profiles are used as starting conditions for an existing finite difference parabolic computer code for the turbulent supersonic combustion of hydrogen. Integrated mixing and flow profile results obtained from the computer code compare favorably with existing data for the supersonic combustion of hydrogen.

A Semi-linear Backward Parabolic Cauchy Problem with Unbounded Coefficients of Hamilton–Jacobi–Bellman Type and Applications to Optimal Control

DOE Office of Scientific and Technical Information (OSTI.GOV)

Addona, Davide, E-mail: d.addona@campus.unimib.it

2015-08-15

We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a semi-linear backward parabolic Cauchy problem, where the differential equation is the Hamilton–Jacobi–Bellman equation of a suitable optimal control problem. Via backward stochastic differential equations, we show that the mild solution is indeed the value function of the controlled equation and that the feedback law is verified.

An approximate Riemann solver for real gas parabolized Navier-Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Urbano, Annafederica, E-mail: annafederica.urbano@uniroma1.it; Nasuti, Francesco, E-mail: francesco.nasuti@uniroma1.it

2013-01-15

Under specific assumptions, parabolized Navier-Stokes equations are a suitable mean to study channel flows. A special case is that of high pressure flow of real gases in cooling channels where large crosswise gradients of thermophysical properties occur. To solve the parabolized Navier-Stokes equations by a space marching approach, the hyperbolicity of the system of governing equations is obtained, even for very low Mach number flow, by recasting equations such that the streamwise pressure gradient is considered as a source term. For this system of equations an approximate Roe's Riemann solver is developed as the core of a Godunov type finitemore » volume algorithm. The properties of the approximated Riemann solver, which is a modification of Roe's Riemann solver for the parabolized Navier-Stokes equations, are presented and discussed with emphasis given to its original features introduced to handle fluids governed by a generic real gas EoS. Sample solutions are obtained for low Mach number high compressible flows of transcritical methane, heated in straight long channels, to prove the solver ability to describe flows dominated by complex thermodynamic phenomena.« less

Application of the Parabolic Approximation to Predict Acoustical Propagation in the Ocean.

ERIC Educational Resources Information Center

McDaniel, Suzanne T.

1979-01-01

A simplified derivation of the parabolic approximation to the acoustical wave equation is presented. Exact solutions to this approximate equation are compared with solutions to the wave equation to demonstrate the applicability of this method to the study of underwater sound propagation. (Author/BB)

A Harnack's inequality for mixed type evolution equations

NASA Astrophysics Data System (ADS)

Paronetto, Fabio

2016-03-01

We define a homogeneous parabolic De Giorgi classes of order 2 which suits a mixed type class of evolution equations whose simplest example is μ (x)∂u/∂t - Δu = 0 where μ can be positive, null and negative, so in particular elliptic-parabolic and forward-backward parabolic equations are included. For functions belonging to this class we prove local boundedness and show a Harnack inequality which, as by-products, gives Hölder-continuity, in particular in the interface I where μ changes sign, and a maximum principle.

Numerical solution of the stochastic parabolic equation with the dependent operator coefficient

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ashyralyev, Allaberen; Department of Mathematics, ITTU, Ashgabat; Okur, Ulker

2015-09-18

In the present paper, a single step implicit difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is presented. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, this abstract result permits us to obtain the convergence estimates for the solution of difference schemes for the numerical solution of initial boundary value problems for parabolic equations. The theoretical statements for the solution of this difference scheme are supported by the results of numerical experiments.

A three-dimensional parabolic equation model of sound propagation using higher-order operator splitting and Padé approximants.

PubMed

Lin, Ying-Tsong; Collis, Jon M; Duda, Timothy F

2012-11-01

An alternating direction implicit (ADI) three-dimensional fluid parabolic equation solution method with enhanced accuracy is presented. The method uses a square-root Helmholtz operator splitting algorithm that retains cross-multiplied operator terms that have been previously neglected. With these higher-order cross terms, the valid angular range of the parabolic equation solution is improved. The method is tested for accuracy against an image solution in an idealized wedge problem. Computational efficiency improvements resulting from the ADI discretization are also discussed.

Hazardous Continuation Backward in Time in Nonlinear Parabolic Equations, and an Experiment in Deblurring Nonlinearly Blurred Imagery

PubMed Central

Carasso, Alfred S

2013-01-01

Identifying sources of ground water pollution, and deblurring nanoscale imagery as well as astronomical galaxy images, are two important applications involving numerical computation of parabolic equations backward in time. Surprisingly, very little is known about backward continuation in nonlinear parabolic equations. In this paper, an iterative procedure originating in spectroscopy in the 1930’s, is adapted into a useful tool for solving a wide class of 2D nonlinear backward parabolic equations. In addition, previously unsuspected difficulties are uncovered that may preclude useful backward continuation in parabolic equations deviating too strongly from the linear, autonomous, self adjoint, canonical model. This paper explores backward continuation in selected 2D nonlinear equations, by creating fictitious blurred images obtained by using several sharp images as initial data in these equations, and capturing the corresponding solutions at some positive time T. Successful backward continuation from t=T to t = 0, would recover the original sharp image. Visual recognition provides meaningful evaluation of the degree of success or failure in the reconstructed solutions. Instructive examples are developed, illustrating the unexpected influence of certain types of nonlinearities. Visually and statistically indistinguishable blurred images are presented, with vastly different deblurring results. These examples indicate that how an image is nonlinearly blurred is critical, in addition to the amount of blur. The equations studied represent nonlinear generalizations of Brownian motion, and the blurred images may be interpreted as visually expressing the results of novel stochastic processes. PMID:26401430

Hazardous Continuation Backward in Time in Nonlinear Parabolic Equations, and an Experiment in Deblurring Nonlinearly Blurred Imagery.

PubMed

Carasso, Alfred S

2013-01-01

Identifying sources of ground water pollution, and deblurring nanoscale imagery as well as astronomical galaxy images, are two important applications involving numerical computation of parabolic equations backward in time. Surprisingly, very little is known about backward continuation in nonlinear parabolic equations. In this paper, an iterative procedure originating in spectroscopy in the 1930's, is adapted into a useful tool for solving a wide class of 2D nonlinear backward parabolic equations. In addition, previously unsuspected difficulties are uncovered that may preclude useful backward continuation in parabolic equations deviating too strongly from the linear, autonomous, self adjoint, canonical model. This paper explores backward continuation in selected 2D nonlinear equations, by creating fictitious blurred images obtained by using several sharp images as initial data in these equations, and capturing the corresponding solutions at some positive time T. Successful backward continuation from t=T to t = 0, would recover the original sharp image. Visual recognition provides meaningful evaluation of the degree of success or failure in the reconstructed solutions. Instructive examples are developed, illustrating the unexpected influence of certain types of nonlinearities. Visually and statistically indistinguishable blurred images are presented, with vastly different deblurring results. These examples indicate that how an image is nonlinearly blurred is critical, in addition to the amount of blur. The equations studied represent nonlinear generalizations of Brownian motion, and the blurred images may be interpreted as visually expressing the results of novel stochastic processes.

Progress and supercomputing in computational fluid dynamics; Proceedings of U.S.-Israel Workshop, Jerusalem, Israel, December 1984

NASA Technical Reports Server (NTRS)

Murman, E. M. (Editor); Abarbanel, S. S. (Editor)

1985-01-01

Current developments and future trends in the application of supercomputers to computational fluid dynamics are discussed in reviews and reports. Topics examined include algorithm development for personal-size supercomputers, a multiblock three-dimensional Euler code for out-of-core and multiprocessor calculations, simulation of compressible inviscid and viscous flow, high-resolution solutions of the Euler equations for vortex flows, algorithms for the Navier-Stokes equations, and viscous-flow simulation by FEM and related techniques. Consideration is given to marching iterative methods for the parabolized and thin-layer Navier-Stokes equations, multigrid solutions to quasi-elliptic schemes, secondary instability of free shear flows, simulation of turbulent flow, and problems connected with weather prediction.

The Extended Parabolic Equation Method and Implication of Results for Atmospheric Millimeter-Wave and Optical Propagation

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2004-01-01

The extended wide-angle parabolic wave equation applied to electromagnetic wave propagation in random media is considered. A general operator equation is derived which gives the statistical moments of an electric field of a propagating wave. This expression is used to obtain the first and second order moments of the wave field and solutions are found that transcend those which incorporate the full paraxial approximation at the outset. Although these equations can be applied to any propagation scenario that satisfies the conditions of application of the extended parabolic wave equation, the example of propagation through atmospheric turbulence is used. It is shown that in the case of atmospheric wave propagation and under the Markov approximation (i.e., the -correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The methodology developed here can be applied to any qualifying situation involving random propagation through turbid or plasma environments that can be represented by a spectral density of permittivity fluctuations.

Numerical computation of space shuttle orbiter flow field

NASA Technical Reports Server (NTRS)

Tannehill, John C.

1988-01-01

A new parabolized Navier-Stokes (PNS) code has been developed to compute the hypersonic, viscous chemically reacting flow fields around 3-D bodies. The flow medium is assumed to be a multicomponent mixture of thermally perfect but calorically imperfect gases. The new PNS code solves the gas dynamic and species conservation equations in a coupled manner using a noniterative, implicit, approximately factored, finite difference algorithm. The space-marching method is made well-posed by special treatment of the streamwise pressure gradient term. The code has been used to compute hypersonic laminar flow of chemically reacting air over cones at angle of attack. The results of the computations are compared with the results of reacting boundary-layer computations and show excellent agreement.

H-division quarterly report, October--December 1977. [Lawrence Livermore Laboratory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1978-02-10

The Theoretical EOS Group develops theoretical techniques for describing material properties under extreme conditions and constructs equation-of-state (EOS) tables for specific applications. Work this quarter concentrated on a Li equation of state, equation of state for equilibrium plasma, improved ion corrections to the Thomas--Fermi--Kirzhnitz theory, and theoretical estimates of high-pressure melting in metals. The Experimental Physics Group investigates properties of materials at extreme conditions of pressure and temperature, and develops new experimental techniques. Effort this quarter concerned the following: parabolic projectile distortion in the two-state light-gas gun, construction of a ballistic range for long-rod penetrators, thermodynamics and sound velocities inmore » liquid metals, isobaric expansion measurements in Pt, and calculation of the velocity--mass profile of a jet produced by a shaped charge. Code development was concentrated on the PELE code, a multimaterial, multiphase, explicit finite-difference Eulerian code for pool suppression dynamics of a hypothetical loss-of-coolant accident in a nuclear reactor. Activities of the Fluid Dynamics Group were directed toward development of a code to compute the equations of state and transport properties of liquid metals (e.g. Li) and partially ionized dense plasmas, jet stability in the Li reactor system, and the study and problem application of fluid dynamic turbulence theory. 19 figures, 5 tables. (RWR)« less

Unified approach for incompressible flows

NASA Astrophysics Data System (ADS)

Chang, Tyne-Hsien

1995-07-01

A unified approach for solving incompressible flows has been investigated in this study. The numerical CTVD (Centered Total Variation Diminishing) scheme used in this study was successfully developed by Sanders and Li for compressible flows, especially for the high speed. The CTVD scheme possesses better mathematical properties to damp out the spurious oscillations while providing high-order accuracy for high speed flows. It leads us to believe that the CTVD scheme can equally well apply to solve incompressible flows. Because of the mathematical difference between the governing equations for incompressible and compressible flows, the scheme can not directly apply to the incompressible flows. However, if one can modify the continuity equation for incompressible flows by introducing pseudo-compressibility, the governing equations for incompressible flows would have the same mathematical characters as compressible flows. The application of the algorithm to incompressible flows thus becomes feasible. In this study, the governing equations for incompressible flows comprise continuity equation and momentum equations. The continuity equation is modified by adding a time-derivative of the pressure term containing the artificial compressibility. The modified continuity equation together with the unsteady momentum equations forms a hyperbolic-parabolic type of time-dependent system of equations. Thus, the CTVD schemes can be implemented. In addition, the physical and numerical boundary conditions are properly implemented by the characteristic boundary conditions. Accordingly, a CFD code has been developed for this research and is currently under testing. Flow past a circular cylinder was chosen for numerical experiments to determine the accuracy and efficiency of the code. The code has shown some promising results.

Unified approach for incompressible flows

NASA Technical Reports Server (NTRS)

Chang, Tyne-Hsien

1995-01-01

A unified approach for solving incompressible flows has been investigated in this study. The numerical CTVD (Centered Total Variation Diminishing) scheme used in this study was successfully developed by Sanders and Li for compressible flows, especially for the high speed. The CTVD scheme possesses better mathematical properties to damp out the spurious oscillations while providing high-order accuracy for high speed flows. It leads us to believe that the CTVD scheme can equally well apply to solve incompressible flows. Because of the mathematical difference between the governing equations for incompressible and compressible flows, the scheme can not directly apply to the incompressible flows. However, if one can modify the continuity equation for incompressible flows by introducing pseudo-compressibility, the governing equations for incompressible flows would have the same mathematical characters as compressible flows. The application of the algorithm to incompressible flows thus becomes feasible. In this study, the governing equations for incompressible flows comprise continuity equation and momentum equations. The continuity equation is modified by adding a time-derivative of the pressure term containing the artificial compressibility. The modified continuity equation together with the unsteady momentum equations forms a hyperbolic-parabolic type of time-dependent system of equations. Thus, the CTVD schemes can be implemented. In addition, the physical and numerical boundary conditions are properly implemented by the characteristic boundary conditions. Accordingly, a CFD code has been developed for this research and is currently under testing. Flow past a circular cylinder was chosen for numerical experiments to determine the accuracy and efficiency of the code. The code has shown some promising results.

Iterative Methods for Solving Nonlinear Parabolic Problem in Pension Saving Management

NASA Astrophysics Data System (ADS)

Koleva, M. N.

2011-11-01

In this work we consider a nonlinear parabolic equation, obtained from Riccati like transformation of the Hamilton-Jacobi-Bellman equation, arising in pension saving management. We discuss two numerical iterative methods for solving the model problem—fully implicit Picard method and mixed Picard-Newton method, which preserves the parabolic characteristics of the differential problem. Numerical experiments for comparison the accuracy and effectiveness of the algorithms are discussed. Finally, observations are given.

Fast wavelet based algorithms for linear evolution equations

NASA Technical Reports Server (NTRS)

Engquist, Bjorn; Osher, Stanley; Zhong, Sifen

1992-01-01

A class was devised of fast wavelet based algorithms for linear evolution equations whose coefficients are time independent. The method draws on the work of Beylkin, Coifman, and Rokhlin which they applied to general Calderon-Zygmund type integral operators. A modification of their idea is applied to linear hyperbolic and parabolic equations, with spatially varying coefficients. A significant speedup over standard methods is obtained when applied to hyperbolic equations in one space dimension and parabolic equations in multidimensions.

Three-Dimensional Shallow Water Acoustics

DTIC Science & Technology

2015-09-30

converts the Helmholtz wave equation of elliptic type to a one-way wave equation of parabolic type. The conversion allows efficient marching solution ...algorithms for 2 solving the boundary value problem posed by the Helmholtz equation . This can reduce significantly the requirement for computational...Fourier parabolic- equation sound propagation solution scheme," J. Acoust. Soc. Am, vol. 132, pp. EL61-EL67 (2012). [6] Y.-T. Lin, J.M. Collis and T.F

Design of supercritical swept wings

NASA Technical Reports Server (NTRS)

Garabedian, P.; Mcfadden, G.

1982-01-01

Computational fluid dynamics are used to discuss problems inherent to transonic three-dimensional flow past supercritical swept wings. The formulation for a boundary value problem for the flow past the wing is provided, including consideration of weak shock waves and the use of parabolic coordinates. A swept wing code is developed which requires a mesh of 152 x 10 x 12 points and 200 time cycles. A formula for wave drag is calculated, based on the idea that the conservation form of the momentum equation becomes an entropy inequality measuring the drag, expressible in terms of a small-disturbance equation for a potential function in two dimensions. The entropy inequality has been incorporated in a two-dimensional code for the analysis of transonic flow over airfoils. A method of artificial viscosity is explored for optimum pressure distributions with design, and involves a free boundary problem considering speed over only a portion of the wing.

Development of a Model and Computer Code to Describe Solar Grade Silicon Production Processes

NASA Technical Reports Server (NTRS)

Srivastava, R.; Gould, R. K.

1979-01-01

Mathematical models and computer codes based on these models, which allow prediction of the product distribution in chemical reactors for converting gaseous silicon compounds to condensed-phase silicon were developed. The following tasks were accomplished: (1) formulation of a model for silicon vapor separation/collection from the developing turbulent flow stream within reactors of the Westinghouse (2) modification of an available general parabolic code to achieve solutions to the governing partial differential equations (boundary layer type) which describe migration of the vapor to the reactor walls, (3) a parametric study using the boundary layer code to optimize the performance characteristics of the Westinghouse reactor, (4) calculations relating to the collection efficiency of the new AeroChem reactor, and (5) final testing of the modified LAPP code for use as a method of predicting Si(1) droplet sizes in these reactors.

PETOOL: MATLAB-based one-way and two-way split-step parabolic equation tool for radiowave propagation over variable terrain

NASA Astrophysics Data System (ADS)

Ozgun, Ozlem; Apaydin, Gökhan; Kuzuoglu, Mustafa; Sevgi, Levent

2011-12-01

A MATLAB-based one-way and two-way split-step parabolic equation software tool (PETOOL) has been developed with a user-friendly graphical user interface (GUI) for the analysis and visualization of radio-wave propagation over variable terrain and through homogeneous and inhomogeneous atmosphere. The tool has a unique feature over existing one-way parabolic equation (PE)-based codes, because it utilizes the two-way split-step parabolic equation (SSPE) approach with wide-angle propagator, which is a recursive forward-backward algorithm to incorporate both forward and backward waves into the solution in the presence of variable terrain. First, the formulation of the classical one-way SSPE and the relatively-novel two-way SSPE is presented, with particular emphasis on their capabilities and the limitations. Next, the structure and the GUI capabilities of the PETOOL software tool are discussed in detail. The calibration of PETOOL is performed and demonstrated via analytical comparisons and/or representative canonical tests performed against the Geometric Optic (GO) + Uniform Theory of Diffraction (UTD). The tool can be used for research and/or educational purposes to investigate the effects of a variety of user-defined terrain and range-dependent refractivity profiles in electromagnetic wave propagation. Program summaryProgram title: PETOOL (Parabolic Equation Toolbox) Catalogue identifier: AEJS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 143 349 No. of bytes in distributed program, including test data, etc.: 23 280 251 Distribution format: tar.gz Programming language: MATLAB (MathWorks Inc.) 2010a. Partial Differential Toolbox and Curve Fitting Toolbox required Computer: PC Operating system: Windows XP and Vista Classification: 10 Nature of problem: Simulation of radio-wave propagation over variable terrain on the Earth's surface, and through homogeneous and inhomogeneous atmosphere. Solution method: The program implements one-way and two-way Split-Step Parabolic Equation (SSPE) algorithm, with wide-angle propagator. The SSPE is, in general, an initial-value problem starting from a reference range (typically from an antenna), and marching out in range by obtaining the field along the vertical direction at each range step, through the use of step-by-step Fourier transformations. The two-way algorithm incorporates the backward-propagating waves into the standard one-way SSPE by utilizing an iterative forward-backward scheme for modeling multipath effects over a staircase-approximated terrain. Unusual features: This is the first software package implementing a recursive forward-backward SSPE algorithm to account for the multipath effects during radio-wave propagation, and enabling the user to easily analyze and visualize the results of the two-way propagation with GUI capabilities. Running time: Problem dependent. Typically, it is about 1.5 ms (for conducting ground) and 4 ms (for lossy ground) per range step for a vertical field profile of vector length 1500, on Intel Core 2 Duo 1.6 GHz with 2 GB RAM under Windows Vista.

Transition between free-space Helmholtz equation solutions with plane sources and parabolic wave equation solutions.

PubMed

Mahillo-Isla, R; Gonźalez-Morales, M J; Dehesa-Martínez, C

2011-06-01

The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well.

Real-time optical laboratory solution of parabolic differential equations

NASA Technical Reports Server (NTRS)

Casasent, David; Jackson, James

1988-01-01

An optical laboratory matrix-vector processor is used to solve parabolic differential equations (the transient diffusion equation with two space variables and time) by an explicit algorithm. This includes optical matrix-vector nonbase-2 encoded laboratory data, the combination of nonbase-2 and frequency-multiplexed data on such processors, a high-accuracy optical laboratory solution of a partial differential equation, new data partitioning techniques, and a discussion of a multiprocessor optical matrix-vector architecture.

Simulation of the pulse propagation by the interacting mode parabolic equation method

NASA Astrophysics Data System (ADS)

Trofimov, M. Yu.; Kozitskiy, S. B.; Zakharenko, A. D.

2018-07-01

A broadband modeling of pulses has been performed by using the previously derived interacting mode parabolic equation through the Fourier synthesis. Test examples on the wedge with the angle 2.86∘ (known as the ASA benchmark) show excellent agreement with the source images method.

An explicit analytical solution for sound propagation in a three-dimensional penetrable wedge with small apex angle.

PubMed

Petrov, Pavel S; Sturm, Frédéric

2016-03-01

A problem of sound propagation in a shallow-water waveguide with a weakly sloping penetrable bottom is considered. The adiabatic mode parabolic equations are used to approximate the solution of the three-dimensional (3D) Helmholtz equation by modal decomposition of the acoustic pressure field. The mode amplitudes satisfy parabolic equations that admit analytical solutions in the special case of the 3D wedge. Using the analytical formula for modal amplitudes, an explicit and remarkably simple expression for the acoustic pressure in the wedge is obtained. The proposed solution is validated by the comparison with a solution of the 3D penetrable wedge problem obtained using a fully 3D parabolic equation that includes a leading-order cross term correction.

Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Demirci, Ali; Ma, Yi-Ping

2016-10-01

Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using step like initial data along a parabolic front. Employing a parabolic similarity reduction exactly reduces the study of such DSWs in two space one time (2 + 1) dimensions to finding DSW solutions of (1 + 1) dimensional equations. With this ansatz, the KP and 2DBO equations can be exactly reduced to the cylindrical Korteweg-de Vries (cKdV) and cylindrical Benjamin-Ono (cBO) equations, respectively. Whitham modulation equations which describe DSW evolution in the cKdV and cBO equations are derived and Riemann type variables are introduced. DSWs obtained from the numerical solutions of the corresponding Whitham systems and direct numerical simulations of the cKdV and cBO equations are compared with very good agreement obtained. In turn, DSWs obtained from direct numerical simulations of the KP and 2DBO equations are compared with the cKdV and cBO equations, again with good agreement. It is concluded that the (2 + 1) DSW behavior along self similar parabolic fronts can be effectively described by the DSW solutions of the reduced (1 + 1) dimensional equations.

A spectrally accurate boundary-layer code for infinite swept wings

NASA Technical Reports Server (NTRS)

Pruett, C. David

1994-01-01

This report documents the development, validation, and application of a spectrally accurate boundary-layer code, WINGBL2, which has been designed specifically for use in stability analyses of swept-wing configurations. Currently, we consider only the quasi-three-dimensional case of an infinitely long wing of constant cross section. The effects of streamwise curvature, streamwise pressure gradient, and wall suction and/or blowing are taken into account in the governing equations and boundary conditions. The boundary-layer equations are formulated both for the attachment-line flow and for the evolving boundary layer. The boundary-layer equations are solved by marching in the direction perpendicular to the leading edge, for which high-order (up to fifth) backward differencing techniques are used. In the wall-normal direction, a spectral collocation method, based upon Chebyshev polynomial approximations, is exploited. The accuracy, efficiency, and user-friendliness of WINGBL2 make it well suited for applications to linear stability theory, parabolized stability equation methodology, direct numerical simulation, and large-eddy simulation. The method is validated against existing schemes for three test cases, including incompressible swept Hiemenz flow and Mach 2.4 flow over an airfoil swept at 70 deg to the free stream.

Research on Nonlinear Dynamical Systems.

DTIC Science & Technology

1983-01-10

Applied Math., to appear. [26] Variational inequalities and flow in porous media, LCDS’Lecture Notes, Brown University #LN 82-1, July 1982. [27] On...approximation schemes for parabolic and hyperbolic systems of partial differential equations, including higher order equations of elasticity based on the...51,58,59,63,64,69]. Finally, stability and bifurcation in parabolic partial differential equations is the focus of [64,65,67,72,73]. In addition to these broad

An Operator Method for Field Moments from the Extended Parabolic Wave Equation and Analytical Solutions of the First and Second Moments for Atmospheric Electromagnetic Wave Propagation

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2004-01-01

The extended wide-angle parabolic wave equation applied to electromagnetic wave propagation in random media is considered. A general operator equation is derived which gives the statistical moments of an electric field of a propagating wave. This expression is used to obtain the first and second order moments of the wave field and solutions are found that transcend those which incorporate the full paraxial approximation at the outset. Although these equations can be applied to any propagation scenario that satisfies the conditions of application of the extended parabolic wave equation, the example of propagation through atmospheric turbulence is used. It is shown that in the case of atmospheric wave propagation and under the Markov approximation (i.e., the delta-correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The comprehensive operator solution also allows one to obtain expressions for the longitudinal (generalized) second order moment. This is also considered and the solution for the atmospheric case is obtained and discussed. The methodology developed here can be applied to any qualifying situation involving random propagation through turbid or plasma environments that can be represented by a spectral density of permittivity fluctuations.

The State-of-the-Art Parabolic Equation Approximation as Applied to Underwater Acoustic Propagation with Discussions on Intensive Computations: An Invited Paper Presented at the Meeting of the Acoustical Society of America (108th) Held in Minneapolis, Minnesota on 8-12 October 1984

DTIC Science & Technology

1984-10-12

MCYwWWm M& de4 l 8.id iW d by N1wk "wt Finite Difference Reference Wavenumber Interface Split-Step Ordinary Difference Equation Wide Angle Parabolic...Problems D. Lee and S. Praiser J. Comp. & Math. with Appls., 7(2), pp. 195-202 (1981) Finite - Difference Solution to the Parabolic Wave Equation D. Lee, G...was incorporated into the ODE and finite difference models. At that time, we did not have a better implementation of the ODE solution, but we

An Explicit Upwind Algorithm for Solving the Parabolized Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Korte, John J.

1991-01-01

An explicit, upwind algorithm was developed for the direct (noniterative) integration of the 3-D Parabolized Navier-Stokes (PNS) equations in a generalized coordinate system. The new algorithm uses upwind approximations of the numerical fluxes for the pressure and convection terms obtained by combining flux difference splittings (FDS) formed from the solution of an approximate Riemann (RP). The approximate RP is solved using an extension of the method developed by Roe for steady supersonic flow of an ideal gas. Roe's method is extended for use with the 3-D PNS equations expressed in generalized coordinates and to include Vigneron's technique of splitting the streamwise pressure gradient. The difficulty associated with applying Roe's scheme in the subsonic region is overcome. The second-order upwind differencing of the flux derivatives are obtained by adding FDS to either an original forward or backward differencing of the flux derivative. This approach is used to modify an explicit MacCormack differencing scheme into an upwind differencing scheme. The second order upwind flux approximations, applied with flux limiters, provide a method for numerically capturing shocks without the need for additional artificial damping terms which require adjustment by the user. In addition, a cubic equation is derived for determining Vegneron's pressure splitting coefficient using the updated streamwise flux vector. Decoding the streamwise flux vector with the updated value of Vigneron's pressure splitting improves the stability of the scheme. The new algorithm is applied to 2-D and 3-D supersonic and hypersonic laminar flow test cases. Results are presented for the experimental studies of Holden and of Tracy. In addition, a flow field solution is presented for a generic hypersonic aircraft at a Mach number of 24.5 and angle of attack of 1 degree. The computed results compare well to both experimental data and numerical results from other algorithms. Computational times required for the upwind PNS code are approximately equal to an explicit PNS MacCormack's code and existing implicit PNS solvers.

Forward Sound Propagation Around Seamounts: Application of Acoustic Models to the Kermit-Roosevelt and Elvis Seamounts

DTIC Science & Technology

2009-06-01

large number of range steps. Brooke et al. [73] developed a Canadian Parabolic Equation model ( PECan ). In the model, the split-step Padé algorithm... PECan : A Canadian parabolic equation model for underwater sound propagation. J. Computational Acoustics, 9(1):69-100, 2001 [74] Michael D

THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)

EPA Science Inventory

A three-point backward finite-difference method has been derived for a system of mixed hyperbolic_¯¯parabolic (convection_¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

Chronology of DIC technique based on the fundamental mathematical modeling and dehydration impact.

PubMed

Alias, Norma; Saipol, Hafizah Farhah Saipan; Ghani, Asnida Che Abd

2014-12-01

A chronology of mathematical models for heat and mass transfer equation is proposed for the prediction of moisture and temperature behavior during drying using DIC (Détente Instantanée Contrôlée) or instant controlled pressure drop technique. DIC technique has the potential as most commonly used dehydration method for high impact food value including the nutrition maintenance and the best possible quality for food storage. The model is governed by the regression model, followed by 2D Fick's and Fourier's parabolic equation and 2D elliptic-parabolic equation in a rectangular slice. The models neglect the effect of shrinkage and radiation effects. The simulations of heat and mass transfer equations with parabolic and elliptic-parabolic types through some numerical methods based on finite difference method (FDM) have been illustrated. Intel®Core™2Duo processors with Linux operating system and C programming language have been considered as a computational platform for the simulation. Qualitative and quantitative differences between DIC technique and the conventional drying methods have been shown as a comparative.

Inlet flowfield investigation. Part 2: Computation of the flow about a supercruise forebody at supersonic speeds

NASA Technical Reports Server (NTRS)

Paynter, G. C.; Salemann, V.; Strom, E. E. I.

1984-01-01

A numerical procedure which solves the parabolized Navier-Stokes (PNS) equations on a body fitted mesh was used to compute the flow about the forebody of an advanced tactical supercruise fighter configuration in an effort to explore the use of a PNS method for design of supersonic cruise forebody geometries. Forebody flow fields were computed at Mach numbers of 1.5, 2.0, and 2.5, and at angles-of-attack of 0 deg, 4 deg, and 8 deg. at each Mach number. Computed results are presented at several body stations and include contour plots of Mach number, total pressure, upwash angle, sidewash angle and cross-plane velocity. The computational analysis procedure was found reliable for evaluating forebody flow fields of advanced aircraft configurations for flight conditions where the vortex shed from the wing leading edge is not a dominant flow phenomenon. Static pressure distributions and boundary layer profiles on the forebody and wing were surveyed in a wind tunnel test, and the analytical results are compared to the data. The current status of the parabolized flow flow field code is described along with desirable improvements in the code.

Optimal linear-quadratic control of coupled parabolic-hyperbolic PDEs

NASA Astrophysics Data System (ADS)

Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

2017-10-01

This paper focuses on the optimal control design for a system of coupled parabolic-hypebolic partial differential equations by using the infinite-dimensional state-space description and the corresponding operator Riccati equation. Some dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the linear-quadratic (LQ)-optimal control problem. A state LQ-feedback operator is computed by solving the operator Riccati equation, which is converted into a set of algebraic and differential Riccati equations, thanks to the eigenvalues and the eigenvectors of the parabolic operator. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ-optimal controller designed in the early portion of the paper is implemented for the original nonlinear model. Numerical simulations are performed to show the controller performances.

An evolution infinity Laplace equation modelling dynamic elasto-plastic torsion

NASA Astrophysics Data System (ADS)

Messelmi, Farid

2017-12-01

We consider in this paper a parabolic partial differential equation involving the infinity Laplace operator and a Leray-Lions operator with no coercitive assumption. We prove the existence and uniqueness of the corresponding approached problem and we show that at the limit the solution solves the parabolic variational inequality arising in the elasto-plastic torsion problem.

Treatment of ice cover and other thin elastic layers with the parabolic equation method.

PubMed

Collins, Michael D

2015-03-01

The parabolic equation method is extended to handle problems involving ice cover and other thin elastic layers. Parabolic equation solutions are based on rational approximations that are designed using accuracy constraints to ensure that the propagating modes are handled properly and stability constrains to ensure that the non-propagating modes are annihilated. The non-propagating modes are especially problematic for problems involving thin elastic layers. It is demonstrated that stable results may be obtained for such problems by using rotated rational approximations [Milinazzo, Zala, and Brooke, J. Acoust. Soc. Am. 101, 760-766 (1997)] and generalizations of these approximations. The approach is applied to problems involving ice cover with variable thickness and sediment layers that taper to zero thickness.

Recent Developments and Open Problems in the Mathematical Theory of Viscoelasticity.

DTIC Science & Technology

1984-11-01

integral terms . At each step of the iteration, we have to solve a linear parabolic equation with time-dependent coefficients. In Sobolevskii’s... parabolic Volterra integro- differential equation, SIAN J. Math. Anal. 13 (1982), ’ ~81-105. :-- 12. Heard, M. L., A class of hyperbolic Volterra ...then puts an n + 1 on the highest derivatives (the "principal terms " in the equation) and an n on lower order derivatives. Two things must then be

Performance of Infinitely Wide Parabolic and Inclined Slider Bearings Lubricated with Couple Stress or Magnetic Fluids

NASA Astrophysics Data System (ADS)

Oladeinde, Mobolaji Humphrey; Akpobi, John Ajokpaoghene

2011-10-01

The hydrodynamic and magnetohydrodynamic (MHD) lubrication problem of infinitely wide inclined and parabolic slider bearings is solved numerically using the finite element method. The bearing configurations are discretized into three-node isoparametric quadratic elements. Stiffness integrals obtained from the weak form of the governing equations are solved using Gauss quadrature to obtain a finite number of stiffness matrices. The global system of equations obtained from enforcing nodal continuity of pressure for the bearings are solved using the Gauss-Seidel iterative scheme with a convergence criterion of 10-10. Numerical computations reveal that, when compared for similar profile and couple stress parameters, greater pressure builds up in a parabolic slider compared to an inclined slider, indicating a greater wedge effect in the parabolic slider. The parabolic slider bearing is also shown to develop a greater load capacity when lubricated with magnetic fluids. The superior performance of parabolic slider bearing is more pronounced at greater Hartmann numbers for identical bearing structural parameters. It is also shown that when load carrying capacity is the yardstick for comparison, the parabolic slider bearings are superior to the inclined bearings when lubricated with couple stress or magnetic lubricants.

Navier-Stokes analysis of cold scramjet-afterbody flows

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Engelund, Walter C.; Eleshaky, Mohamed E.

1989-01-01

The progress of two efforts in coding solutions of Navier-Stokes equations is summarized. The first effort concerns a 3-D space marching parabolized Navier-Stokes (PNS) code being modified to compute the supersonic mixing flow through an internal/external expansion nozzle with multicomponent gases. The 3-D PNS equations, coupled with a set of species continuity equations, are solved using an implicit finite difference scheme. The completed work is summarized and includes code modifications for four chemical species, computing the flow upstream of the upper cowl for a theoretical air mixture, developing an initial plane solution for the inner nozzle region, and computing the flow inside the nozzle for both a N2/O2 mixture and a Freon-12/Ar mixture, and plotting density-pressure contours for the inner nozzle region. The second effort concerns a full Navier-Stokes code. The species continuity equations account for the diffusion of multiple gases. This 3-D explicit afterbody code has the ability to use high order numerical integration schemes such as the 4th order MacCormack, and the Gottlieb-MacCormack schemes. Changes to the work are listed and include, but are not limited to: (1) internal/external flow capability; (2) new treatments of the cowl wall boundary conditions and relaxed computations around the cowl region and cowl tip; (3) the entering of the thermodynamic and transport properties of Freon-12, Ar, O, and N; (4) modification to the Baldwin-Lomax turbulence model to account for turbulent eddies generated by cowl walls inside and external to the nozzle; and (5) adopting a relaxation formula to account for the turbulence in the mixing shear layer.

Application of an Extended Parabolic Equation to the Calculation of the Mean Field and the Transverse and Longitudinal Mutual Coherence Functions Within Atmospheric Turbulence

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2005-01-01

Solutions are derived for the generalized mutual coherence function (MCF), i.e., the second order moment, of a random wave field propagating through a random medium within the context of the extended parabolic equation. Here, "generalized" connotes the consideration of both the transverse as well as the longitudinal second order moments (with respect to the direction of propagation). Such solutions will afford a comparison between the results of the parabolic equation within the pararaxial approximation and those of the wide-angle extended theory. To this end, a statistical operator method is developed which gives a general equation for an arbitrary spatial statistical moment of the wave field. The generality of the operator method allows one to obtain an expression for the second order field moment in the direction longitudinal to the direction of propagation. Analytical solutions to these equations are derived for the Kolmogorov and Tatarskii spectra of atmospheric permittivity fluctuations within the Markov approximation.

Undetermined Coefficient Problems for Quasi-Linear Parabolic Equations

DTIC Science & Technology

1989-12-18

a student of John Burns, spent 3 years at Brown working with Tom Banks. His speciality is in control theory, in particular for viscoelastic...diffusion equation, SIAM J. Appld Maih, 39, (2), (1980), 272-289. [ 3 ] J. R. Cannon and H. M. Yin, A uniqueness theorem for a class of parabolic inverse...2.6) where H is a C’ function. This equation is of second kind Volterra type and can be u!uiquely solved for the function 0. Thus k = A

Jordan form, parabolicity and other features of change of type transition for hydrodynamic type systems

NASA Astrophysics Data System (ADS)

Konopelchenko, B. G.; Ortenzi, G.

2017-05-01

Changes of type transitions for two-component hydrodynamic type systems are discussed. It is shown that these systems generically assume the Jordan form (with 2 × 2 Jordan block) on the transition line with hodograph equations becoming parabolic. Conditions which allow or forbid the transition from the hyperbolic domain to elliptic one are discussed. Hamiltonian systems and their special subclasses and equations, such as dispersionless nonlinear Schrödinger, dispersionless Boussinesq, one-dimensional isentropic gas dynamics equations, and nonlinear wave equations are studied. Numerical results concerning the crossing of transition line for the dispersionless Boussinesq equation are also presented.

Development of a 3-D upwind PNS code for chemically reacting hypersonic flowfields

NASA Technical Reports Server (NTRS)

Tannehill, J. C.; Wadawadigi, G.

1992-01-01

Two new parabolized Navier-Stokes (PNS) codes were developed to compute the three-dimensional, viscous, chemically reacting flow of air around hypersonic vehicles such as the National Aero-Space Plane (NASP). The first code (TONIC) solves the gas dynamic and species conservation equations in a fully coupled manner using an implicit, approximately-factored, central-difference algorithm. This code was upgraded to include shock fitting and the capability of computing the flow around complex body shapes. The revised TONIC code was validated by computing the chemically-reacting (M(sub infinity) = 25.3) flow around a 10 deg half-angle cone at various angles of attack and the Ames All-Body model at 0 deg angle of attack. The results of these calculations were in good agreement with the results from the UPS code. One of the major drawbacks of the TONIC code is that the central-differencing of fluxes across interior flowfield discontinuities tends to introduce errors into the solution in the form of local flow property oscillations. The second code (UPS), originally developed for a perfect gas, has been extended to permit either perfect gas, equilibrium air, or nonequilibrium air computations. The code solves the PNS equations using a finite-volume, upwind TVD method based on Roe's approximate Riemann solver that was modified to account for real gas effects. The dissipation term associated with this algorithm is sufficiently adaptive to flow conditions that, even when attempting to capture very strong shock waves, no additional smoothing is required. For nonequilibrium calculations, the code solves the fluid dynamic and species continuity equations in a loosely-coupled manner. This code was used to calculate the hypersonic, laminar flow of chemically reacting air over cones at various angles of attack. In addition, the flow around the McDonnel Douglas generic option blended-wing-body was computed and comparisons were made between the perfect gas, equilibrium air, and the nonequilibrium air results.

Stability of hyperbolic-parabolic mixed type equations with partial boundary condition

NASA Astrophysics Data System (ADS)

Zhan, Huashui; Feng, Zhaosheng

2018-06-01

In this paper, we are concerned with the hyperbolic-parabolic mixed type equations with the non-homogeneous boundary condition. If it is degenerate on the boundary, the part of the boundary whose boundary value should be imposed, is determined by the entropy condition from the convection term. If there is no convection term in the equation, we show that the stability of solutions can be proved without any boundary condition. If the equation is completely degenerate, we show that the stability of solutions can be established just based on the partial boundary condition.

Non-Parabolic Hydrodynamic Formulations for the Simulation of Inhomogeneous Semiconductor Devices

NASA Technical Reports Server (NTRS)

Smith, A. W.; Brennan, K. F.

1996-01-01

Hydrodynamic models are becoming prevalent design tools for small scale devices and other devices in which high energy effects can dominate transport. Most current hydrodynamic models use a parabolic band approximation to obtain fairly simple conservation equations. Interest in accounting for band structure effects in hydrodynamic device simulation has begun to grow since parabolic models cannot fully describe the transport in state of the art devices due to the distribution populating non-parabolic states within the band. This paper presents two different non-parabolic formulations or the hydrodynamic model suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship ((hk)(exp 2)/2m = W(1 + alphaW). The second formulation makes use of a power law ((hk)(exp 2)/2m = xW(exp y)) for the dispersion relation. Hydrodynamic models which use the first formulation rely on the binomial expansion to obtain moment equations with closed form coefficients. This limits the energy range over which the model is valid. The power law formulation readily produces closed form coefficients similar to those obtained using the parabolic band approximation. However, the fitting parameters (x,y) are only valid over a limited energy range. The physical significance of the band non-parabolicity is discussed as well as the advantages/disadvantages and approximations of the two non-parabolic models. A companion paper describes device simulations based on the three dispersion relationships; parabolic, Kane dispersion and power law dispersion.

Non-parabolic hydrodynamic formulations for the simulation of inhomogeneous semiconductor devices

NASA Technical Reports Server (NTRS)

Smith, Arlynn W.; Brennan, Kevin F.

1995-01-01

Hydrodynamic models are becoming prevalent design tools for small scale devices and other devices in which high energy effects can dominate transport. Most current hydrodynamic models use a parabolic band approximation to obtain fairly simple conservation equations. Interest in accounting for band structure effects in hydrodynamic device simulation has begun to grow since parabolic models can not fully describe the transport in state of the art devices due to the distribution populating non-parabolic states within the band. This paper presents two different non-parabolic formulations of the hydrodynamic model suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship (hk)(exp 2)/2m = W(1 + alpha(W)). The second formulation makes use of a power law ((hk)(exp 2)/2m = xW(sup y)) for the dispersion relation. Hydrodynamic models which use the first formulation rely on the binomial expansion to obtain moment equations with closed form coefficients. This limits the energy range over which the model is valid. The power law formulation readily produces closed form coefficients similar to those obtained using the parabolic band approximation. However, the fitting parameters (x,y) are only valid over a limited energy range. The physical significance of the band non-parabolicity is discussed as well as the advantages/disadvantages and approximations of the two non-parabolic models. A companion paper describes device simulations based on the three dispersion relationships: parabolic, Kane dispersion, and power low dispersion.

On stability of the solutions of inverse problem for determining the right-hand side of a degenerate parabolic equation with two independent variables

NASA Astrophysics Data System (ADS)

Kamynin, V. L.; Bukharova, T. I.

2017-01-01

We prove the estimates of stability with respect to perturbations of input data for the solutions of inverse problems for degenerate parabolic equations with unbounded coefficients. An important feature of these estimates is that the constants in these estimates are written out explicitly by the input data of the problem.

Numerical Analysis of Ginzburg-Landau Models for Superconductivity.

NASA Astrophysics Data System (ADS)

Coskun, Erhan

Thin film conventional, as well as High T _{c} superconductors of various geometric shapes placed under both uniform and variable strength magnetic field are studied using the universially accepted macroscopic Ginzburg-Landau model. A series of new theoretical results concerning the properties of solution is presented using the semi -discrete time-dependent Ginzburg-Landau equations, staggered grid setup and natural boundary conditions. Efficient serial algorithms including a novel adaptive algorithm is developed and successfully implemented for solving the governing highly nonlinear parabolic system of equations. Refinement technique used in the adaptive algorithm is based on modified forward Euler method which was also developed by us to ease the restriction on time step size for stability considerations. Stability and convergence properties of forward and modified forward Euler schemes are studied. Numerical simulations of various recent physical experiments of technological importance such as vortes motion and pinning are performed. The numerical code for solving time-dependent Ginzburg-Landau equations is parallelized using BlockComm -Chameleon and PCN. The parallel code was run on the distributed memory multiprocessors intel iPSC/860, IBM-SP1 and cluster of Sun Sparc workstations, all located at Mathematics and Computer Science Division, Argonne National Laboratory.

Semi-discrete Galerkin solution of the compressible boundary-layer equations with viscous-inviscid interaction

NASA Technical Reports Server (NTRS)

Day, Brad A.; Meade, Andrew J., Jr.

1993-01-01

A semi-discrete Galerkin (SDG) method is under development to model attached, turbulent, and compressible boundary layers for transonic airfoil analysis problems. For the boundary-layer formulation the method models the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby providing high resolution near the wall and permitting the use of a uniform finite element grid which automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past RAE 2822 and NACA 0012 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack.

Controllable parabolic-cylinder optical rogue wave.

PubMed

Zhong, Wei-Ping; Chen, Lang; Belić, Milivoj; Petrović, Nikola

2014-10-01

We demonstrate controllable parabolic-cylinder optical rogue waves in certain inhomogeneous media. An analytical rogue wave solution of the generalized nonlinear Schrödinger equation with spatially modulated coefficients and an external potential in the form of modulated quadratic potential is obtained by the similarity transformation. Numerical simulations are performed for comparison with the analytical solutions and to confirm the stability of the rogue wave solution obtained. These optical rogue waves are built by the products of parabolic-cylinder functions and the basic rogue wave solution of the standard nonlinear Schrödinger equation. Such rogue waves may appear in different forms, as the hump and paw profiles.

Pile-Driving Pressure and Particle Velocity at the Seabed: Quantifying Effects on Crustaceans and Groundfish.

PubMed

Miller, James H; Potty, Gopu R; Kim, Hui-Kwan

2016-01-01

We modeled the effects of pile driving on crustaceans, groundfish, and other animals near the seafloor. Three different waves were investigated, including the compressional wave, shear wave, and interface wave. A finite element (FE) technique was employed in and around the pile, whereas a parabolic equation (PE) code was used to predict propagation at long ranges from the pile. Pressure, particle displacement, and particle velocity are presented as a function of range at the seafloor for a shallow-water environment near Rhode Island. We discuss the potential effects on animals near the seafloor.

Numerical investigation of internal high-speed viscous flows using a parabolic technique

NASA Technical Reports Server (NTRS)

Anderson, O. L.; Power, G. D.

1985-01-01

A feasibility study has been conducted to assess the applicability of an existing parabolic analysis (ADD-Axisymmetric Diffuser Duct), developed previously for subsonic viscous internal flows, to mixed supersonic/subsonic flows with heat addition simulating a SCRAMJET combustor. A study was conducted with the ADD code modified to include additional convection effects in the normal momentum equation when supersonic expansion and compression waves are present. A set of test problems with weak shock and expansion waves have been analyzed with this modified ADD method and stable and accurate solutions were demonstrated provided the streamwise step size was maintained at levels larger than the boundary layer displacement thickness. Calculations made with further reductions in step size encountered departure solutions consistent with strong interaction theory. Calculations were also performed for a flow field with a flame front in which a specific heat release was imposed to simulate a SCRAMJET combustor. In this case the flame front generated relatively thick shear layers which aggravated the departure solution problem. Qualitatively correct results were obtained for these cases using a marching technique with the convective terms in the normal momentum equation suppressed. It is concluded from the present study that for the class of problems where strong viscous/inviscid interactions are present a global iteration procedure is required.

A Bifurcation Problem for a Nonlinear Partial Differential Equation of Parabolic Type,

DTIC Science & Technology

NONLINEAR DIFFERENTIAL EQUATIONS, INTEGRATION), (*PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS), BANACH SPACE , MAPPING (TRANSFORMATIONS), SET THEORY, TOPOLOGY, ITERATIONS, STABILITY, THEOREMS

The semi-discrete Galerkin finite element modelling of compressible viscous flow past an airfoil

NASA Technical Reports Server (NTRS)

Meade, Andrew J., Jr.

1992-01-01

A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid which provides high resolution near the wall and automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes, through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past NACA 0012 and RAE 2822 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack. All results show good agreement with experiment, and the coupled code proved to be a computationally-efficient and accurate airfoil analysis tool.

Schottky diode model for non-parabolic dispersion in narrow-gap semiconductor and few-layer graphene

NASA Astrophysics Data System (ADS)

Ang, Yee Sin; Ang, L. K.; Zubair, M.

Despite the fact that the energy dispersions are highly non-parabolic in many Schottky interfaces made up of 2D material, experimental results are often interpreted using the conventional Schottky diode equation which, contradictorily, assumes a parabolic energy dispersion. In this work, the Schottky diode equation is derived for narrow-gap semiconductor and few-layer graphene where the energy dispersions are highly non-parabolic. Based on Kane's non-parabolic band model, we obtained a more general Kane-Schottky scaling relation of J (T2 + γkBT3) which connects the contrasting J T2 in the conventional Schottky interface and the J T3 scaling in graphene-based Schottky interface via a non-parabolicity parameter, γ. For N-layer graphene of ABC -stacking and of ABA -stacking, the scaling relation follows J T 2 / N + 1 and J T3 respectively. Intriguingly, the Richardson constant extracted from the experimental data using an incorrect scaling can differ with the actual value by more than two orders of magnitude. Our results highlights the importance of using the correct scaling relation in order to accurately extract important physical properties, such as the Richardson constant and the Schottky barrier's height.

Conference on Ordinary and Partial Differential Equations, 29 March to 2 April 1982.

DTIC Science & Technology

1982-04-02

Azztr. Boundary value problems for elliptic and parabolic equations in domains with corners The paper concerns initial - Dirichlet and initial - mixed...boundary value problems for parabolic equations. a ij(x,t)u x + ai(x,t)Ux. + a(x,t)u-u = f(x,t) i3 1 x Xl,...,Xn , n 2. We consider the case of...moment II Though it is well known, that the electron possesses an anomalous magnetic moment, this term has not been considered so far in the mathematical

Backward semi-linear parabolic equations with time-dependent coefficients and local Lipschitz source

NASA Astrophysics Data System (ADS)

Nho Hào, Dinh; Van Duc, Nguyen; Van Thang, Nguyen

2018-05-01

Let H be a Hilbert space with the inner product and the norm , a positive self-adjoint unbounded time-dependent operator on H and . We establish stability estimates of Hölder type and propose a regularization method with error estimates of Hölder type for the ill-posed backward semi-linear parabolic equation with the source function f satisfying a local Lipschitz condition.

A wide angle and high Mach number parabolic equation.

PubMed

Lingevitch, Joseph F; Collins, Michael D; Dacol, Dalcio K; Drob, Douglas P; Rogers, Joel C W; Siegmann, William L

2002-02-01

Various parabolic equations for advected acoustic waves have been derived based on the assumptions of small Mach number and narrow propagation angles, which are of limited validity in atmospheric acoustics. A parabolic equation solution that does not require these assumptions is derived in the weak shear limit, which is appropriate for frequencies of about 0.1 Hz and above for atmospheric acoustics. When the variables are scaled appropriately in this limit, terms involving derivatives of the sound speed, density, and wind speed are small but can have significant cumulative effects. To obtain a solution that is valid at large distances from the source, it is necessary to account for linear terms in the first derivatives of these quantities [A. D. Pierce, J. Acoust. Soc. Am. 87, 2292-2299 (1990)]. This approach is used to obtain a scalar wave equation for advected waves. Since this equation contains two depth operators that do not commute with each other, it does not readily factor into outgoing and incoming solutions. An approximate factorization is obtained that is correct to first order in the commutator of the depth operators.

Incompressible Navier-Stokes and parabolized Navier-Stokes solution procedures and computational techniques

NASA Technical Reports Server (NTRS)

Rubin, S. G.

1982-01-01

Recent developments with finite-difference techniques are emphasized. The quotation marks reflect the fact that any finite discretization procedure can be included in this category. Many so-called finite element collocation and galerkin methods can be reproduced by appropriate forms of the differential equations and discretization formulas. Many of the difficulties encountered in early Navier-Stokes calculations were inherent not only in the choice of the different equations (accuracy), but also in the method of solution or choice of algorithm (convergence and stability, in the manner in which the dependent variables or discretized equations are related (coupling), in the manner that boundary conditions are applied, in the manner that the coordinate mesh is specified (grid generation), and finally, in recognizing that for many high Reynolds number flows not all contributions to the Navier-Stokes equations are necessarily of equal importance (parabolization, preferred direction, pressure interaction, asymptotic and mathematical character). It is these elements that are reviewed. Several Navier-Stokes and parabolized Navier-Stokes formulations are also presented.

A modified dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1981-01-01

A revised version of a split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three-dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard successive overrelaxation iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition.

Well-posedness of nonlocal parabolic differential problems with dependent operators.

PubMed

Ashyralyev, Allaberen; Hanalyev, Asker

2014-01-01

The nonlocal boundary value problem for the parabolic differential equation v'(t) + A(t)v(t) = f(t) (0 ≤ t ≤ T), v(0) = v(λ) + φ, 0 < λ ≤ T in an arbitrary Banach space E with the dependent linear positive operator A(t) is investigated. The well-posedness of this problem is established in Banach spaces C 0 (β,γ) (E α-β ) of all E α-β -valued continuous functions φ(t) on [0, T] satisfying a Hölder condition with a weight (t + τ)(γ). New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.

Some remarks on the numerical solution of parabolic partial differential equations

NASA Astrophysics Data System (ADS)

Campagna, R.; Cuomo, S.; Leveque, S.; Toraldo, G.; Giannino, F.; Severino, G.

2017-11-01

Numerous environmental/engineering applications relying upon the theory of diffusion phenomena into chaotic environments have recently stimulated the interest toward the numerical solution of parabolic partial differential equations (PDEs). In the present paper, we outline a formulation of the mathematical problem underlying a quite general diffusion mechanism in the natural environments, and we shortly emphasize some remarks concerning the applicability of the (straightforward) finite difference method. An illustration example is also presented.

Modeling Pulse Transmission in the Monterey Bay Using Parabolic Equation Methods

DTIC Science & Technology

1991-12-01

Collins 9-13 was chosen for this purpose due its energy conservation scheme , and its ability to efficiently incorporate higher order terms in its...pressure field generated by the PE model into normal modes. Additionally, this process provides increased physical understanding of mode coupling and...separation of variables (i.e. normal modes or fast field), as well as pure numerical schemes such as the parabolic equation methods, can be used. However, as

ShiftNMFk 1.2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alexandrov, Boian S.; Vesselinov, Velimir V.; Stanev, Valentin

The ShiftNMFk1.2 code, or as we call it, GreenNMFk, represents a hybrid algorithm combining unsupervised adaptive machine learning and Green's function inverse method. GreenNMFk allows an efficient and high performance de-mixing and feature extraction of a multitude of nonnegative signals that change their shape propagating through the medium. The signals are mixed and recorded by a network of uncorrelated sensors. The code couples Non-negative Matrix Factorization (NMF) and inverse-analysis Green's functions method. GreenNMF synergistically performs decomposition of the recorded mixtures, finds the number of the unknown sources and uses the Green's function of the governing partial differential equation to identifymore » the unknown sources and their charecteristics. GreenNMF can be applied directly to any problem controlled by a known partial-differential parabolic equation where mixtures of an unknown number of sources are measured at multiple locations. Full GreenNMFk method is a subject LANL U.S. Patent application S133364.000 August, 2017. The ShiftNMFk 1.2 version here is a toy version of this method that can work with a limited number of unknown sources (4 or less).« less

Numerical simulation of flow through the Langley parametric scramjet engine

NASA Technical Reports Server (NTRS)

Srinivasan, Shivakumar; Kamath, Pradeep S.; Mcclinton, Charles R.

1989-01-01

The numerical simulation of a three-dimensional turbulent, reacting flow through the entire Langley parametric scramjet engine has been obtained using a piecewise elliptic approach. The last section in the combustor has been analyzed using a parabolized Navier-Stokes code. The facility nozzle flow was analyzed as a first step. The outflow conditions from the nozzle were chosen as the inflow conditions of the scramjet inlet. The nozzle and the inlet simulation were accomplished by solving the three-dimensional Navier-Stokes equations with a perfect gas assumption. The inlet solution downstream of the scramjet throat was used to provide inflow conditions for the combustor region. The first two regions of the combustor were analyzed using the MacCormack's explicit scheme. However, the source terms in the species equations were solved implicitly. The finite rate chemistry was modeled using the two-step reaction model of Rogers and Chinitz. A complete reaction model was used in the PNS code to solve the last combustor region. The numerical solutions provide an insight of the flow details in a complete hydrogen-fueled scramjet engine module.

Validation of three-dimensional incompressible spatial direct numerical simulation code: A comparison with linear stability and parabolic stability equation theories for boundary-layer transition on a flat plate

NASA Technical Reports Server (NTRS)

Joslin, Ronald D.; Streett, Craig L.; Chang, Chau-Lyan

1992-01-01

Spatially evolving instabilities in a boundary layer on a flat plate are computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. In a truncated physical domain, a nonstaggered mesh is used for the grid. A Chebyshev-collocation method is used normal to the wall; finite difference and compact difference methods are used in the streamwise direction; and a Fourier series is used in the spanwise direction. For time stepping, implicit Crank-Nicolson and explicit Runge-Kutta schemes are used to the time-splitting method. The influence-matrix technique is used to solve the pressure equation. At the outflow boundary, the buffer-domain technique is used to prevent convective wave reflection or upstream propagation of information from the boundary. Results of the DNS are compared with those from both linear stability theory (LST) and parabolized stability equation (PSE) theory. Computed disturbance amplitudes and phases are in very good agreement with those of LST (for small inflow disturbance amplitudes). A measure of the sensitivity of the inflow condition is demonstrated with both LST and PSE theory used to approximate inflows. Although the DNS numerics are very different than those of PSE theory, the results are in good agreement. A small discrepancy in the results that does occur is likely a result of the variation in PSE boundary condition treatment in the far field. Finally, a small-amplitude wave triad is forced at the inflow, and simulation results are compared with those of LST. Again, very good agreement is found between DNS and LST results for the 3-D simulations, the implication being that the disturbance amplitudes are sufficiently small that nonlinear interactions are negligible.

A boundary condition to the Khokhlov-Zabolotskaya equation for modeling strongly focused nonlinear ultrasound fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rosnitskiy, P., E-mail: pavrosni@yandex.ru; Yuldashev, P., E-mail: petr@acs366.phys.msu.ru; Khokhlova, V., E-mail: vera@acs366.phys.msu.ru

2015-10-28

An equivalent source model was proposed as a boundary condition to the nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation to simulate high intensity focused ultrasound (HIFU) fields generated by medical ultrasound transducers with the shape of a spherical shell. The boundary condition was set in the initial plane; the aperture, the focal distance, and the initial pressure of the source were chosen based on the best match of the axial pressure amplitude and phase distributions in the Rayleigh integral analytic solution for a spherical transducer and the linear parabolic approximation solution for the equivalent source. Analytic expressions for the equivalent source parametersmore » were derived. It was shown that the proposed approach allowed us to transfer the boundary condition from the spherical surface to the plane and to achieve a very good match between the linear field solutions of the parabolic and full diffraction models even for highly focused sources with F-number less than unity. The proposed method can be further used to expand the capabilities of the KZ nonlinear parabolic equation for efficient modeling of HIFU fields generated by strongly focused sources.« less

High speed transition prediction

NASA Technical Reports Server (NTRS)

Gasperas, Gediminis

1993-01-01

The main objective of this work period was to develop, maintain and exercise state-of-the-art methods for transition prediction in supersonic flow fields. Basic state and stability codes, acquired during the last work period, were exercised and applied to calculate the properties of various flowfields. The development of a code for the prediction of transition location using a currently novel method (the PSE or Parabolized Stability Equation method), initiated during the last work period and continued during the present work period, was cancelled at mid-year for budgetary reasons. Other activities during this period included the presentation of a paper at the APS meeting in Tallahassee, Florida entitled 'Stability of Two-Dimensional Compressible Boundary Layers', as well as the initiation of a paper co-authored with H. Reed of the Arizona State University entitled 'Stability of Boundary Layers'.

High Energy Laser Beam Propagation in the Atmosphere: The Integral Invariants of the Nonlinear Parabolic Equation and the Method of Moments

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2012-01-01

The method of moments is used to define and derive expressions for laser beam deflection and beam radius broadening for high-energy propagation through the Earth s atmosphere. These expressions are augmented with the integral invariants of the corresponding nonlinear parabolic equation that describes the electric field of high-energy laser beam to propagation to yield universal equations for the aforementioned quantities; the beam deflection is a linear function of the propagation distance whereas the beam broadening is a quadratic function of distance. The coefficients of these expressions are then derived from a thin screen approximation solution of the nonlinear parabolic equation to give corresponding analytical expressions for a target located outside the Earth s atmospheric layer. These equations, which are graphically presented for a host of propagation scenarios, as well as the thin screen model, are easily amenable to the phase expansions of the wave front for the specification and design of adaptive optics algorithms to correct for the inherent phase aberrations. This work finds application in, for example, the analysis of beamed energy propulsion for space-based vehicles.

Marching iterative methods for the parabolized and thin layer Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Israeli, M.

1985-01-01

Downstream marching iterative schemes for the solution of the Parabolized or Thin Layer (PNS or TL) Navier-Stokes equations are described. Modifications of the primitive equation global relaxation sweep procedure result in efficient second-order marching schemes. These schemes take full account of the reduced order of the approximate equations as they behave like the SLOR for a single elliptic equation. The improved smoothing properties permit the introduction of Multi-Grid acceleration. The proposed algorithm is essentially Reynolds number independent and therefore can be applied to the solution of the subsonic Euler equations. The convergence rates are similar to those obtained by the Multi-Grid solution of a single elliptic equation; the storage is also comparable as only the pressure has to be stored on all levels. Extensions to three-dimensional and compressible subsonic flows are discussed. Numerical results are presented.

Alternating direction implicit methods for parabolic equations with a mixed derivative

NASA Technical Reports Server (NTRS)

Beam, R. M.; Warming, R. F.

1980-01-01

Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A(0)-stable linear two-step methods in conjunction with the method of approximate factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A(0)-stable method. The parameter space for which the resulting ADI schemes are second-order accurate and unconditionally stable is determined. Some numerical examples are given.

Alternating direction implicit methods for parabolic equations with a mixed derivative

NASA Technical Reports Server (NTRS)

Beam, R. M.; Warming, R. F.

1979-01-01

Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A sub 0-stable linear two-step methods in conjunction with the method of approximation factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A sub 0-stable method. The parameter space for which the resulting ADI schemes are second order accurate and unconditionally stable is determined. Some numerical examples are given.

Unsteady transonic flow analysis for low aspect ratio, pointed wings.

NASA Technical Reports Server (NTRS)

Kimble, K. R.; Ruo, S. Y.; Wu, J. M.; Liu, D. Y.

1973-01-01

Oswatitsch and Keune's parabolic method for steady transonic flow is applied and extended to thin slender wings oscillating in the sonic flow field. The parabolic constant for the wing was determined from the equivalent body of revolution. Laplace transform methods were used to derive the asymptotic equations for pressure coefficient, and the Adams-Sears iterative procedure was employed to solve the equations. A computer program was developed to find the pressure distributions, generalized force coefficients, and stability derivatives for delta, convex, and concave wing planforms.

Sparse Recovery via l1 and L1 Optimization

DTIC Science & Technology

2014-11-01

problem, with t being the descent direc- tion, obtaining ut = uxx + f − 1 µ p(u) (6) as an evolution equation. We can hope that these L1 regularized (or...implementation. He considered a wide class of second–order elliptic equations and, with Friedman [14], an extension to parabolic equa- tions. In [15, 16...obtaining an elliptic PDE, or by gradi- ent descent to obtain a parabolic PDE. Addition- ally, some PDEs can be rewritten using the L1 subgradient such as the

Multiscale techniques for parabolic equations.

PubMed

Målqvist, Axel; Persson, Anna

2018-01-01

We use the local orthogonal decomposition technique introduced in Målqvist and Peterseim (Math Comput 83(290):2583-2603, 2014) to derive a generalized finite element method for linear and semilinear parabolic equations with spatial multiscale coefficients. We consider nonsmooth initial data and a backward Euler scheme for the temporal discretization. Optimal order convergence rate, depending only on the contrast, but not on the variations of the coefficients, is proven in the [Formula: see text]-norm. We present numerical examples, which confirm our theoretical findings.

A higher-order split-step Fourier parabolic-equation sound propagation solution scheme.

PubMed

Lin, Ying-Tsong; Duda, Timothy F

2012-08-01

A three-dimensional Cartesian parabolic-equation model with a higher-order approximation to the square-root Helmholtz operator is presented for simulating underwater sound propagation in ocean waveguides. The higher-order approximation includes cross terms with the free-space square-root Helmholtz operator and the medium phase speed anomaly. It can be implemented with a split-step Fourier algorithm to solve for sound pressure in the model. Two idealized ocean waveguide examples are presented to demonstrate the performance of this numerical technique.

Fast Time and Space Parallel Algorithms for Solution of Parabolic Partial Differential Equations

NASA Technical Reports Server (NTRS)

Fijany, Amir

1993-01-01

In this paper, fast time- and Space -Parallel agorithms for solution of linear parabolic PDEs are developed. It is shown that the seemingly strictly serial iterations of the time-stepping procedure for solution of the problem can be completed decoupled.

A modified Dodge algorithm for the parabolized Navier-Stokes equation and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1981-01-01

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitive agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions.

Elastic parabolic equation and normal mode solutions for seismo-acoustic propagation in underwater environments with ice covers.

PubMed

Collis, Jon M; Frank, Scott D; Metzler, Adam M; Preston, Kimberly S

2016-05-01

Sound propagation predictions for ice-covered ocean acoustic environments do not match observational data: received levels in nature are less than expected, suggesting that the effects of the ice are substantial. Effects due to elasticity in overlying ice can be significant enough that low-shear approximations, such as effective complex density treatments, may not be appropriate. Building on recent elastic seafloor modeling developments, a range-dependent parabolic equation solution that treats the ice as an elastic medium is presented. The solution is benchmarked against a derived elastic normal mode solution for range-independent underwater acoustic propagation. Results from both solutions accurately predict plate flexural modes that propagate in the ice layer, as well as Scholte interface waves that propagate at the boundary between the water and the seafloor. The parabolic equation solution is used to model a scenario with range-dependent ice thickness and a water sound speed profile similar to those observed during the 2009 Ice Exercise (ICEX) in the Beaufort Sea.

Optimal control of coupled parabolic-hyperbolic non-autonomous PDEs: infinite-dimensional state-space approach

NASA Astrophysics Data System (ADS)

Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

2018-04-01

This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic-hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolic-associated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ optimal controller designed in the early portion of the paper is implemented for the original non-linear model. Numerical simulations are performed to show the controller performances.

Scalable Parallel Computation for Extended MHD Modeling of Fusion Plasmas

NASA Astrophysics Data System (ADS)

Glasser, Alan H.

2008-11-01

Parallel solution of a linear system is scalable if simultaneously doubling the number of dependent variables and the number of processors results in little or no increase in the computation time to solution. Two approaches have this property for parabolic systems: multigrid and domain decomposition. Since extended MHD is primarily a hyperbolic rather than a parabolic system, additional steps must be taken to parabolize the linear system to be solved by such a method. Such physics-based preconditioning (PBP) methods have been pioneered by Chac'on, using finite volumes for spatial discretization, multigrid for solution of the preconditioning equations, and matrix-free Newton-Krylov methods for the accurate solution of the full nonlinear preconditioned equations. The work described here is an extension of these methods using high-order spectral element methods and FETI-DP domain decomposition. Application of PBP to a flux-source representation of the physics equations is discussed. The resulting scalability will be demonstrated for simple wave and for ideal and Hall MHD waves.

Recent Progress in the Development and Application of the Parabolic Equation

DTIC Science & Technology

1984-05-07

awarded a research grant to NUSC to encourage technical collaboration with university scientists at the Yale University Center for Scientific Computa...TD 7145 REFERENCES 1.F. U. Tappert, "The Parabolic Approximation Metthod ,ŕ Wave Propagation ano Unoierwater Acoustics, editeu by J. B

Accurate spectral solutions for the parabolic and elliptic partial differential equations by the ultraspherical tau method

NASA Astrophysics Data System (ADS)

Doha, E. H.; Abd-Elhameed, W. M.

2005-09-01

We present a double ultraspherical spectral methods that allow the efficient approximate solution for the parabolic partial differential equations in a square subject to the most general inhomogeneous mixed boundary conditions. The differential equations with their boundary and initial conditions are reduced to systems of ordinary differential equations for the time-dependent expansion coefficients. These systems are greatly simplified by using tensor matrix algebra, and are solved by using the step-by-step method. Numerical applications of how to use these methods are described. Numerical results obtained compare favorably with those of the analytical solutions. Accurate double ultraspherical spectral approximations for Poisson's and Helmholtz's equations are also noted. Numerical experiments show that spectral approximation based on Chebyshev polynomials of the first kind is not always better than others based on ultraspherical polynomials.

GRADSPMHD: A parallel MHD code based on the SPH formalism

NASA Astrophysics Data System (ADS)

Vanaverbeke, S.; Keppens, R.; Poedts, S.

2014-03-01

We present GRADSPMHD, a completely Lagrangian parallel magnetohydrodynamics code based on the SPH formalism. The implementation of the equations of SPMHD in the “GRAD-h” formalism assembles known results, including the derivation of the discretized MHD equations from a variational principle, the inclusion of time-dependent artificial viscosity, resistivity and conductivity terms, as well as the inclusion of a mixed hyperbolic/parabolic correction scheme for satisfying the ∇ṡB→ constraint on the magnetic field. The code uses a tree-based formalism for neighbor finding and can optionally use the tree code for computing the self-gravity of the plasma. The structure of the code closely follows the framework of our parallel GRADSPH FORTRAN 90 code which we added previously to the CPC program library. We demonstrate the capabilities of GRADSPMHD by running 1, 2, and 3 dimensional standard benchmark tests and we find good agreement with previous work done by other researchers. The code is also applied to the problem of simulating the magnetorotational instability in 2.5D shearing box tests as well as in global simulations of magnetized accretion disks. We find good agreement with available results on this subject in the literature. Finally, we discuss the performance of the code on a parallel supercomputer with distributed memory architecture. Catalogue identifier: AERP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERP_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 620503 No. of bytes in distributed program, including test data, etc.: 19837671 Distribution format: tar.gz Programming language: FORTRAN 90/MPI. Computer: HPC cluster. Operating system: Unix. Has the code been vectorized or parallelized?: Yes, parallelized using MPI. RAM: ˜30 MB for a Sedov test including 15625 particles on a single CPU. Classification: 12. Nature of problem: Evolution of a plasma in the ideal MHD approximation. Solution method: The equations of magnetohydrodynamics are solved using the SPH method. Running time: The test provided takes approximately 20 min using 4 processors.

A modified Dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.; Dwoyer, D. M.

1983-01-01

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitative agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions. Previously announced in STAR as N82-16363

Prescribing the mixed scalar curvature of a foliated Riemann-Cartan manifold

NASA Astrophysics Data System (ADS)

Rovenski, Vladimir Y.; Zelenko, Leonid

2018-03-01

The mixed scalar curvature is the simplest curvature invariant of a foliated Riemannian manifold. We explore the problem of prescribing the leafwise constant mixed scalar curvature of a foliated Riemann-Cartan manifold by conformal change of the structure in tangent and normal to the leaves directions. Under certain geometrical assumptions and in two special cases: along a compact leaf and for a closed fibered manifold, we reduce the problem to solution of a nonlinear leafwise elliptic equation for the conformal factor. We are looking for its solutions that are stable stationary solutions of the associated parabolic equation. Our main tool is using of majorizing and minorizing nonlinear heat equations with constant coefficients and application of comparison theorems for solutions of Cauchy's problem for parabolic equations.

Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations

NASA Astrophysics Data System (ADS)

Jiang, Daijun; Li, Zhiyuan; Liu, Yikan; Yamamoto, Masahiro

2017-05-01

In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic equations. The result is weaker than its parabolic counterpart in the sense that we additionally impose the homogeneous boundary condition. As a direct application, we prove the uniqueness for an inverse problem on determining the spatial component in the source term by interior measurements. Numerically, we reformulate our inverse source problem as an optimization problem, and propose an iterative thresholding algorithm. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

Survey mirrors and lenses and their required surface accuracy. Volume 2. Concentrator optical performance software (COPS) user's manual. Final report for September 15, 1978-December 1, 1979

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1980-01-01

The mathematical modeling of 11 different concentrating collectors is documented and instructions are given for use of the computer code. The 11 concentrators modeled are: faceted mirror concentration; fixed mirror, two-axis tracking receiver; parabolic trough collector; linear Fresnel; incremental reflector; inflated cylindrical concentrator; CPC-involute reflector with evacuated receiver; CPC-parabolic/involute reflector; V trough collectors, imaging collapsing concentrator; and parabolic dish collector. (MHR)

SolTrace Background | Concentrating Solar Power | NREL

Science.gov Websites

codes was written to model a very specific optical geometry, and each one built upon the others in an evolutionary way. Examples of such codes include: OPTDSH, a code written to model circular aperture parabolic

Elastic parabolic equation solutions for oceanic T-wave generation and propagation from deep seismic sources.

PubMed

Frank, Scott D; Collis, Jon M; Odom, Robert I

2015-06-01

Oceanic T-waves are earthquake signals that originate when elastic waves interact with the fluid-elastic interface at the ocean bottom and are converted to acoustic waves in the ocean. These waves propagate long distances in the Sound Fixing and Ranging (SOFAR) channel and tend to be the largest observed arrivals from seismic events. Thus, an understanding of their generation is important for event detection, localization, and source-type discrimination. Recently benchmarked seismic self-starting fields are used to generate elastic parabolic equation solutions that demonstrate generation and propagation of oceanic T-waves in range-dependent underwater acoustic environments. Both downward sloping and abyssal ocean range-dependent environments are considered, and results demonstrate conversion of elastic waves into water-borne oceanic T-waves. Examples demonstrating long-range broadband T-wave propagation in range-dependent environments are shown. These results confirm that elastic parabolic equation solutions are valuable for characterization of the relationships between T-wave propagation and variations in range-dependent bathymetry or elastic material parameters, as well as for modeling T-wave receptions at hydrophone arrays or coastal receiving stations.

The full Keller-Segel model is well-posed on nonsmooth domains

NASA Astrophysics Data System (ADS)

Horstmann, D.; Meinlschmidt, H.; Rehberg, J.

2018-04-01

In this paper we prove that the full Keller-Segel system, a quasilinear strongly coupled reaction-crossdiffusion system of four parabolic equations, is well-posed in the sense that it always admits an unique local-in-time solution in an adequate function space, provided that the initial values are suitably regular. The proof is done via an abstract solution theorem for nonlocal quasilinear equations by Amann and is carried out for general source terms. It is fundamentally based on recent nontrivial elliptic and parabolic regularity results which hold true even on rather general nonsmooth spatial domains. For space dimensions 2 and 3, this enables us to work in a nonsmooth setting which is not available in classical parabolic systems theory. Apparently, there exists no comparable existence result for the full Keller-Segel system up to now. Due to the large class of possibly nonsmooth domains admitted, we also obtain new results for the ‘standard’ Keller-Segel system consisting of only two equations as a special case. This work is dedicated to Prof Willi Jäger.

Accelerating Airy beams with non-parabolic trajectories

NASA Astrophysics Data System (ADS)

Besieris, Ioannis M.; Shaarawi, Amr M.

2014-11-01

A class of Airy accelerating beams with non-parabolic trajectories are derived by means of a novel application of a conformal transformation originally due to Bateman. It is also shown that the salient features of these beams are very simply incorporated in a solution which is derived by applying a conventional conformal transformation together with a Galilean translation to the basic accelerating Airy beam solution of the two-dimensional paraxial equation. Motivation for the non-parabolic beam trajectories is provided and the effects of finite-energy requirements are discussed.

Regularity gradient estimates for weak solutions of singular quasi-linear parabolic equations

NASA Astrophysics Data System (ADS)

Phan, Tuoc

2017-12-01

This paper studies the Sobolev regularity for weak solutions of a class of singular quasi-linear parabolic problems of the form ut -div [ A (x , t , u , ∇u) ] =div [ F ] with homogeneous Dirichlet boundary conditions over bounded spatial domains. Our main focus is on the case that the vector coefficients A are discontinuous and singular in (x , t)-variables, and dependent on the solution u. Global and interior weighted W 1 , p (ΩT , ω)-regularity estimates are established for weak solutions of these equations, where ω is a weight function in some Muckenhoupt class of weights. The results obtained are even new for linear equations, and for ω = 1, because of the singularity of the coefficients in (x , t)-variables.

On a Parabolic-Elliptic system with chemotaxis and logistic type growth

NASA Astrophysics Data System (ADS)

Galakhov, Evgeny; Salieva, Olga; Tello, J. Ignacio

2016-10-01

We consider a nonlinear PDEs system of two equations of Parabolic-Elliptic type with chemotactic terms. The system models the movement of a biological population ;u; towards a higher concentration of a chemical agent ;w; in a bounded and regular domain Ω ⊂RN for arbitrary N ∈ N. After normalization, the system is as follows

Strongly nonlinear parabolic variational inequalities.

PubMed

Browder, F E; Brézis, H

1980-02-01

An existence and uniqueness result is established for a general class of variational inequalities for parabolic partial differential equations of the form partial differentialu/ partial differentialt + A(u) + g(u) = f with g nondecreasing but satisfying no growth condition. The proof is based upon a type of compactness result for solutions of variational inequalities that should find a variety of other applications.

Strict parabolicity of the multifractal spectrum at the Anderson transition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suslov, I. M., E-mail: suslov@kapitza.ras.ru

Using the well-known “algebra of multifractality,” we derive the functional equation for anomalous dimensions Δ{sub q}, whose solution Δ = χq(q–1) corresponds to strict parabolicity of the multifractal spectrum. This result demonstrates clearly that a correspondence of the nonlinear σ-models with the initial disordered systems is not exact.

Noniterative three-dimensional grid generation using parabolic partial differential equations

NASA Technical Reports Server (NTRS)

Edwards, T. A.

1985-01-01

A new algorithm for generating three-dimensional grids has been developed and implemented which numerically solves a parabolic partial differential equation (PDE). The solution procedure marches outward in two coordinate directions, and requires inversion of a scalar tridiagonal system in the third. Source terms have been introduced to control the spacing and angle of grid lines near the grid boundaries, and to control the outer boundary point distribution. The method has been found to generate grids about 100 times faster than comparable grids generated via solution of elliptic PDEs, and produces smooth grids for finite-difference flow calculations.

On the initial-boundary value problem for some quasilinear parabolic equations of divergence form

NASA Astrophysics Data System (ADS)

Nakao, Mitsuhiro

2017-12-01

In this paper we give an existence theorem of global classical solution to the initial boundary value problem for the quasilinear parabolic equations of divergence form ut -div { σ (| ∇u|2) ∇u } = f (∇u , u , x , t) where σ (| ∇u|2) may not be bounded as | ∇u | → ∞. As an application the logarithmic type nonlinearity σ (| ∇u|2) = log ⁡ (1 + | ∇u|2) which is growing as | ∇u | → ∞ and degenerate at | ∇u | = 0 is considered under f ≡ 0.

Miscellaneous: Various Low-Mach-Number Fluid Problems and Motions

NASA Astrophysics Data System (ADS)

Zeytounian, Radyadour Kh.

In this last chapter, we consider, first, in Sect. 7.1, mainly the asymptotic derivation of the KZK equation of nonlinear acoustics, which generalizes the well-known Burgers' unsteady one-dimensional dissipative model equation (Burgers 1948) to an equation with a diffraction and parabolic effect.

Stochastic Modeling of Laminar-Turbulent Transition

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Choudhari, Meelan

2002-01-01

Stochastic versions of stability equations are developed in order to develop integrated models of transition and turbulence and to understand the effects of uncertain initial conditions on disturbance growth. Stochastic forms of the resonant triad equations, a high Reynolds number asymptotic theory, and the parabolized stability equations are developed.

Strongly nonlinear parabolic variational inequalities

PubMed Central

Browder, Felix E.; Brézis, Haim

1980-01-01

An existence and uniqueness result is established for a general class of variational inequalities for parabolic partial differential equations of the form ∂u/∂t + A(u) + g(u) = f with g nondecreasing but satisfying no growth condition. The proof is based upon a type of compactness result for solutions of variational inequalities that should find a variety of other applications. PMID:16592776

Time domain simulation of nonlinear acoustic beams generated by rectangular pistons with application to harmonic imaging

NASA Astrophysics Data System (ADS)

Yang, Xinmai; Cleveland, Robin O.

2005-01-01

A time-domain numerical code (the so-called Texas code) that solves the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation has been extended from an axis-symmetric coordinate system to a three-dimensional (3D) Cartesian coordinate system. The code accounts for diffraction (in the parabolic approximation), nonlinearity and absorption and dispersion associated with thermoviscous and relaxation processes. The 3D time domain code was shown to be in agreement with benchmark solutions for circular and rectangular sources, focused and unfocused beams, and linear and nonlinear propagation. The 3D code was used to model the nonlinear propagation of diagnostic ultrasound pulses through tissue. The prediction of the second-harmonic field was sensitive to the choice of frequency-dependent absorption: a frequency squared f2 dependence produced a second-harmonic field which peaked closer to the transducer and had a lower amplitude than that computed for an f1.1 dependence. In comparing spatial maps of the harmonics we found that the second harmonic had dramatically reduced amplitude in the near field and also lower amplitude side lobes in the focal region than the fundamental. These findings were consistent for both uniform and apodized sources and could be contributing factors in the improved imaging reported with clinical scanners using tissue harmonic imaging. .

Time domain simulation of nonlinear acoustic beams generated by rectangular pistons with application to harmonic imaging.

PubMed

Yang, Xinmai; Cleveland, Robin O

2005-01-01

A time-domain numerical code (the so-called Texas code) that solves the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation has been extended from an axis-symmetric coordinate system to a three-dimensional (3D) Cartesian coordinate system. The code accounts for diffraction (in the parabolic approximation), nonlinearity and absorption and dispersion associated with thermoviscous and relaxation processes. The 3D time domain code was shown to be in agreement with benchmark solutions for circular and rectangular sources, focused and unfocused beams, and linear and nonlinear propagation. The 3D code was used to model the nonlinear propagation of diagnostic ultrasound pulses through tissue. The prediction of the second-harmonic field was sensitive to the choice of frequency-dependent absorption: a frequency squared f2 dependence produced a second-harmonic field which peaked closer to the transducer and had a lower amplitude than that computed for an f1.1 dependence. In comparing spatial maps of the harmonics we found that the second harmonic had dramatically reduced amplitude in the near field and also lower amplitude side lobes in the focal region than the fundamental. These findings were consistent for both uniform and apodized sources and could be contributing factors in the improved imaging reported with clinical scanners using tissue harmonic imaging.

A new method of imposing boundary conditions for hyperbolic equations

NASA Technical Reports Server (NTRS)

Funaro, D.; ative.

1987-01-01

A new method to impose boundary conditions for pseudospectral approximations to hyperbolic equations is suggested. This method involves the collocation of the equation at the boundary nodes as well as satisfying boundary conditions. Stability and convergence results are proven for the Chebyshev approximation of linear scalar hyperbolic equations. The eigenvalues of this method applied to parabolic equations are shown to be real and negative.

Hyperbolic/parabolic development for the GIM-STAR code. [flow fields in supersonic inlets

NASA Technical Reports Server (NTRS)

Spradley, L. W.; Stalnaker, J. F.; Ratliff, A. W.

1980-01-01

Flow fields in supersonic inlet configurations were computed using the eliptic GIM code on the STAR computer. Spillage flow under the lower cowl was calculated to be 33% of the incoming stream. The shock/boundary layer interaction on the upper propulsive surface was computed including separation. All shocks produced by the flow system were captured. Linearized block implicit (LBI) schemes were examined to determine their application to the GIM code. Pure explicit methods have stability limitations and fully implicit schemes are inherently inefficient; however, LBI schemes show promise as an effective compromise. A quasiparabolic version of the GIM code was developed using elastical parabolized Navier-Stokes methods combined with quasitime relaxation. This scheme is referred to as quasiparabolic although it applies equally well to hyperbolic supersonic inviscid flows. Second order windward differences are used in the marching coordinate and either explicit or linear block implicit time relaxation can be incorporated.

Elastic parabolic equation solutions for underwater acoustic problems using seismic sources.

PubMed

Frank, Scott D; Odom, Robert I; Collis, Jon M

2013-03-01

Several problems of current interest involve elastic bottom range-dependent ocean environments with buried or earthquake-type sources, specifically oceanic T-wave propagation studies and interface wave related analyses. Additionally, observed deep shadow-zone arrivals are not predicted by ray theoretic methods, and attempts to model them with fluid-bottom parabolic equation solutions suggest that it may be necessary to account for elastic bottom interactions. In order to study energy conversion between elastic and acoustic waves, current elastic parabolic equation solutions must be modified to allow for seismic starting fields for underwater acoustic propagation environments. Two types of elastic self-starter are presented. An explosive-type source is implemented using a compressional self-starter and the resulting acoustic field is consistent with benchmark solutions. A shear wave self-starter is implemented and shown to generate transmission loss levels consistent with the explosive source. Source fields can be combined to generate starting fields for source types such as explosions, earthquakes, or pile driving. Examples demonstrate the use of source fields for shallow sources or deep ocean-bottom earthquake sources, where down slope conversion, a known T-wave generation mechanism, is modeled. Self-starters are interpreted in the context of the seismic moment tensor.

Comparison of Non-Parabolic Hydrodynamic Simulations for Semiconductor Devices

NASA Technical Reports Server (NTRS)

Smith, A. W.; Brennan, K. F.

1996-01-01

Parabolic drift-diffusion simulators are common engineering level design tools for semiconductor devices. Hydrodynamic simulators, based on the parabolic band approximation, are becoming more prevalent as device dimensions shrink and energy transport effects begin to dominate device characteristic. However, band structure effects present in state-of-the-art devices necessitate relaxing the parabolic band approximation. This paper presents simulations of ballistic diodes, a benchmark device, of Si and GaAs using two different non-parabolic hydrodynamic formulations. The first formulation uses the Kane dispersion relationship in the derivation of the conservation equations. The second model uses a power law dispersion relation {(hk)(exp 2)/2m = xW(exp Y)}. Current-voltage relations show that for the ballistic diodes considered. the non-parabolic formulations predict less current than the parabolic case. Explanations of this will be provided by examination of velocity and energy profiles. At low bias, the simulations based on the Kane formulation predict greater current flow than the power law formulation. As the bias is increased this trend changes and the power law predicts greater current than the Kane formulation. It will be shown that the non-parabolicity and energy range of the hydrodynamic model based on the Kane dispersion relation are limited due to the binomial approximation which was utilized in the derivation.

Geometry of Conservation Laws for a Class of Parabolic Partial Differential Equations

NASA Astrophysics Data System (ADS)

Clelland, Jeanne Nielsen

1996-08-01

I consider the problem of computing the space of conservation laws for a second-order, parabolic partial differential equation for one function of three independent variables. The PDE is formulated as an exterior differential system {cal I} on a 12 -manifold M, and its conservation laws are identified with the vector space of closed 3-forms in the infinite prolongation of {cal I} modulo the so -called "trivial" conservation laws. I use the tools of exterior differential systems and Cartan's method of equivalence to study the structure of the space of conservation laws. My main result is:. Theorem. Any conservation law for a second-order, parabolic PDE for one function of three independent variables can be represented by a closed 3-form in the differential ideal {cal I} on the original 12-manifold M. I show that if a nontrivial conservation law exists, then {cal I} has a deprolongation to an equivalent system {cal J} on a 7-manifold N, and any conservation law for {cal I} can be expressed as a closed 3-form on N which lies in {cal J}. Furthermore, any such system in the real analytic category is locally equivalent to a system generated by a (parabolic) equation of the formA(u _{xx}u_{yy}-u_sp {xy}{2}) + B_1u_{xx }+2B_2u_{xy} +B_3u_ {yy}+C=0crwhere A, B_{i}, C are functions of x, y, t, u, u_{x}, u _{y}, u_{t}. I compute the space of conservation laws for several examples, and I begin the process of analyzing the general case using Cartan's method of equivalence. I show that the non-linearizable equation u_{t} = {1over2}e ^{-u}(u_{xx}+u_ {yy})has an infinite-dimensional space of conservation laws. This stands in contrast to the two-variable case, for which Bryant and Griffiths showed that any equation whose space of conservation laws has dimension 4 or more is locally equivalent to a linear equation, i.e., is linearizable.

Preserving the Helmholtz dispersion relation: One-way acoustic wave propagation using matrix square roots

NASA Astrophysics Data System (ADS)

Keefe, Laurence

2016-11-01

Parabolized acoustic propagation in transversely inhomogeneous media is described by the operator update equation U (x , y , z + Δz) =eik0 (- 1 +√{ 1 + Z }) U (x , y , z) for evolution of the envelope of a wavetrain solution to the original Helmholtz equation. Here the operator, Z =∇T2 + (n2 - 1) , involves the transverse Laplacian and the refractive index distribution. Standard expansion techniques (on the assumption Z << 1)) produce pdes that approximate, to greater or lesser extent, the full dispersion relation of the original Helmholtz equation, except that none of them describe evanescent/damped waves without special modifications to the expansion coefficients. Alternatively, a discretization of both the envelope and the operator converts the operator update equation into a matrix multiply, and existing theorems on matrix functions demonstrate that the complete (discrete) Helmholtz dispersion relation, including evanescent/damped waves, is preserved by this discretization. Propagation-constant/damping-rates contour comparisons for the operator equation and various approximations demonstrate this point, and how poorly the lowest-order, textbook, parabolized equation describes propagation in lined ducts.

SOSPAC- SOLAR SPACE POWER ANALYSIS CODE

NASA Technical Reports Server (NTRS)

Selcuk, M. K.

1994-01-01

The Solar Space Power Analysis Code, SOSPAC, was developed to examine the solar thermal and photovoltaic power generation options available for a satellite or spacecraft in low earth orbit. SOSPAC is a preliminary systems analysis tool and enables the engineer to compare the areas, weights, and costs of several candidate electric and thermal power systems. The configurations studied include photovoltaic arrays and parabolic dish systems to produce electricity only, and in various combinations to provide both thermal and electric power. SOSPAC has been used for comparison and parametric studies of proposed power systems for the NASA Space Station. The initial requirements are projected to be about 40 kW of electrical power, and a similar amount of thermal power with temperatures above 1000 degrees Centigrade. For objects in low earth orbit, the aerodynamic drag caused by suitably large photovoltaic arrays is very substantial. Smaller parabolic dishes can provide thermal energy at a collection efficiency of about 80%, but at increased cost. SOSPAC allows an analysis of cost and performance factors of five hybrid power generating systems. Input includes electrical and thermal power requirements, sun and shade durations for the satellite, and unit weight and cost for subsystems and components. Performance equations of the five configurations are derived, and the output tabulates total weights of the power plant assemblies, area of the arrays, efficiencies, and costs. SOSPAC is written in FORTRAN IV for batch execution and has been implemented on an IBM PC computer operating under DOS with a central memory requirement of approximately 60K of 8 bit bytes. This program was developed in 1985.

Udzawa-type iterative method with parareal preconditioner for a parabolic optimal control problem

NASA Astrophysics Data System (ADS)

Lapin, A.; Romanenko, A.

2016-11-01

The article deals with the optimal control problem with the parabolic equation as state problem. There are point-wise constraints on the state and control functions. The objective functional involves the observation given in the domain at each moment. The conditions for convergence Udzawa's type iterative method are given. The parareal method to inverse preconditioner is given. The results of calculations are presented.

(2 + 1)-dimensional bright optical solitons in metamaterials with Kerr, power and parabolic law nonlinearities

NASA Astrophysics Data System (ADS)

Boubir, Badreddine

2018-06-01

In this paper, we investigate the dynamics of bright optical solitons in nonlinear metamaterials governed by a (2 + 1)-dimensional nonlinear Schrödinger equation. Three types of nonlinearities have been considered, Kerr law, power law and parabolic law. We based on the solitary wave ansatz method to find these optical soliton solutions. All necessary parametric conditions for their existence are driven.

Modeling of ultrashort pulsed laser irradiation in the cornea based on parabolic and hyperbolic heat equations using electrical analogy

NASA Astrophysics Data System (ADS)

Gheitaghy, A. M.; Takabi, B.; Alizadeh, M.

2014-03-01

Hyperbolic and parabolic heat equations are formulated to study a nonperfused homogeneous transparent cornea irradiated by high power and ultrashort pulsed laser in the Laser Thermo Keratoplasty (LTK) surgery. Energy absorption inside the cornea is modeled using the Beer-Lambert law that is incorporated as an exponentially decaying heat source. The hyperbolic and parabolic bioheat models of the tissue were solved by exploiting the mathematical analogy between thermal and electrical systems, by using robust circuit simulation program called Hspice to get the solutions of simultaneous RLC and RC transmission line networks. This method can be used to rapidly calculate the temperature in laser-irradiated tissue at time and space domain. It is found that internal energy gained from the irradiated field results in a rapid rise of temperature in the cornea surface during the early heating period, while the hyperbolic wave model predicts a higher temperature rise than the classical heat diffusion model. In addition, this paper investigates and examines the effect of some critical parameters such as relaxation time, convection coefficient, radiation, tear evaporation and variable thermal conductivity of cornea. Accordingly, it is found that a better accordance between hyperbolic and parabolic models will be achieved by time.

Optimization method for an evolutional type inverse heat conduction problem

NASA Astrophysics Data System (ADS)

Deng, Zui-Cha; Yu, Jian-Ning; Yang, Liu

2008-01-01

This paper deals with the determination of a pair (q, u) in the heat conduction equation u_t-u_{xx}+q(x,t)u=0, with initial and boundary conditions u(x,0)=u_0(x),\\qquad u_x|_{x=0}=u_x|_{x=1}=0, from the overspecified data u(x, t) = g(x, t). By the time semi-discrete scheme, the problem is transformed into a sequence of inverse problems in which the unknown coefficients are purely space dependent. Based on the optimal control framework, the existence, uniqueness and stability of the solution (q, u) are proved. A necessary condition which is a couple system of a parabolic equation and parabolic variational inequality is deduced.

The generic gradient-like structure of certain asymptotically autonomous semilinear parabolic equations

NASA Astrophysics Data System (ADS)

Jänig, A.

2018-05-01

We consider asymptotically autonomous semilinear parabolic equations u_t + Au = f(t,u). Suppose that $f(t,.)\\to f^\\pm$ as $t\\to\\pm\\infty$, where the semiflows induced by \\label{eq:140602-1511} u_t + Au = f^\\pm(u) \\tag{*} are gradient-like. Under certain assumptions, it is shown that generically with respect to a perturbation $g$ with $g(t)\\to 0$ as $|t|\\to\\infty$, every solution of u_t + Au = f(t,u) + g(t) is a connection between equilibria $e^\\pm$ of \\eqref{eq:140602-1511} with $m(e^-)\\geq m(e^+)$. Moreover, if the Morse indices satisfy $m(e^-) = m(e^+)$, then $u$ is isolated by linearization.

Rapidly accelerating Mathieu and Weber surface plasmon beams.

PubMed

Libster-Hershko, Ana; Epstein, Itai; Arie, Ady

2014-09-19

We report the generation of two types of self-accelerating surface plasmon beams which are solutions of the nonparaxial Helmholtz equation in two dimensions. These beams preserve their shape while propagating along either elliptic (Mathieu beam) or parabolic (Weber beam) trajectories. We show that owing to the nonparaxial nature of the Weber beam, it maintains its shape over a much larger distance along the parabolic trajectory, with respect to the corresponding solution of the paraxial equation-the Airy beam. Dynamic control of the trajectory is realized by translating the position of the illuminating free-space beam. Finally, the ability of these beams to self-heal after blocking obstacles is demonstrated as well.

CAFE: A New Relativistic MHD Code

NASA Astrophysics Data System (ADS)

Lora-Clavijo, F. D.; Cruz-Osorio, A.; Guzmán, F. S.

2015-06-01

We introduce CAFE, a new independent code designed to solve the equations of relativistic ideal magnetohydrodynamics (RMHD) in three dimensions. We present the standard tests for an RMHD code and for the relativistic hydrodynamics regime because we have not reported them before. The tests include the one-dimensional Riemann problems related to blast waves, head-on collisions of streams, and states with transverse velocities, with and without magnetic field, which is aligned or transverse, constant or discontinuous across the initial discontinuity. Among the two-dimensional (2D) and 3D tests without magnetic field, we include the 2D Riemann problem, a one-dimensional shock tube along a diagonal, the high-speed Emery wind tunnel, the Kelvin-Helmholtz (KH) instability, a set of jets, and a 3D spherical blast wave, whereas in the presence of a magnetic field we show the magnetic rotor, the cylindrical explosion, a case of Kelvin-Helmholtz instability, and a 3D magnetic field advection loop. The code uses high-resolution shock-capturing methods, and we present the error analysis for a combination that uses the Harten, Lax, van Leer, and Einfeldt (HLLE) flux formula combined with a linear, piecewise parabolic method and fifth-order weighted essentially nonoscillatory reconstructors. We use the flux-constrained transport and the divergence cleaning methods to control the divergence-free magnetic field constraint.

Projection scheme for a reflected stochastic heat equation with additive noise

NASA Astrophysics Data System (ADS)

Higa, Arturo Kohatsu; Pettersson, Roger

2005-02-01

We consider a projection scheme as a numerical solution of a reflected stochastic heat equation driven by a space-time white noise. Convergence is obtained via a discrete contraction principle and known convergence results for numerical solutions of parabolic variational inequalities.

The Development of the Ducted Fan Noise Propagation and Radiation Code CDUCT-LaRC

NASA Technical Reports Server (NTRS)

Nark, Douglas M.; Farassat, F.; Pope, D. Stuart; Vatsa, Veer

2003-01-01

The development of the ducted fan noise propagation and radiation code CDUCT-LaRC at NASA Langley Research Center is described. This code calculates the propagation and radiation of given acoustic modes ahead of the fan face or aft of the exhaust guide vanes in the inlet or exhaust ducts, respectively. This paper gives a description of the modules comprising CDUCT-LaRC. The grid generation module provides automatic creation of numerical grids for complex (non-axisymmetric) geometries that include single or multiple pylons. Files for performing automatic inviscid mean flow calculations are also generated within this module. The duct propagation is based on the parabolic approximation theory of R. P. Dougherty. This theory allows the handling of complex internal geometries and the ability to study the effect of non-uniform (i.e. circumferentially and axially segmented) liners. Finally, the duct radiation module is based on the Ffowcs Williams-Hawkings (FW-H) equation with a penetrable data surface. Refraction of sound through the shear layer between the external flow and bypass duct flow is included. Results for benchmark annular ducts, as well as other geometries with pylons, are presented and compared with available analytical data.

Laser pulse propagation in inhomogeneous magnetoplasma channels and wakefield acceleration

NASA Astrophysics Data System (ADS)

Sharma, B. S.; Jain, Archana; Jaiman, N. K.; Gupta, D. N.; Jang, D. G.; Suk, H.; Kulagin, V. V.

2014-02-01

Wakefield excitation in a preformed inhomogeneous parabolic plasma channel by an intense relativistic (≃1019 W/cm2) circularly polarized Gaussian laser pulse is investigated analytically and numerically in the presence of an external longitudinal magnetic field. A three dimensional envelope equation for the evolution of the laser pulse is derived, which includes the effect of the nonparaxial and applied external magnetic field. A relation for the channel radius with the laser spot size is derived and examines numerically to see the external magnetic field effect. It is observed that the channel radius depends on the applied external magnetic field. An analytical expression for the wakefield is derived and validated with the help of a two dimensional particle in cell (2D PIC) simulation code. It is shown that the electromagnetic nature of the wakes in an inhomogeneous plasma channel makes their excitation nonlocal, which results in change of fields with time and external magnetic field due to phase mixing of the plasma oscillations with spatially varying frequencies. The magnetic field effect on perturbation of the plasma density and decreasing length is also analyzed numerically. In addition, it has been shown that the electron energy gain in the inhomogeneous parabolic magnetoplasma channel can be increased significantly compared with the homogeneous plasma channel.

Least-squares/parabolized Navier-Stokes procedure for optimizing hypersonic wind tunnel nozzles

NASA Technical Reports Server (NTRS)

Korte, John J.; Kumar, Ajay; Singh, D. J.; Grossman, B.

1991-01-01

A new procedure is demonstrated for optimizing hypersonic wind-tunnel-nozzle contours. The procedure couples a CFD computer code to an optimization algorithm, and is applied to both conical and contoured hypersonic nozzles for the purpose of determining an optimal set of parameters to describe the surface geometry. A design-objective function is specified based on the deviation from the desired test-section flow-field conditions. The objective function is minimized by optimizing the parameters used to describe the nozzle contour based on the solution to a nonlinear least-squares problem. The effect of the changes in the nozzle wall parameters are evaluated by computing the nozzle flow using the parabolized Navier-Stokes equations. The advantage of the new procedure is that it directly takes into account the displacement effect of the boundary layer on the wall contour. The new procedure provides a method for optimizing hypersonic nozzles of high Mach numbers which have been designed by classical procedures, but are shown to produce poor flow quality due to the large boundary layers present in the test section. The procedure is demonstrated by finding the optimum design parameters for a Mach 10 conical nozzle and a Mach 6 and a Mach 15 contoured nozzle.

User’s Guide for the VTRPE (Variable Terrain Radio Parabolic Equation) Computer Model

DTIC Science & Technology

1991-10-01

propagation effects and antenna characteristics in radar system performance calculations. the radar transmission equation is oiten employed. Fol- lowing Kerr.2...electromagnetic wave equations for the complex electric and magnetic radiation fields. The model accounts for the effects of nonuniform atmospheric refractivity...mission equation, that is used in the performance prediction and analysis of radar and communication systems. Optimized fast Fourier transform (FFT

The development of a three-dimensional partially elliptic flow computer program for combustor research

NASA Technical Reports Server (NTRS)

Pan, Y. S.

1978-01-01

A three dimensional, partially elliptic, computer program was developed. Without requiring three dimensional computer storage locations for all flow variables, the partially elliptic program is capable of predicting three dimensional combustor flow fields with large downstream effects. The program requires only slight increase of computer storage over the parabolic flow program from which it was developed. A finite difference formulation for a three dimensional, fully elliptic, turbulent, reacting, flow field was derived. Because of the negligible diffusion effects in the main flow direction in a supersonic combustor, the set of finite-difference equations can be reduced to a partially elliptic form. Only the pressure field was governed by an elliptic equation and requires three dimensional storage; all other dependent variables are governed by parabolic equations. A numerical procedure which combines a marching integration scheme with an iterative scheme for solving the elliptic pressure was adopted.

Stochastic modeling of mode interactions via linear parabolized stability equations

NASA Astrophysics Data System (ADS)

Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo

2017-11-01

Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.

Asymptotic analysis of quasilinear parabolic-hyperbolic equations describing the large longitudinal motion of a light viscoelastic bar with a heavy attachment

NASA Astrophysics Data System (ADS)

Yip, Shui Cheung

We study the longitudinal motion of a nonlinearly viscoelastic bar with one end fixed and the other end attached to a heavy tip mass. This problem is a precise continuum mechanical analog of the basic discrete mechanical problem of the motion of a mass point on a (massless) spring. This motion is governed by an initial-boundary-value problem for a class of third-order quasilinear parabolic-hyperbolic partial differential equations subject to a nonstandard boundary condition, which is the equation of motion of the tip mass. The ratio of the mass of the bar to that of the tip mass is taken to be a small parameter varepsilon. We prove that this problem has a unique regular solution that admits a valid asymptotic expansion, including an initial-layer expansion, in powers of varepsilon for varepsilon near 0. The fundamental constitutive hypothesis that the tension be a uniformly monotone function of the strain rate plays a critical role in a delicate proof that each term of the initial layer expansion decays exponentially in time. These results depend on new decay estimates for the solution of quasilinear parabolic equations. The constitutive hypothesis that the viscosity become large where the bar nears total compression leads to important uniform bounds for the strain and the strain rate. Higher-order energy estimates support the proof by the Schauder Fixed-Point Theorem of the existence of solutions having a level of regularity appropriate for the asymptotics.

Designing High-Efficiency Thin Silicon Solar Cells Using Parabolic-Pore Photonic Crystals

NASA Astrophysics Data System (ADS)

Bhattacharya, Sayak; John, Sajeev

2018-04-01

We demonstrate the efficacy of wave-interference-based light trapping and carrier transport in parabolic-pore photonic-crystal, thin-crystalline silicon (c -Si) solar cells to achieve above 29% power conversion efficiencies. Using a rigorous solution of Maxwell's equations through a standard finite-difference time domain scheme, we optimize the design of the vertical-parabolic-pore photonic crystal (PhC) on a 10 -μ m -thick c -Si solar cell to obtain a maximum achievable photocurrent density (MAPD) of 40.6 mA /cm2 beyond the ray-optical, Lambertian light-trapping limit. For a slanted-parabolic-pore PhC that breaks x -y symmetry, improved light trapping occurs due to better coupling into parallel-to-interface refraction modes. We achieve the optimum MAPD of 41.6 mA /cm2 for a tilt angle of 10° with respect to the vertical axis of the pores. This MAPD is further improved to 41.72 mA /cm2 by introducing a 75-nm SiO2 antireflective coating on top of the solar cell. We use this MAPD and the associated charge-carrier generation profile as input for a numerical solution of Poisson's equation coupled with semiconductor drift-diffusion equations using a Shockley-Read-Hall and Auger recombination model. Using experimentally achieved surface recombination velocities of 10 cm /s , we identify semiconductor doping profiles that yield power conversion efficiencies over 29%. Practical considerations of additional upper-contact losses suggest efficiencies close to 28%. This improvement beyond the current world record is largely due to an open-circuit voltage approaching 0.8 V enabled by reduced bulk recombination in our thin silicon architecture while maintaining a high short-circuit current through wave-interference-based light trapping.

An H(mo) Interpolation Result

DTIC Science & Technology

1989-11-14

9] V. A. Kondrat’ev. Boundary problems for parabolic equations in closed domains. Trans. Mosc . Math. Soc., 15:450-504, 1966. [10] V. A. Kondrat’ev...Boundary problems for elliptic equations in domains with conical or angular points. Trans. Mosc . Math. Soc., 16:227-313, 1967. [11] Y. Maday. Analysis

Dark optical, singular solitons and conservation laws to the nonlinear Schrödinger’s equation with spatio-temporal dispersion

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi

2017-05-01

This paper studies the dynamics of solitons to the nonlinear Schrödinger’s equation (NLSE) with spatio-temporal dispersion (STD). The integration algorithm that is employed in this paper is the Riccati-Bernoulli sub-ODE method. This leads to dark and singular soliton solutions that are important in the field of optoelectronics and fiber optics. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. There are four types of nonlinear media studied in this paper. They are Kerr law, power law, parabolic law and dual law. The conservation laws (Cls) for the Kerr law and parabolic law nonlinear media are constructed using the conservation theorem presented by Ibragimov.

A single-scattering correction for the seismo-acoustic parabolic equation.

PubMed

Collins, Michael D

2012-04-01

An efficient single-scattering correction that does not require iterations is derived and tested for the seismo-acoustic parabolic equation. The approach is applicable to problems involving gradual range dependence in a waveguide with fluid and solid layers, including the key case of a sloping fluid-solid interface. The single-scattering correction is asymptotically equivalent to a special case of a single-scattering correction for problems that only have solid layers [Küsel et al., J. Acoust. Soc. Am. 121, 808-813 (2007)]. The single-scattering correction has a simple interpretation (conservation of interface conditions in an average sense) that facilitated its generalization to problems involving fluid layers. Promising results are obtained for problems in which the ocean bottom interface has a small slope.

Numerical solution of supersonic three-dimensional free-mixing flows using the parabolic-elliptic Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Hirsh, R. S.

1976-01-01

A numerical method is presented for solving the parabolic-elliptic Navier-Stokes equations. The solution procedure is applied to three-dimensional supersonic laminar jet flow issuing parallel with a supersonic free stream. A coordinate transformation is introduced which maps the boundaries at infinity into a finite computational domain in order to eliminate difficulties associated with the imposition of free-stream boundary conditions. Results are presented for an approximate circular jet, a square jet, varying aspect ratio rectangular jets, and interacting square jets. The solution behavior varies from axisymmetric to nearly two-dimensional in character. For cases where comparisons of the present results with those obtained from shear layer calculations could be made, agreement was good.

Terrain and refractivity effects on non-optical paths

NASA Astrophysics Data System (ADS)

Barrios, Amalia E.

1994-07-01

The split-step parabolic equation (SSPE) has been used extensively to model tropospheric propagation over the sea, but recent efforts have extended this method to propagation over arbitrary terrain. At the Naval Command, Control and Ocean Surveillance Center (NCCOSC), Research, Development, Test and Evaluation Division, a split-step Terrain Parabolic Equation Model (TPEM) has been developed that takes into account variable terrain and range-dependent refractivity profiles. While TPEM has been previously shown to compare favorably with measured data and other existing terrain models, two alternative methods to model radiowave propagation over terrain, implemented within TPEM, will be presented that give a two to ten-fold decrease in execution time. These two methods are also shown to agree well with measured data.

Semidiscrete Galerkin modelling of compressible viscous flow past a circular cone at incidence. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Meade, Andrew James, Jr.

1989-01-01

A numerical study of the laminar and compressible boundary layer, about a circular cone in a supersonic free stream, is presented. It is thought that if accurate and efficient numerical schemes can be produced to solve the boundary layer equations, they can be joined to numerical codes that solve the inviscid outer flow. The combination of these numerical codes is competitive with the accurate, but computationally expensive, Navier-Stokes schemes. The primary goal is to develop a finite element method for the calculation of 3-D compressible laminar boundary layer about a yawed cone. The proposed method can, in principle, be extended to apply to the 3-D boundary layer of pointed bodies of arbitrary cross section. The 3-D boundary layer equations governing supersonic free stream flow about a cone are examined. The 3-D partial differential equations are reduced to 2-D integral equations by applying the Howarth, Mangler, Crocco transformations, a linear relation between viscosity, and a Blasius-type of similarity variable. This is equivalent to a Dorodnitsyn-type formulation. The reduced equations are independent of density and curvature effects, and resemble the weak form of the 2-D incompressible boundary layer equations in Cartesian coordinates. In addition the coordinate normal to the wall has been stretched, which reduces the gradients across the layer and provides high resolution near the surface. Utilizing the parabolic nature of the boundary layer equations, a finite element method is applied to the Dorodnitsyn formulation. The formulation is presented in a Petrov-Galerkin finite element form and discretized across the layer using linear interpolation functions. The finite element discretization yields a system of ordinary differential equations in the circumferential direction. The circumferential derivatives are solved by an implicit and noniterative finite difference marching scheme. Solutions are presented for a 15 deg half angle cone at angles of attack of 5 and 10 deg. The numerical solutions assume a laminar boundary layer with free stream Mach number of 7. Results include circumferential distribution of skin friction and surface heat transfer, and cross flow velocity distributions across the layer.

Focusing Light Rays Back to the Vertex of a Reflecting Parabolic Collector: The Equivalent of Dionysius Ear Effect in Optical Systems

ERIC Educational Resources Information Center

De Luca, R.; Fedullo, A.

2009-01-01

A vertical light ray coming from infinity is reflected by a primary parabolic mirror M[subscript 1] having focus at F[subscript 1]. At a small distance from F[subscript 1] a secondary mirror M[subscript 2], symmetric with respect to the vertical axis, is placed. One would like to find the analytic equation of the mirror M[subscript 2], so that all…

Scalable explicit implementation of anisotropic diffusion with Runge-Kutta-Legendre super-time stepping

NASA Astrophysics Data System (ADS)

Vaidya, Bhargav; Prasad, Deovrat; Mignone, Andrea; Sharma, Prateek; Rickler, Luca

2017-12-01

An important ingredient in numerical modelling of high temperature magnetized astrophysical plasmas is the anisotropic transport of heat along magnetic field lines from higher to lower temperatures. Magnetohydrodynamics typically involves solving the hyperbolic set of conservation equations along with the induction equation. Incorporating anisotropic thermal conduction requires to also treat parabolic terms arising from the diffusion operator. An explicit treatment of parabolic terms will considerably reduce the simulation time step due to its dependence on the square of the grid resolution (Δx) for stability. Although an implicit scheme relaxes the constraint on stability, it is difficult to distribute efficiently on a parallel architecture. Treating parabolic terms with accelerated super-time-stepping (STS) methods has been discussed in literature, but these methods suffer from poor accuracy (first order in time) and also have difficult-to-choose tuneable stability parameters. In this work, we highlight a second-order (in time) Runge-Kutta-Legendre (RKL) scheme (first described by Meyer, Balsara & Aslam 2012) that is robust, fast and accurate in treating parabolic terms alongside the hyperbolic conversation laws. We demonstrate its superiority over the first-order STS schemes with standard tests and astrophysical applications. We also show that explicit conduction is particularly robust in handling saturated thermal conduction. Parallel scaling of explicit conduction using RKL scheme is demonstrated up to more than 104 processors.

A CFD-based aerodynamic design procedure for hypersonic wind-tunnel nozzles

NASA Technical Reports Server (NTRS)

Korte, John J.

1993-01-01

A new procedure which unifies the best of current classical design practices, computational fluid dynamics (CFD), and optimization procedures is demonstrated for designing the aerodynamic lines of hypersonic wind-tunnel nozzles. The new procedure can be used to design hypersonic wind tunnel nozzles with thick boundary layers where the classical design procedure has been shown to break down. An efficient CFD code, which solves the parabolized Navier-Stokes (PNS) equations using an explicit upwind algorithm, is coupled to a least-squares (LS) optimization procedure. A LS problem is formulated to minimize the difference between the computed flow field and the objective function, consisting of the centerline Mach number distribution and the exit Mach number and flow angle profiles. The aerodynamic lines of the nozzle are defined using a cubic spline, the slopes of which are optimized with the design procedure. The advantages of the new procedure are that it allows full use of powerful CFD codes in the design process, solves an optimization problem to determine the new contour, can be used to design new nozzles or improve sections of existing nozzles, and automatically compensates the nozzle contour for viscous effects as part of the unified design procedure. The new procedure is demonstrated by designing two Mach 15, a Mach 12, and a Mach 18 helium nozzles. The flexibility of the procedure is demonstrated by designing the two Mach 15 nozzles using different constraints, the first nozzle for a fixed length and exit diameter and the second nozzle for a fixed length and throat diameter. The computed flow field for the Mach 15 least squares parabolized Navier-Stokes (LS/PNS) designed nozzle is compared with the classically designed nozzle and demonstrates a significant improvement in the flow expansion process and uniform core region.

On the coupling of hyperbolic and parabolic systems: Analytical and numerical approach

NASA Technical Reports Server (NTRS)

Gastaldi, Fabio; Quarteroni, Alfio

1988-01-01

The coupling of hyperbolic and parabolic systems is discussed in a domain Omega divided into two distinct subdomains omega(+) and omega(-). The main concern is to find the proper interface conditions to be fulfilled at the surface separating the two domains. Next, they are used in the numerical approximation of the problem. The justification of the interface conditions is based on a singular perturbation analysis, i.e., the hyperbolic system is rendered parabolic by adding a small artifical viscosity. As this goes to zero, the coupled parabolic-parabolic problem degenerates into the original one, yielding some conditions at the interface. These are taken as interface conditions for the hyperbolic-parabolic problem. Actually, two alternative sets of interface conditions are discussed according to whether the regularization procedure is variational or nonvariational. It is shown how these conditions can be used in the frame of a numerical approximation to the given problem. Furthermore, a method of resolution is discussed which alternates the resolution of the hyperbolic problem within omega(-) and of the parabolic one within omega(+). The spectral collocation method is proposed, as an example of space discretization (different methods could be used as well); both explicit and implicit time-advancing schemes are considered. The present study is a preliminary step toward the analysis of the coupling between Euler and Navier-Stokes equations for compressible flows.

Enforcing the Courant-Friedrichs-Lewy condition in explicitly conservative local time stepping schemes

NASA Astrophysics Data System (ADS)

Gnedin, Nickolay Y.; Semenov, Vadim A.; Kravtsov, Andrey V.

2018-04-01

An optimally efficient explicit numerical scheme for solving fluid dynamics equations, or any other parabolic or hyperbolic system of partial differential equations, should allow local regions to advance in time with their own, locally constrained time steps. However, such a scheme can result in violation of the Courant-Friedrichs-Lewy (CFL) condition, which is manifestly non-local. Although the violations can be considered to be "weak" in a certain sense and the corresponding numerical solution may be stable, such calculation does not guarantee the correct propagation speed for arbitrary waves. We use an experimental fluid dynamics code that allows cubic "patches" of grid cells to step with independent, locally constrained time steps to demonstrate how the CFL condition can be enforced by imposing a constraint on the time steps of neighboring patches. We perform several numerical tests that illustrate errors introduced in the numerical solutions by weak CFL condition violations and show how strict enforcement of the CFL condition eliminates these errors. In all our tests the strict enforcement of the CFL condition does not impose a significant performance penalty.

Convection equation modeling: A non-iterative direct matrix solution algorithm for use with SINDA

NASA Technical Reports Server (NTRS)

Schrage, Dean S.

1993-01-01

The determination of the boundary conditions for a component-level analysis, applying discrete finite element and finite difference modeling techniques often requires an analysis of complex coupled phenomenon that cannot be described algebraically. For example, an analysis of the temperature field of a coldplate surface with an integral fluid loop requires a solution to the parabolic heat equation and also requires the boundary conditions that describe the local fluid temperature. However, the local fluid temperature is described by a convection equation that can only be solved with the knowledge of the locally-coupled coldplate temperatures. Generally speaking, it is not computationally efficient, and sometimes, not even possible to perform a direct, coupled phenomenon analysis of the component-level and boundary condition models within a single analysis code. An alternative is to perform a disjoint analysis, but transmit the necessary information between models during the simulation to provide an indirect coupling. For this approach to be effective, the component-level model retains full detail while the boundary condition model is simplified to provide a fast, first-order prediction of the phenomenon in question. Specifically for the present study, the coldplate structure is analyzed with a discrete, numerical model (SINDA) while the fluid loop convection equation is analyzed with a discrete, analytical model (direct matrix solution). This indirect coupling allows a satisfactory prediction of the boundary condition, while not subjugating the overall computational efficiency of the component-level analysis. In the present study a discussion of the complete analysis of the derivation and direct matrix solution algorithm of the convection equation is presented. Discretization is analyzed and discussed to extend of solution accuracy, stability and computation speed. Case studies considering a pulsed and harmonic inlet disturbance to the fluid loop are analyzed to assist in the discussion of numerical dissipation and accuracy. In addition, the issues of code melding or integration with standard class solvers such as SINDA are discussed to advise the user of the potential problems to be encountered.

An efficient mode-splitting method for a curvilinear nearshore circulation model

USGS Publications Warehouse

Shi, Fengyan; Kirby, James T.; Hanes, Daniel M.

2007-01-01

A mode-splitting method is applied to the quasi-3D nearshore circulation equations in generalized curvilinear coordinates. The gravity wave mode and the vorticity wave mode of the equations are derived using the two-step projection method. Using an implicit algorithm for the gravity mode and an explicit algorithm for the vorticity mode, we combine the two modes to derive a mixed difference–differential equation with respect to surface elevation. McKee et al.'s [McKee, S., Wall, D.P., and Wilson, S.K., 1996. An alternating direction implicit scheme for parabolic equations with mixed derivative and convective terms. J. Comput. Phys., 126, 64–76.] ADI scheme is then used to solve the parabolic-type equation in dealing with the mixed derivative and convective terms from the curvilinear coordinate transformation. Good convergence rates are found in two typical cases which represent respectively the motions dominated by the gravity mode and the vorticity mode. Time step limitations imposed by the vorticity convective Courant number in vorticity-mode-dominant cases are discussed. Model efficiency and accuracy are verified in model application to tidal current simulations in San Francisco Bight.

An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology

NASA Astrophysics Data System (ADS)

Beretta, Elena; Cavaterra, Cecilia; Cerutti, M. Cristina; Manzoni, Andrea; Ratti, Luca

2017-10-01

In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the electric potential in the myocardial tissue. The goal is the detection of an inhomogeneity \

Output Feedback-Based Boundary Control of Uncertain Coupled Semilinear Parabolic PDE Using Neurodynamic Programming.

PubMed

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

In this paper, neurodynamic programming-based output feedback boundary control of distributed parameter systems governed by uncertain coupled semilinear parabolic partial differential equations (PDEs) under Neumann or Dirichlet boundary control conditions is introduced. First, Hamilton-Jacobi-Bellman (HJB) equation is formulated in the original PDE domain and the optimal control policy is derived using the value functional as the solution of the HJB equation. Subsequently, a novel observer is developed to estimate the system states given the uncertain nonlinearity in PDE dynamics and measured outputs. Consequently, the suboptimal boundary control policy is obtained by forward-in-time estimation of the value functional using a neural network (NN)-based online approximator and estimated state vector obtained from the NN observer. Novel adaptive tuning laws in continuous time are proposed for learning the value functional online to satisfy the HJB equation along system trajectories while ensuring the closed-loop stability. Local uniformly ultimate boundedness of the closed-loop system is verified by using Lyapunov theory. The performance of the proposed controller is verified via simulation on an unstable coupled diffusion reaction process.

Uniqueness of solutions for Keller-Segel system of porous medium type coupled to fluid equations

NASA Astrophysics Data System (ADS)

Bae, Hantaek; Kang, Kyungkeun; Kim, Seick

2018-04-01

We prove the uniqueness of Hölder continuous weak solutions via duality argument and vanishing viscosity method for the Keller-Segel system of porous medium type equations coupled to the Stokes system in dimensions three. An important step is the estimate of the Green function of parabolic equations with lower order terms of variable coefficients, which seems to be of independent interest.

The Discrete Hanging Cable

ERIC Educational Resources Information Center

Peters, James V.

2004-01-01

Using the methods of finite difference equations the discrete analogue of the parabolic and catenary cable are analysed. The fibonacci numbers and the golden ratio arise in the treatment of the catenary.

Stability of an abstract system of coupled hyperbolic and parabolic equations

NASA Astrophysics Data System (ADS)

Hao, Jianghao; Liu, Zhuangyi

2013-08-01

In this paper, we provide a complete stability analysis for an abstract system of coupled hyperbolic and parabolic equations = -Au + γ A^{α} θ, quad θ_t = -γ A^{α}u_t - kA^{β}θ, u(0) = u_0, quad u_t(0) = v_0, quad θ(0) = θ_0 where A is a self-adjoint, positive definite operator on a Hilbert space H. For {(α,β) in [0,1] × [0,1]} , the region of exponential stability had been identified in Ammar-Khodja et al. (ESAIM Control Optim Calc Var 4:577-593,1999). Our contribution is to show that the rest of the region can be classified as region of polynomial stability and region of instability. Moreover, we obtain the optimality of the order of polynomial stability.

A viscous flow analysis for the tip vortex generation process

NASA Technical Reports Server (NTRS)

Shamroth, S. J.; Briley, W. R.

1979-01-01

A three dimensional, forward-marching, viscous flow analysis is applied to the tip vortex generation problem. The equations include a streamwise momentum equation, a streamwise vorticity equation, a continuity equation, and a secondary flow stream function equation. The numerical method used combines a consistently split linearized scheme for parabolic equations with a scalar iterative ADI scheme for elliptic equations. The analysis is used to identify the source of the tip vortex generation process, as well as to obtain detailed flow results for a rectangular planform wing immersed in a high Reynolds number free stream at 6 degree incidence.

A stabilized Runge–Kutta–Legendre method for explicit super-time-stepping of parabolic and mixed equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meyer, Chad D.; Balsara, Dinshaw S.; Aslam, Tariq D.

2014-01-15

Parabolic partial differential equations appear in several physical problems, including problems that have a dominant hyperbolic part coupled to a sub-dominant parabolic component. Explicit methods for their solution are easy to implement but have very restrictive time step constraints. Implicit solution methods can be unconditionally stable but have the disadvantage of being computationally costly or difficult to implement. Super-time-stepping methods for treating parabolic terms in mixed type partial differential equations occupy an intermediate position. In such methods each superstep takes “s” explicit Runge–Kutta-like time-steps to advance the parabolic terms by a time-step that is s{sup 2} times larger than amore » single explicit time-step. The expanded stability is usually obtained by mapping the short recursion relation of the explicit Runge–Kutta scheme to the recursion relation of some well-known, stable polynomial. Prior work has built temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Chebyshev polynomials. Since their stability is based on the boundedness of the Chebyshev polynomials, these methods have been called RKC1 and RKC2. In this work we build temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Legendre polynomials. We call these methods RKL1 and RKL2. The RKL1 method is first-order accurate in time; the RKL2 method is second-order accurate in time. We verify that the newly-designed RKL1 and RKL2 schemes have a very desirable monotonicity preserving property for one-dimensional problems – a solution that is monotone at the beginning of a time step retains that property at the end of that time step. It is shown that RKL1 and RKL2 methods are stable for all values of the diffusion coefficient up to the maximum value. We call this a convex monotonicity preserving property and show by examples that it is very useful in parabolic problems with variable diffusion coefficients. This includes variable coefficient parabolic equations that might give rise to skew symmetric terms. The RKC1 and RKC2 schemes do not share this convex monotonicity preserving property. One-dimensional and two-dimensional von Neumann stability analyses of RKC1, RKC2, RKL1 and RKL2 are also presented, showing that the latter two have some advantages. The paper includes several details to facilitate implementation. A detailed accuracy analysis is presented to show that the methods reach their design accuracies. A stringent set of test problems is also presented. To demonstrate the robustness and versatility of our methods, we show their successful operation on problems involving linear and non-linear heat conduction and viscosity, resistive magnetohydrodynamics, ambipolar diffusion dominated magnetohydrodynamics, level set methods and flux limited radiation diffusion. In a prior paper (Meyer, Balsara and Aslam 2012 [36]) we have also presented an extensive test-suite showing that the RKL2 method works robustly in the presence of shocks in an anisotropically conducting, magnetized plasma.« less

A stabilized Runge-Kutta-Legendre method for explicit super-time-stepping of parabolic and mixed equations

NASA Astrophysics Data System (ADS)

Meyer, Chad D.; Balsara, Dinshaw S.; Aslam, Tariq D.

2014-01-01

Parabolic partial differential equations appear in several physical problems, including problems that have a dominant hyperbolic part coupled to a sub-dominant parabolic component. Explicit methods for their solution are easy to implement but have very restrictive time step constraints. Implicit solution methods can be unconditionally stable but have the disadvantage of being computationally costly or difficult to implement. Super-time-stepping methods for treating parabolic terms in mixed type partial differential equations occupy an intermediate position. In such methods each superstep takes “s” explicit Runge-Kutta-like time-steps to advance the parabolic terms by a time-step that is s2 times larger than a single explicit time-step. The expanded stability is usually obtained by mapping the short recursion relation of the explicit Runge-Kutta scheme to the recursion relation of some well-known, stable polynomial. Prior work has built temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Chebyshev polynomials. Since their stability is based on the boundedness of the Chebyshev polynomials, these methods have been called RKC1 and RKC2. In this work we build temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Legendre polynomials. We call these methods RKL1 and RKL2. The RKL1 method is first-order accurate in time; the RKL2 method is second-order accurate in time. We verify that the newly-designed RKL1 and RKL2 schemes have a very desirable monotonicity preserving property for one-dimensional problems - a solution that is monotone at the beginning of a time step retains that property at the end of that time step. It is shown that RKL1 and RKL2 methods are stable for all values of the diffusion coefficient up to the maximum value. We call this a convex monotonicity preserving property and show by examples that it is very useful in parabolic problems with variable diffusion coefficients. This includes variable coefficient parabolic equations that might give rise to skew symmetric terms. The RKC1 and RKC2 schemes do not share this convex monotonicity preserving property. One-dimensional and two-dimensional von Neumann stability analyses of RKC1, RKC2, RKL1 and RKL2 are also presented, showing that the latter two have some advantages. The paper includes several details to facilitate implementation. A detailed accuracy analysis is presented to show that the methods reach their design accuracies. A stringent set of test problems is also presented. To demonstrate the robustness and versatility of our methods, we show their successful operation on problems involving linear and non-linear heat conduction and viscosity, resistive magnetohydrodynamics, ambipolar diffusion dominated magnetohydrodynamics, level set methods and flux limited radiation diffusion. In a prior paper (Meyer, Balsara and Aslam 2012 [36]) we have also presented an extensive test-suite showing that the RKL2 method works robustly in the presence of shocks in an anisotropically conducting, magnetized plasma.

Modeling boundary-layer transition in direct and large-eddy simulations using parabolized stability equations

NASA Astrophysics Data System (ADS)

Lozano-Durán, A.; Hack, M. J. P.; Moin, P.

2018-02-01

We examine the potential of the nonlinear parabolized stability equations (PSE) to provide an accurate yet computationally efficient treatment of the growth of disturbances in H-type transition to turbulence. The PSE capture the nonlinear interactions that eventually induce breakdown to turbulence and can as such identify the onset of transition without relying on empirical correlations. Since the local PSE solution at the onset of transition is a close approximation of the Navier-Stokes equations, it provides a natural inflow condition for direct numerical simulations (DNS) and large-eddy simulations (LES) by avoiding nonphysical transients. We show that a combined PSE-DNS approach, where the pretransitional region is modeled by the PSE, can reproduce the skin-friction distribution and downstream turbulent statistics from a DNS of the full domain. When the PSE are used in conjunction with wall-resolved and wall-modeled LES, the computational cost in both the laminar and turbulent regions is reduced by several orders of magnitude compared to DNS.

A fourth-order box method for solving the boundary layer equations

NASA Technical Reports Server (NTRS)

Wornom, S. F.

1977-01-01

A fourth order box method for calculating high accuracy numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations is presented. The method is the natural extension of the second order Keller Box scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary layer equations. Numerical results for high accuracy test cases show the method to be significantly faster than other higher order and second order methods.

On several aspects and applications of the multigrid method for solving partial differential equations

NASA Technical Reports Server (NTRS)

Dinar, N.

1978-01-01

Several aspects of multigrid methods are briefly described. The main subjects include the development of very efficient multigrid algorithms for systems of elliptic equations (Cauchy-Riemann, Stokes, Navier-Stokes), as well as the development of control and prediction tools (based on local mode Fourier analysis), used to analyze, check and improve these algorithms. Preliminary research on multigrid algorithms for time dependent parabolic equations is also described. Improvements in existing multigrid processes and algorithms for elliptic equations were studied.

Fully-Implicit Reconstructed Discontinuous Galerkin Method for Stiff Multiphysics Problems

NASA Astrophysics Data System (ADS)

Nourgaliev, Robert

2015-11-01

A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method's capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing. We focus on the method's accuracy (in both space and time), as well as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, and funded by the LDRD at LLNL under project tracking code 13-SI-002.

Highly Parallel Alternating Directions Algorithm for Time Dependent Problems

NASA Astrophysics Data System (ADS)

Ganzha, M.; Georgiev, K.; Lirkov, I.; Margenov, S.; Paprzycki, M.

2011-11-01

In our work, we consider the time dependent Stokes equation on a finite time interval and on a uniform rectangular mesh, written in terms of velocity and pressure. For this problem, a parallel algorithm based on a novel direction splitting approach is developed. Here, the pressure equation is derived from a perturbed form of the continuity equation, in which the incompressibility constraint is penalized in a negative norm induced by the direction splitting. The scheme used in the algorithm is composed of two parts: (i) velocity prediction, and (ii) pressure correction. This is a Crank-Nicolson-type two-stage time integration scheme for two and three dimensional parabolic problems in which the second-order derivative, with respect to each space variable, is treated implicitly while the other variable is made explicit at each time sub-step. In order to achieve a good parallel performance the solution of the Poison problem for the pressure correction is replaced by solving a sequence of one-dimensional second order elliptic boundary value problems in each spatial direction. The parallel code is implemented using the standard MPI functions and tested on two modern parallel computer systems. The performed numerical tests demonstrate good level of parallel efficiency and scalability of the studied direction-splitting-based algorithm.

Linear and Nonlinear Optical Properties of Spherical Quantum Dots: Effects of Hydrogenic Impurity and Conduction Band Non-Parabolicity

NASA Astrophysics Data System (ADS)

Rezaei, G.; Vaseghi, B.; Doostimotlagh, N. A.

2012-03-01

Simultaneous effects of an on-center hydrogenic impurity and band edge non-parabolicity on intersubband optical absorption coefficients and refractive index changes of a typical GaAs/AlxGa1-x As spherical quantum dot are theoretically investigated, using the Luttinger—Kohn effective mass equation. So, electronic structure and optical properties of the system are studied by means of the matrix diagonalization technique and compact density matrix approach, respectively. Finally, effects of an impurity, band edge non-parabolicity, incident light intensity and the dot size on the linear, the third-order nonlinear and the total optical absorption coefficients and refractive index changes are investigated. Our results indicate that, the magnitudes of these optical quantities increase and their peaks shift to higher energies as the influences of the impurity and the band edge non-parabolicity are considered. Moreover, incident light intensity and the dot size have considerable effects on the optical absorption coefficients and refractive index changes.

Parabolized Navier-Stokes Code for Computing Magneto-Hydrodynamic Flowfields

NASA Technical Reports Server (NTRS)

Mehta, Unmeel B. (Technical Monitor); Tannehill, J. C.

2003-01-01

This report consists of two published papers, 'Computation of Magnetohydrodynamic Flows Using an Iterative PNS Algorithm' and 'Numerical Simulation of Turbulent MHD Flows Using an Iterative PNS Algorithm'.

Study of thermal and hydraulic efficiency of supersonic tube of temperature stratification

NASA Astrophysics Data System (ADS)

Tsynaeva, Anna A.; Nikitin, Maxim N.; Tsynaeva, Ekaterina A.

2017-10-01

Efficiency of supersonic pipe for temperature stratification with finned subsonic surface of heat transfer is the major of this paper. Thermal and hydraulic analyses of this pipe were conducted to asses effects from installation of longitudinal rectangular and parabolic fins as well as studs of cylindrical, rectangular and parabolic profiles. The analysis was performed based on refined empirical equations of similarity, dedicated to heat transfer of high-speed gas flow with plain wall, and Kármán equation with Nikuradze constants. Results revealed cylindrical studs (with height-to-diameter ratio of 5:1) to be 1.5 times more efficient than rectangular fins of the same height. At the same time rectangular fins (with height-to-thickness ratio of 5:1) were tend to enhance heat transfer rate up to 2.67 times compared to bare walls from subsonic side of the pipe. Longitudinal parabolic fins have minuscule effect on combined efficiency of considered pipe since extra head losses void any gain of heat transfer. Obtained results provide perspective of increasing efficiency of supersonic tube for temperature stratification. This significantly broadens device applicability in thermostatting systems for equipment, cooling systems for energy converting machinery, turbine blades and aerotechnics.

Causal Diffusion and the Survival of Charge Fluctuations

NASA Astrophysics Data System (ADS)

Abdel-Aziz, Mohamed; Gavin, Sean

2004-10-01

Diffusion may obliterate fluctuation signals of the QCD phase transition in nuclear collisions at SPS and RHIC energies. We propose a hyperbolic diffusion equation to study the dissipation of net charge fluctuations [1]. This equation is needed in a relativistic context, because the classic parabolic diffusion equation violates causality. We find that causality substantially limits the extent to which diffusion can dissipate these fluctuations. [1] M. Abdel-Aziz and S. Gavin, nucl-th/0404058

On uniformly valid high-frequency far-field asymptotic solutions of the Helmholtz equation

NASA Technical Reports Server (NTRS)

Mcaninch, G. L.

1986-01-01

An asymptotic, large wave number approximation for the Helmholtz equation is derived. The theory is an extension of the geometric acoustic theory, and provides corrections to that theory in the form of multiplicative functions which satisfy parabolic equations. A simple example is used both to illustrate failure of the geometric theory for large propagation distances, and to show the improvement obtained by use of the new theory.

Second-harmonic generation in shear wave beams with different polarizations

NASA Astrophysics Data System (ADS)

Spratt, Kyle S.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.

2015-10-01

A coupled pair of nonlinear parabolic equations was derived by Zabolotskaya [1] that model the transverse components of the particle motion in a collimated shear wave beam propagating in an isotropic elastic solid. Like the KZK equation, the parabolic equation for shear wave beams accounts consistently for the leading order effects of diffraction, viscosity and nonlinearity. The nonlinearity includes a cubic nonlinear term that is equivalent to that present in plane shear waves, as well as a quadratic nonlinear term that is unique to diffracting beams. The work by Wochner et al. [2] considered shear wave beams with translational polarizations (linear, circular and elliptical), wherein second-order nonlinear effects vanish and the leading order nonlinear effect is third-harmonic generation by the cubic nonlinearity. The purpose of the current work is to investigate the quadratic nonlinear term present in the parabolic equation for shear wave beams by considering second-harmonic generation in Gaussian beams as a second-order nonlinear effect using standard perturbation theory. In order for second-order nonlinear effects to be present, a broader class of source polarizations must be considered that includes not only the familiar translational polarizations, but also polarizations accounting for stretching, shearing and rotation of the source plane. It is found that the polarization of the second harmonic generated by the quadratic nonlinearity is not necessarily the same as the polarization of the source-frequency beam, and we are able to derive a general analytic solution for second-harmonic generation from a Gaussian source condition that gives explicitly the relationship between the polarization of the source-frequency beam and the polarization of the second harmonic.

High speed transition prediction

NASA Technical Reports Server (NTRS)

Gasperas, Gediminis

1992-01-01

The main objective of this work period was to develop, acquire and apply state-of-the-art tools for the prediction of transition at high speeds at NASA Ames. Although various stability codes as well as basic state codes were acquired, the development of a new Parabolized Stability Equation (PSE) code was minimal. The time that was initially allocated for development was used on other tasks, in particular for the Leading Edge Suction problem, in acquiring proficiency in various graphics tools, and in applying these tools to evaluate various Navier-Stokes and Euler solutions. The second objective of this work period was to attend the Transition and Turbulence Workshop at NASA Langley in July and August, 1991. A report on the Workshop follows. From July 8, 1991 to August 2, 1991, the author participated in the Transition and Turbulence Workshop at NASA Langley. For purposes of interest here, analysis can be said to consist of solving simplified governing equations by various analytical methods, such as asymptotic methods, or by use of very meager computer resources. From the composition of the various groups at the Workshop, it can be seen that analytical methods are generally more popular in Great Britain than they are in the U.S., possibly due to historical factors and the lack of computer resources. Experimenters at the Workshop were mostly concerned with subsonic flows, and a number of demonstrations were provided, among which were a hot-wire experiment to probe the boundary layer on a rotating disc, a hot-wire rake to map a free shear layer behind a cylinder, and the use of heating strips on a flat plate to control instability waves and consequent transition. A highpoint of the demonstrations was the opportunity to observe the rather noisy 'quiet' supersonic pilot tunnel in operation.

A hybridized method for computing high-Reynolds-number hypersonic flow about blunt bodies

NASA Technical Reports Server (NTRS)

Weilmuenster, K. J.; Hamilton, H. H., II

1979-01-01

A hybridized method for computing the flow about blunt bodies is presented. In this method the flow field is split into its viscid and inviscid parts. The forebody flow field about a parabolic body is computed. For the viscous solution, the Navier-Stokes equations are solved on orthogonal parabolic coordinates using explicit finite differencing. The inviscid flow is determined by using a Moretti type scheme in which the Euler equations are solved, using explicit finite differences, on a nonorthogonal coordinate system which uses the bow shock as an outer boundary. The two solutions are coupled along a common data line and are marched together in time until a converged solution is obtained. Computed results, when compared with experimental and analytical results, indicate the method works well over a wide range of Reynolds numbers and Mach numbers.

Shock-capturing parabolized Navier-Stokes model /SCIPVIS/ for the analysis of turbulent underexpanded jets

NASA Technical Reports Server (NTRS)

Dash, S. M.; Wolf, D. E.

1983-01-01

A new computational model, SCIPVIS, has been developed to predict the multiple-cell wave/shock structure in under or over-expanded turbulent jets. SCIPVIS solves the parabolized Navier-Stokes jet mixing equations utilizing a shock-capturing approach in supersonic regions of the jet and a pressure-split approach in subsonic regions. Turbulence processes are represented by the solution of compressibility corrected two-equation turbulence models. The formation of Mach discs in the jet and the interactive turbulent mixing process occurring behind the disc are handled in a detailed fashion. SCIPVIS presently analyzes jets exhausting into a quiescent or supersonic external stream for which a single-pass spatial marching solution can be obtained. The iterative coupling of SCIPVIS with a potential flow solver for the analysis of subsonic/transonic external streams is under development.

Double-Wronskian solitons and rogue waves for the inhomogeneous nonlinear Schrödinger equation in an inhomogeneous plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, Wen-Rong; Tian, Bo, E-mail: tian_bupt@163.com; Jiang, Yan

2014-04-15

Plasmas are the main constituent of the Universe and the cause of a vast variety of astrophysical, space and terrestrial phenomena. The inhomogeneous nonlinear Schrödinger equation is hereby investigated, which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and constant interactional damping. By virtue of the double Wronskian identities, the equation is proved to possess the double-Wronskian soliton solutions. Analytic one- and two-soliton solutions are discussed. Amplitude and velocity of the soliton are related to the damping coefficient. Asymptotic analysis is applied for us tomore » investigate the interaction between the two solitons. Overtaking interaction, head-on interaction and bound state of the two solitons are given. From the non-zero potential Lax pair, the first- and second-order rogue-wave solutions are constructed via a generalized Darboux transformation, and influence of the linear and parabolic density profiles on the background density and amplitude of the rogue wave is discussed. -- Highlights: •Double-Wronskian soliton solutions are obtained and proof is finished by virtue of some double Wronskian identities. •Asymptotic analysis is applied for us to investigate the interaction between the two solitons. •First- and second-order rogue-wave solutions are constructed via a generalized Darboux transformation. •Influence of the linear and parabolic density profiles on the background density and amplitude of the rogue wave is discussed.« less

Nearly Interactive Parabolized Navier-Stokes Solver for High Speed Forebody and Inlet Flows

NASA Technical Reports Server (NTRS)

Benson, Thomas J.; Liou, May-Fun; Jones, William H.; Trefny, Charles J.

2009-01-01

A system of computer programs is being developed for the preliminary design of high speed inlets and forebodies. The system comprises four functions: geometry definition, flow grid generation, flow solver, and graphics post-processor. The system runs on a dedicated personal computer using the Windows operating system and is controlled by graphical user interfaces written in MATLAB (The Mathworks, Inc.). The flow solver uses the Parabolized Navier-Stokes equations to compute millions of mesh points in several minutes. Sample two-dimensional and three-dimensional calculations are demonstrated in the paper.

Heat-transfer distributions on biconics at incidence in hypersonic-hypervelocity He, N2, air, and CO2 flows

NASA Technical Reports Server (NTRS)

Miller, C. G.; Micol, J. R.; Gnoffo, P. A.; Wilder, S. E.

1983-01-01

Laminar heat transfer rates were measured on spherically blunted, 13 deg/7 deg on axis and bent biconics (fore cone bent 7 deg upward relative to aft cone) at hypersonic hypervelocity flow conditions in the Langley Expansion Tube. Freestream velocities from 4.5 to 6.9 km/sec and Mach numbers from 6 to 9 were generated using helium, nitrogen, air, and carbon dioxide test gases, resulting in normal shock density ratios from 4 to 19. Angle of attack, referenced to the axis of the aft cone, was varied from 0 to 20 deg in 4 deg increments. The effect of nose bend, angle of attack, and real gas phenomena on heating distributions are presented along with comparisons of measurement to prediction from a code which solves the three dimensional parabolized Navier-Stokes equations.

Detailed Comparison of DNS to PSE for Oblique Breakdown at Mach 3

NASA Technical Reports Server (NTRS)

Mayer, Christian S. J.; Fasel, Hermann F.; Choudhari, Meelan; Chang, Chau-Lyan

2010-01-01

A pair of oblique waves at low amplitudes is introduced in a supersonic flat-plate boundary layer. Their downstream development and the concomitant process of laminar to turbulent transition is then investigated numerically using Direct Numerical Simulations (DNS) and Parabolized Stability Equations (PSE). This abstract is the last part of an extensive study of the complete transition process initiated by oblique breakdown at Mach 3. In contrast to the previous simulations, the symmetry condition in the spanwise direction is removed for the simulation presented in this abstract. By removing the symmetry condition, we are able to confirm that the flow is indeed symmetric over the entire computational domain. Asymmetric modes grow in the streamwise direction but reach only small amplitude values at the outflow. Furthermore, this abstract discusses new time-averaged data from our previous simulation CASE 3 and compares PSE data obtained from NASA's LASTRAC code to DNS results.

Wetting layer effect on impurity-related electronic properties of different (In,Ga)N QD-shapes

NASA Astrophysics Data System (ADS)

El Ghazi, Haddou; Jorio, Anouar; Zorkani, Izeddine; Feddi, El Mustapha; El Mouchtachi, Ahmed

2018-05-01

In this paper, we have investigated the electronic properties of (In,Ga)N/GaN coupled wetting layer-quantum dot system using the numerical approach. The finite element method code is used to solve the Schrödinger equation, in the presence of the impurity. In our model, parallelepiped-shape, circular and square based-pyramidal and their wetting layers embedded in GaN matrix were considered. Based on the single band parabolic and the effective mass approximations, the envelop function and its corresponding energy eigenvalue are obtained assuming a finite potential barrier. Our results reveal that: (1) the wetting layer has a great influence on the electronic properties especially for a small quantum dot and acts in the opposite sense of the geometrical confinement, (2) a wetting layer-dependent critical QD-size is obtained limiting two different behaviors and (3) its effect is strongly-dependent on the quantum dot-shape.

A refined finite element method for bending analysis of laminated plates integrated with piezoelectric fiber-reinforced composite actuators

NASA Astrophysics Data System (ADS)

Rouzegar, J.; Abbasi, A.

2018-03-01

This research presents a finite element formulation based on four-variable refined plate theory for bending analysis of cross-ply and angle-ply laminated composite plates integrated with a piezoelectric fiber-reinforced composite actuator under electromechanical loading. The four-variable refined plate theory is a simple and efficient higher-order shear deformation theory, which predicts parabolic variation of transverse shear stresses across the plate thickness and satisfies zero traction conditions on the plate free surfaces. The weak form of governing equations is derived using the principle of minimum potential energy, and a 4-node non-conforming rectangular plate element with 8 degrees of freedom per node is introduced for discretizing the domain. Several benchmark problems are solved by the developed MATLAB code and the obtained results are compared with those from exact and other numerical solutions, showing good agreement.

Numerical prediction of three-dimensional juncture region flow using the parabolic Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.; Orzechowski, J. A.

1979-01-01

A numerical solution algorithm is established for prediction of subsonic turbulent three-dimensional flows in aerodynamic configuration juncture regions. A turbulence closure model is established using the complete Reynolds stress. Pressure coupling is accomplished using the concepts of complementary and particular solutions to a Poisson equation. Specifications for data input juncture geometry modification are presented.

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for the Convective Wave Equation

NASA Technical Reports Server (NTRS)

Baumeister, K. J.; Kreider, K. L.

1996-01-01

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Parabolic equation for nonlinear acoustic wave propagation in inhomogeneous moving media

NASA Astrophysics Data System (ADS)

Aver'yanov, M. V.; Khokhlova, V. A.; Sapozhnikov, O. A.; Blanc-Benon, Ph.; Cleveland, R. O.

2006-12-01

A new parabolic equation is derived to describe the propagation of nonlinear sound waves in inhomogeneous moving media. The equation accounts for diffraction, nonlinearity, absorption, scalar inhomogeneities (density and sound speed), and vectorial inhomogeneities (flow). A numerical algorithm employed earlier to solve the KZK equation is adapted to this more general case. A two-dimensional version of the algorithm is used to investigate the propagation of nonlinear periodic waves in media with random inhomogeneities. For the case of scalar inhomogeneities, including the case of a flow parallel to the wave propagation direction, a complex acoustic field structure with multiple caustics is obtained. Inclusion of the transverse component of vectorial random inhomogeneities has little effect on the acoustic field. However, when a uniform transverse flow is present, the field structure is shifted without changing its morphology. The impact of nonlinearity is twofold: it produces strong shock waves in focal regions, while, outside the caustics, it produces higher harmonics without any shocks. When the intensity is averaged across the beam propagating through a random medium, it evolves similarly to the intensity of a plane nonlinear wave, indicating that the transverse redistribution of acoustic energy gives no considerable contribution to nonlinear absorption.

Helmholtz and parabolic equation solutions to a benchmark problem in ocean acoustics.

PubMed

Larsson, Elisabeth; Abrahamsson, Leif

2003-05-01

The Helmholtz equation (HE) describes wave propagation in applications such as acoustics and electromagnetics. For realistic problems, solving the HE is often too expensive. Instead, approximations like the parabolic wave equation (PE) are used. For low-frequency shallow-water environments, one persistent problem is to assess the accuracy of the PE model. In this work, a recently developed HE solver that can handle a smoothly varying bathymetry, variable material properties, and layered materials, is used for an investigation of the errors in PE solutions. In the HE solver, a preconditioned Krylov subspace method is applied to the discretized equations. The preconditioner combines domain decomposition and fast transform techniques. A benchmark problem with upslope-downslope propagation over a penetrable lossy seamount is solved. The numerical experiments show that, for the same bathymetry, a soft and slow bottom gives very similar HE and PE solutions, whereas the PE model is far from accurate for a hard and fast bottom. A first attempt to estimate the error is made by computing the relative deviation from the energy balance for the PE solution. This measure gives an indication of the magnitude of the error, but cannot be used as a strict error bound.

Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models

NASA Astrophysics Data System (ADS)

Giona, M.; Brasiello, A.; Crescitelli, S.

2015-11-01

One of the main differences between parabolic transport, associated with Langevin equations driven by Wiener processes, and hyperbolic models related to generalized Kac equations driven by Poisson processes, is the occurrence in the latter of multiple stable invariant densities (Frobenius multiplicity) in certain regions of the parameter space. This phenomenon is associated with the occurrence in linear hyperbolic balance equations of a typical bifurcation, referred to as the ergodicity-breaking bifurcation, the properties of which are thoroughly analyzed.

Approximate controllability of a system of parabolic equations with delay

NASA Astrophysics Data System (ADS)

Carrasco, Alexander; Leiva, Hugo

2008-09-01

In this paper we give necessary and sufficient conditions for the approximate controllability of the following system of parabolic equations with delay: where [Omega] is a bounded domain in , D is an n×n nondiagonal matrix whose eigenvalues are semi-simple with nonnegative real part, the control and B[set membership, variant]L(U,Z) with , . The standard notation zt(x) defines a function from [-[tau],0] to (with x fixed) by zt(x)(s)=z(t+s,x), -[tau][less-than-or-equals, slant]s[less-than-or-equals, slant]0. Here [tau][greater-or-equal, slanted]0 is the maximum delay, which is supposed to be finite. We assume that the operator is linear and bounded, and [phi]0[set membership, variant]Z, [phi][set membership, variant]L2([-[tau],0];Z). To this end: First, we reformulate this system into a standard first-order delay equation. Secondly, the semigroup associated with the first-order delay equation on an appropriate product space is expressed as a series of strongly continuous semigroups and orthogonal projections related with the eigenvalues of the Laplacian operator (); this representation allows us to reduce the controllability of this partial differential equation with delay to a family of ordinary delay equations. Finally, we use the well-known result on the rank condition for the approximate controllability of delay system to derive our main result.

Nonlocal operators, parabolic-type equations, and ultrametric random walks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chacón-Cortes, L. F., E-mail: fchaconc@math.cinvestav.edu.mx; Zúñiga-Galindo, W. A., E-mail: wazuniga@math.cinvestav.edu.mx

2013-11-15

In this article, we introduce a new type of nonlocal operators and study the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated to these operators. Some of these equations are the p-adic master equations of certain models of complex systems introduced by Avetisov, V. A. and Bikulov, A. Kh., “On the ultrametricity of the fluctuation dynamicmobility of protein molecules,” Proc. Steklov Inst. Math. 265(1), 75–81 (2009) [Tr. Mat. Inst. Steklova 265, 82–89 (2009) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Zubarev, A. P., “First passage time distribution and the numbermore » of returns for ultrametric random walks,” J. Phys. A 42(8), 085003 (2009); Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic models of ultrametric diffusion in the conformational dynamics of macromolecules,” Proc. Steklov Inst. Math. 245(2), 48–57 (2004) [Tr. Mat. Inst. Steklova 245, 55–64 (2004) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic description of characteristic relaxation in complex systems,” J. Phys. A 36(15), 4239–4246 (2003); Avetisov, V. A., Bikulov, A. H., Kozyrev, S. V., and Osipov, V. A., “p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes,” J. Phys. A 35(2), 177–189 (2002); Avetisov, V. A., Bikulov, A. Kh., and Kozyrev, S. V., “Description of logarithmic relaxation by a model of a hierarchical random walk,” Dokl. Akad. Nauk 368(2), 164–167 (1999) (in Russian). The fundamental solutions of these parabolic-type equations are transition functions of random walks on the n-dimensional vector space over the field of p-adic numbers. We study some properties of these random walks, including the first passage time.« less

On two parabolic systems: Convergence and blowup

NASA Astrophysics Data System (ADS)

Huang, Yamin

1998-12-01

This dissertation studies two parabolic systems. It consists of two parts. In part one (chapter one), we prove a convergence result, namely, the solution (AK,/ BK) of a system of chemical diffusion-reaction equations (with reaction rate K) converges to the solution (A, B) of a diffusion- instantaneous-reaction equation. To prove our main result, we use some L1 and L2 'energy' estimates and a compactness result due to Aubin (1). As a by-product we also prove that as K approaches infinity, the limit solution exhibits phase separation between A and B. In part two (chapter two), we study the blowup rate for a system of heat equations ut=/Delta u,/ vt=/Delta v in a bounded domain Ωtimes(0,T) coupled in the nonlinear Neumann boundary conditions [/partial u/over/partial n]=vp,/ [/partial v/over/partial n]=uq on ∂Omega×[ 0,T), where p>0,/ q>0,/ pq>1 and n is the exterior normal vector on ∂Omega. Under certain assumptions, we establish exact blowup rate which generalizes the corresponding results of some authors' recent work including Deng (2), Deng-Fila-Levine (3) and Hu-Yin (4). ftn (1) J. P. A scUBIN, Un theoreme de compacite, C. R. Acad. Sci., 256(1963), pp. 5042-5044. (2) K. D scENG, Blow-up rates for parabolic systems, Z. Angew. Math. Phys., 47(1996), No. 1, pp. 132-143. (3) K. D scENG, M. F scILA AND H. A. L scEVINE, On critical exponents for a system of heat equations coupled in the boundary conditions, Acta Math. Univ. Comenian. (N.S.), 36(1994), No. 2, pp. 169-192. (4) B. H scU scAND H. M. Y scIN, The profile near blowup time for solutions of the heat equation with a nonlinear boundary condition, Trans. Amer. Math. Soc., 346(1994), pp. 117-135.

Optical solitons to the resonance nonlinear Schrödinger equation by Sine-Gordon equation method

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru

2018-01-01

In this paper, we examined the optical solitons to the resonant nonlinear Schrödinger equation (R-NLSE) which describes the propagation of solitons through optical fibers. Three types of nonlinear media fibers are studied. They are; quadratic-cubic law, Kerr law and parabolic law. Dark, bright, dark-bright or combined optical and singular soliton solutions are derived using the sine-Gordon equation method (SGEM). The constraint conditions that naturally fall out of the solution structure which guarantee the existence of these solitons are also reported.

Parabolic transformation cloaks for unbounded and bounded cloaking of matter waves

NASA Astrophysics Data System (ADS)

Chang, Yu-Hsuan; Lin, De-Hone

2014-01-01

Parabolic quantum cloaks with unbounded and bounded invisible regions are presented with the method of transformation design. The mass parameters of particles for perfect cloaking are shown to be constant along the parabolic coordinate axes of the cloaking shells. The invisibility performance of the cloaks is inspected from the viewpoints of waves and probability currents. The latter shows the controllable characteristic of a probability current by a quantum cloak. It also provides us with a simpler and more efficient way of exhibiting the performance of a quantum cloak without the solutions of the transformed wave equation. Through quantitative analysis of streamline structures in the cloaking shell, one defines the efficiency of the presented quantum cloak in the situation of oblique incidence. The cloaking models presented here give us more choices for testing and applying quantum cloaking.

Enforcing the Courant–Friedrichs–Lewy condition in explicitly conservative local time stepping schemes

DOE PAGES

Gnedin, Nickolay Y.; Semenov, Vadim A.; Kravtsov, Andrey V.

2018-01-30

In this study, an optimally efficient explicit numerical scheme for solving fluid dynamics equations, or any other parabolic or hyperbolic system of partial differential equations, should allow local regions to advance in time with their own, locally constrained time steps. However, such a scheme can result in violation of the Courant-Friedrichs-Lewy (CFL) condition, which is manifestly non-local. Although the violations can be considered to be "weak" in a certain sense and the corresponding numerical solution may be stable, such calculation does not guarantee the correct propagation speed for arbitrary waves. We use an experimental fluid dynamics code that allows cubicmore » "patches" of grid cells to step with independent, locally constrained time steps to demonstrate how the CFL condition can be enforced by imposing a condition on the time steps of neighboring patches. We perform several numerical tests that illustrate errors introduced in the numerical solutions by weak CFL condition violations and show how strict enforcement of the CFL condition eliminates these errors. In all our tests the strict enforcement of the CFL condition does not impose a significant performance penalty.« less

Stabilization of numerical interchange in spectral-element magnetohydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sovinec, C. R.

In this study, auxiliary numerical projections of the divergence of flow velocity and vorticity parallel to magnetic field are developed and tested for the purpose of suppressing unphysical interchange instability in magnetohydrodynamic simulations. The numerical instability arises with equal-order C 0 finite- and spectral-element expansions of the flow velocity, magnetic field, and pressure and is sensitive to behavior at the limit of resolution. The auxiliary projections are motivated by physical field-line bending, and coercive responses to the projections are added to the flow-velocity equation. Their incomplete expansions are limited to the highest-order orthogonal polynomial in at least one coordinate ofmore » the spectral elements. Cylindrical eigenmode computations show that the projections induce convergence from the stable side with first-order ideal-MHD equations during h-refinement and p-refinement. Hyperbolic and parabolic projections and responses are compared, together with different methods for avoiding magnetic divergence error. Lastly, the projections are also shown to be effective in linear and nonlinear time-dependent computations with the NIMROD code [C. R. Sovinec, et al., J. Comput. Phys. 195 (2004) 355-386], provided that the projections introduce numerical dissipation.« less

Stabilization of numerical interchange in spectral-element magnetohydrodynamics

DOE PAGES

Sovinec, C. R.

2016-05-10

In this study, auxiliary numerical projections of the divergence of flow velocity and vorticity parallel to magnetic field are developed and tested for the purpose of suppressing unphysical interchange instability in magnetohydrodynamic simulations. The numerical instability arises with equal-order C 0 finite- and spectral-element expansions of the flow velocity, magnetic field, and pressure and is sensitive to behavior at the limit of resolution. The auxiliary projections are motivated by physical field-line bending, and coercive responses to the projections are added to the flow-velocity equation. Their incomplete expansions are limited to the highest-order orthogonal polynomial in at least one coordinate ofmore » the spectral elements. Cylindrical eigenmode computations show that the projections induce convergence from the stable side with first-order ideal-MHD equations during h-refinement and p-refinement. Hyperbolic and parabolic projections and responses are compared, together with different methods for avoiding magnetic divergence error. Lastly, the projections are also shown to be effective in linear and nonlinear time-dependent computations with the NIMROD code [C. R. Sovinec, et al., J. Comput. Phys. 195 (2004) 355-386], provided that the projections introduce numerical dissipation.« less

Nonuniform depth grids in parabolic equation solutions.

PubMed

Sanders, William M; Collins, Michael D

2013-04-01

The parabolic wave equation is solved using a finite-difference solution in depth that involves a nonuniform grid. The depth operator is discretized using Galerkin's method with asymmetric hat functions. Examples are presented to illustrate that this approach can be used to improve efficiency for problems in ocean acoustics and seismo-acoustics. For shallow water problems, accuracy is sensitive to the precise placement of the ocean bottom interface. This issue is often addressed with the inefficient approach of using a fine grid spacing over all depth. Efficiency may be improved by using a relatively coarse grid with nonuniform sampling to precisely position the interface. Efficiency may also be improved by reducing the sampling in the sediment and in an absorbing layer that is used to truncate the computational domain. Nonuniform sampling may also be used to improve the implementation of a single-scattering approximation for sloping fluid-solid interfaces.

Chaos and wave propagation regimes

NASA Astrophysics Data System (ADS)

Colosi, John

2003-04-01

Ray chaos theory and parabolic equation numerical modeling were two thrusts of Fred Tappert's research that were perpetually in tension. Fred was interested in the problem of identifying wave propagation regimes, most notably the strong focusing caustic regime and its evolution into the saturation regime. On the one hand, chaos theory held the seed of the complexity Fred believed existed in ocean acoustic wavefields; on the other hand ocean acoustic ray chaos theory (which Fred helped to pioneer) was a disdainful approximation to the full wave treatments offered by parabolic equation calculations. Fred was convinced that the saturation limit could not be obtained using ray theory and therefore he examined a new field of inquiry: a blend of chaotic ray insight and full wave dynamics called wave chaos. This talk will discuss some of Fred's insights on this topic and how they relate to observations from basin scale acoustic transmissions.

Weakly nonparallel and curvature effects on stationary crossflow instability: Comparison of results from multiple-scales analysis and parabolized stability equations

NASA Technical Reports Server (NTRS)

Singer, Bart A.; Choudhari, Meelan; Li, Fei

1995-01-01

A multiple-scales approach is used to approximate the effects of nonparallelism and streamwise surface curvature on the growth of stationary crossflow vortices in incompressible, three-dimesional boundary layers. The results agree with results predicted by solving the parabolized stability equations in regions where the nonparallelism is sufficiently weak. As the nonparallelism increases, the agreement between the two approaches worsens. An attempt has been made to quantify the nonparallelism on flow stability in terms of a nondimensional number that describes the rate of change of the mean flow relative to the disturbance wavelength. We find that the above nondimensional number provides useful information about the adequacy of the multiple-scales approximation for different disturbances for a given flow geometry, but the number does not collapse data for different flow geometries onto a single curve.

Spatial optimal disturbances in swept-wing boundary layers

NASA Astrophysics Data System (ADS)

Chen, Cheng

2018-04-01

With the use of the adjoint-based optimization method proposed by Tempelmann et al. (J. Fluid Mech., vol. 704, 2012, pp. 251-279), in which the parabolized stability equation (PSE) and so-called adjoint parabolized stability equation (APSE) are solved iteratively, we obtain the spatial optimal disturbance shape and investigate its dependence on the parameters of disturbance wave and wall condition, such as radial frequency ω and wall temperature Twall, in a swept-wing boundary layer flow. Further, the non-modal growth mechanism of this optimal disturbance has been also discussed, regarding its spatial evolution way in the streamwise direction. The results imply that the spanwise wavenumber, disturbance frequency and wall cooling do not change the physical mechanism of perturbation growth, just with a substantial effect on the magnitude of perturbation growth. Further, wall cooling may have enhancing or suppressing effect on spatial optimal disturbance growth, depending on the streamwise location.

Parallel SOR methods with a parabolic-diffusion acceleration technique for solving an unstructured-grid Poisson equation on 3D arbitrary geometries

NASA Astrophysics Data System (ADS)

Zapata, M. A. Uh; Van Bang, D. Pham; Nguyen, K. D.

2016-05-01

This paper presents a parallel algorithm for the finite-volume discretisation of the Poisson equation on three-dimensional arbitrary geometries. The proposed method is formulated by using a 2D horizontal block domain decomposition and interprocessor data communication techniques with message passing interface. The horizontal unstructured-grid cells are reordered according to the neighbouring relations and decomposed into blocks using a load-balanced distribution to give all processors an equal amount of elements. In this algorithm, two parallel successive over-relaxation methods are presented: a multi-colour ordering technique for unstructured grids based on distributed memory and a block method using reordering index following similar ideas of the partitioning for structured grids. In all cases, the parallel algorithms are implemented with a combination of an acceleration iterative solver. This solver is based on a parabolic-diffusion equation introduced to obtain faster solutions of the linear systems arising from the discretisation. Numerical results are given to evaluate the performances of the methods showing speedups better than linear.

Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

PubMed

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.

CHOLLA: A New Massively Parallel Hydrodynamics Code for Astrophysical Simulation

NASA Astrophysics Data System (ADS)

Schneider, Evan E.; Robertson, Brant E.

2015-04-01

We present Computational Hydrodynamics On ParaLLel Architectures (Cholla ), a new three-dimensional hydrodynamics code that harnesses the power of graphics processing units (GPUs) to accelerate astrophysical simulations. Cholla models the Euler equations on a static mesh using state-of-the-art techniques, including the unsplit Corner Transport Upwind algorithm, a variety of exact and approximate Riemann solvers, and multiple spatial reconstruction techniques including the piecewise parabolic method (PPM). Using GPUs, Cholla evolves the fluid properties of thousands of cells simultaneously and can update over 10 million cells per GPU-second while using an exact Riemann solver and PPM reconstruction. Owing to the massively parallel architecture of GPUs and the design of the Cholla code, astrophysical simulations with physically interesting grid resolutions (≳2563) can easily be computed on a single device. We use the Message Passing Interface library to extend calculations onto multiple devices and demonstrate nearly ideal scaling beyond 64 GPUs. A suite of test problems highlights the physical accuracy of our modeling and provides a useful comparison to other codes. We then use Cholla to simulate the interaction of a shock wave with a gas cloud in the interstellar medium, showing that the evolution of the cloud is highly dependent on its density structure. We reconcile the computed mixing time of a turbulent cloud with a realistic density distribution destroyed by a strong shock with the existing analytic theory for spherical cloud destruction by describing the system in terms of its median gas density.

Parameter estimation problems for distributed systems using a multigrid method

NASA Technical Reports Server (NTRS)

Ta'asan, Shlomo; Dutt, Pravir

1990-01-01

The problem of estimating spatially varying coefficients of partial differential equations is considered from observation of the solution and of the right hand side of the equation. It is assumed that the observations are distributed in the domain and that enough observations are given. A method of discretization and an efficient multigrid method for solving the resulting discrete systems are described. Numerical results are presented for estimation of coefficients in an elliptic and a parabolic partial differential equation.

Weak Solution Classes for Parabolic Integro-Differential Equations

DTIC Science & Technology

1982-09-01

different existence argument for solutions of (I). It is partly based on a method that was used in (2) and (6] to treat a Hilbert - space version of (I) and...xx Differential Equations 35 (1980), 200-231. 121 V. Barbut Integro-Oifferential Squatton. in Hilbert Spaces. Ann. St. Univ. *Al. 1. Cuaxa 19 (1973... Greenberg : O,% the Existence, Uniqueness, and stability of the Equation 00 Xtt - 3(XX)X) AX *x . J Math. Anal. Appl. 25 (1969), S75-591. (131 7

ASYMPTOTIC STEADY-STATE SOLUTION TO A BOW SHOCK WITH AN INFINITE MACH NUMBER

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yalinewich, Almog; Sari, Re’em

2016-08-01

The problem of a cold gas flowing past a stationary obstacle is considered. We study the bow shock that forms around the obstacle and show that at large distances from the obstacle the shock front forms a parabolic solid of revolution. The profiles of the hydrodynamic variables in the interior of the shock are obtained by solution of the hydrodynamic equations in parabolic coordinates. The results are verified with a hydrodynamic simulation. The drag force on the obstacle is also calculated. Finally, we use these results to model the bow shock around an isolated neutron star.

On the parallel solution of parabolic equations

NASA Technical Reports Server (NTRS)

Gallopoulos, E.; Saad, Youcef

1989-01-01

Parallel algorithms for the solution of linear parabolic problems are proposed. The first of these methods is based on using polynomial approximation to the exponential. It does not require solving any linear systems and is highly parallelizable. The two other methods proposed are based on Pade and Chebyshev approximations to the matrix exponential. The parallelization of these methods is achieved by using partial fraction decomposition techniques to solve the resulting systems and thus offers the potential for increased time parallelism in time dependent problems. Experimental results from the Alliant FX/8 and the Cray Y-MP/832 vector multiprocessors are also presented.

Summation by parts, projections, and stability

NASA Technical Reports Server (NTRS)

Olsson, Pelle

1993-01-01

We have derived stability results for high-order finite difference approximations of mixed hyperbolic-parabolic initial-boundary value problems (IBVP). The results are obtained using summation by parts and a new way of representing general linear boundary conditions as an orthogonal projection. By slightly rearranging the analytic equations, we can prove strict stability for hyperbolic-parabolic IBVP. Furthermore, we generalize our technique so as to yield strict stability on curvilinear non-smooth domains in two space dimensions. Finally, we show how to incorporate inhomogeneous boundary data while retaining strict stability. Using the same procedure one can prove strict stability in higher dimensions as well.

Enhanced propagation modeling of directional aviation noise: A hybrid parabolic equation-fast field program method

NASA Astrophysics Data System (ADS)

Rosenbaum, Joyce E.

2011-12-01

Commercial air traffic is anticipated to increase rapidly in the coming years. The impact of aviation noise on communities surrounding airports is, therefore, a growing concern. Accurate prediction of noise can help to mitigate the impact on communities and foster smoother integration of aerospace engineering advances. The problem of accurate sound level prediction requires careful inclusion of all mechanisms that affect propagation, in addition to correct source characterization. Terrain, ground type, meteorological effects, and source directivity can have a substantial influence on the noise level. Because they are difficult to model, these effects are often included only by rough approximation. This dissertation presents a model designed for sound propagation over uneven terrain, with mixed ground type and realistic meteorological conditions. The model is a hybrid of two numerical techniques: the parabolic equation (PE) and fast field program (FFP) methods, which allow for physics-based inclusion of propagation effects and ensure the low frequency content, a factor in community impact, is predicted accurately. Extension of the hybrid model to a pseudo-three-dimensional representation allows it to produce aviation noise contour maps in the standard form. In order for the model to correctly characterize aviation noise sources, a method of representing arbitrary source directivity patterns was developed for the unique form of the parabolic equation starting field. With this advancement, the model can represent broadband, directional moving sound sources, traveling along user-specified paths. This work was prepared for possible use in the research version of the sound propagation module in the Federal Aviation Administration's new standard predictive tool.

Wind Code Application to External Forebody Flowfields with Comparisons to Experimental Results

NASA Technical Reports Server (NTRS)

Frate, F. C.; Kim, H. D.

2001-01-01

The WIND Code, a general purpose Navier-Stokes solver, has been utilized to obtain supersonic external flowfield Computational Fluid Dynamics (CFD) solutions over an axisymmetric, parabolic forebody with comparisons made to wind tunnel experimental results. Various cases have been investigated at supersonic freestream conditions ranging from Mach 2.0 to 3.5, at 0 deg and 3 deg angles-of-attack, and with either a sharp-nose or blunt-nose forebody configuration. Both a turbulent (Baldwin-Lomax algebraic turbulence model) and a laminar model have been implemented in the CFD. Obtaining the solutions involved utilizing either the parabolized- or full-Navier-Stokes analyses supplied in WIND. Comparisons have been made with static pressure measurements, with boundary-layer rake and flowfield rake pitot pressure measurements, and with temperature sensitive paint experimental results. Using WIND's parabolized Navier-Stokes capability, grid sequencing, and the Baldwin-Lomax algebraic turbulence model allowed for significant reductions in computational time while still providing good agreement with experiment. Given that CFD and experiment compare well, WIND is found to be a good computational platform for solving this type of forebody problem, and the grids developed in conjunction with it will be used in the future to investigate varying freestream conditions not tested experimentally.

The numerical modelling of MHD astrophysical flows with chemistry

NASA Astrophysics Data System (ADS)

Kulikov, I.; Chernykh, I.; Protasov, V.

2017-10-01

The new code for numerical simulation of magnetic hydrodynamical astrophysical flows with consideration of chemical reactions is given in the paper. At the heart of the code - the new original low-dissipation numerical method based on a combination of operator splitting approach and piecewise-parabolic method on the local stencil. The chemodynamics of the hydrogen while the turbulent formation of molecular clouds is modeled.

Calculation of three dimensional viscous flows in annular cascades using parabolized Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Lawerenz, M.

Numerical algorithms for describing the endwall boundary layers and secondary flows in high turning turbine cascades are described. Partially-parabolic methods which cover three-dimensional viscous flow effects are outlined. Introduction of tip-clearance models and modifications of no-slip conditions without the use of wall functions expand the range of application and improve accuracy. Simultaneous computation of the profile boundary layers by refinement of the mesh size in the circumferential direction makes it possible to describe the boundary layer interaction in the corners formed by the bladings and the endwalls. The partially-parabolic method means that the streamwise elliptic coupling is well represented by the given pressure field and that separation does not occur, but it is not possible to describe the separation of the endwall boundary layer near the leading edge and the horse-shoe vortex there properly.

The well-posedness of the Kuramoto-Sivashinsky equation

NASA Technical Reports Server (NTRS)

Tadmor, E.

1984-01-01

The Kuramoto-Sivashinsky equation arises in a variety of applications, among which are modeling reaction diffusion systems, flame propagation and viscous flow problems. It is considered here, as a prototype to the larger class of generalized Burgers equations: those consist of a quadratic nonlinearity and an arbitrary linear parabolic part. It is shown that such equations are well posed, thus admitting a unique smooth solution, continuously dependent on its initial data. As an attractive alternative to standard energy methods, existence and stability are derived in this case, by patching in the large short time solutions without loss of derivatives.

The well-posedness of the Kuramoto-Sivashinsky equation

NASA Technical Reports Server (NTRS)

Tadmor, E.

1986-01-01

The Kuramoto-Sivashinsky equation arises in a variety of applications, among which are modeling reaction diffusion systems, flame propagation and viscous flow problems. It is considered here, as a prototype to the larger class of generalized Burgers equations: those consist of a quadratic nonlinearity and an arbitrary linear parabolic part. It is shown that such equations are well posed, thus admitting a unique smooth solution, continuously dependent on its initial data. As an attractive alternative to standard energy methods, existence and stability are derived in this case, by patching in the large short time solutions without 'loss of derivatives'.

Analytical and numerical solutions of the equation for the beam propagation in a photovoltaic-photorefractive media

NASA Astrophysics Data System (ADS)

Lin, Ji; Wang, Hou

2013-07-01

We use the classical Lie-group method to study the evolution equation describing a photovoltaic-photorefractive media with the effects of diffusion process and the external electric field. We reduce it to some similarity equations firstly, and then obtain some analytically exact solutions including the soliton solution, the exponential solution and the oscillatory solution. We also obtain the numeric solitons from these similarity equations. Moreover, We show theoretically that these solutions have two types of trajectories. One type is a straight line. The other is a parabolic curve, which indicates these solitons have self-deflection.

Acoustic Microscopy and Nonlinear Effects in Pressurized Superfluid Helium

DTIC Science & Technology

1993-08-31

Fresnel or parabolic approxi nations [16,17]. With the development of the Khokhlov-Zabolotskaya-Kuznetsov ( KZK ) paratolic equation [18,191, which...sound waves in a thermoviscous liquid by means of the KZK equation. (2) Hart and Hamilton [261 employed a con- vergent coordinate system that...improves the efficiency of the numerical solution of the KZK equa- tion for focused beams. (3) Lucas and Muir [27] developed an equivalency relationship

An approximation theory for nonlinear partial differential equations with applications to identification and control

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kunisch, K.

1982-01-01

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

Dielectric response properties of parabolically-confined nanostructures in a quantizing magnetic field

NASA Astrophysics Data System (ADS)

Sabeeh, Kashif

This thesis presents theoretical studies of dielectric response properties of parabolically-confined nanostructures in a magnetic field. We have determined the retarded Schrodinger Green's function for an electron in such a parabolically confined system in the presence of a time dependent electric field and an ambient magnetic field. Following an operator equation of motion approach developed by Schwinger, we calculate the result in closed form in terms of elementary functions in direct-time representation. From the retarded Schrodinger Green's function we construct the closed-form thermodynamic Green's function for a parabolically confined quantum-dot in a magnetic field to determine its plasmon spectrum. Due to confinement and Landau quantization this system is fully quantized, with an infinite number of collective modes. The RPA integral equation for the inverse dielectric function is solved using Fredholm theory in the nondegenerate and quantum limit to determine the frequencies with which the plasmons participate in response to excitation by an external potential. We exhibit results for the variation of plasmon frequency as a function of magnetic field strength and of confinement frequency. A calculation of the van der Waals interaction energy between two harmonically confined quantum dots is discussed in terms of the dipole-dipole correlation function. The results are presented as a function of confinement strength and distance between the dots. We also rederive a result of Fertig & Halperin [32] for the tunneling-scattering of an electron through a saddle potential which is also known as a quantum point contact (QPC), in the presence of a magnetic field. Using the retarded Green's function we confirm the result for the transmission coefficient and analyze it.

Simulation of Structures Exhibiting Instability Under Thermal-Mechanical Transient Loading

DTIC Science & Technology

2015-08-25

4 2.1.4 Application to half- sine arches...shallow arches ....................................................... 9 2.2.2 Half- sine arches... sine arches, parabolic arches and cylindrical panels. 2.1 Arches with Geometric Imperfections The nonlinear equilibrium and buckling equations are

An investigation of underwater sound propagation from pile driving.

DOT National Transportation Integrated Search

2011-12-01

The underwater noise from impact pile driving was studied by using a finite element model for the sound generation and a parabolic equation model for propagation. Results were compared with measurements taken with a vertical line array deployed durin...

Problems in Nonlinear Acoustics: Pulsed Finite Amplitude Sound Beams, Nonlinear Propagation of Sound in Layered Media, Time Domain Solutions for Focused Sound Beams, Focusing of Sound with an Ellipsoidal Mirror, and Modeling Finite Amplitude Propagation in Waveguides.

DTIC Science & Technology

1991-08-01

performed entirely in the time domain, solves the KZK (Khokhlov-Zabolotskaya-Kuznetsov) nonlinear parabolic wdve equation for pulsed, axisymmetric...finite amplitude sound beams. The KZK equation accounts for the combined effects of nonlinearity, diffraction and thermoviscous absorption on the...those used by Naze Tjotta, Tjotta, and Vefring to produce Fig. 7 of Ref. 4 with a frequency domain numerical solution of the KZK equation. However

Generation of three-dimensional body-fitted grids by solving hyperbolic and parabolic partial differential equations

NASA Technical Reports Server (NTRS)

Steger, Joseph L.

1989-01-01

Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.

Chaotic motion of comets in near-parabolic orbit: Mapping aproaches

NASA Astrophysics Data System (ADS)

Liu, Jie; Sun, Yi-Sui

1994-09-01

There exist many comets with near-parabolic orbits in the solar system. Among various theories proposed to explain their origin, the Oort cloud hypothesis seems to be the most reasonable. The theory assumes that there is a cometary cloud at a distance 103 to 107 from the sun and that perturbing forces from planets or stars make orbits of some of these comets become the near-parabolic type. Concerning the evolution of these orbits under planetary perturbations, we can raise the question: Will they stay in the solar system forever or will they escape from it? This is an attractive dynamical problem. If we go ahead by directly solving the dynamical differential equations, we may encounter the difficulty of long-time computation. For the orbits of these comets are near-parabolic and their periods are too long to study on their long-term evolution. With mapping approaches the difficulty will be overcome. In another aspect, the study of this model has special meaning for chaotic dynamics. We know that in the neighborhood of any separatrix i.e. the trajectory with zero frequency of the uperturbed motion of a Hamiltonian system, some chaotic motions have to be expected. Actually, the simplest example of separatrix is the parabolic trajectory of the two-body problem which separates the bounded and unbounded motion. From this point of view, the dynamical study of near-parabolic motion is very important. Petrosky's elegant but more abstract deduction gives a Kepler mapping which describes the dynamics of the cometary motion. In this paper we derive a similar mapping directly and discuss its dynamical characters.

Optimal discrete-time LQR problems for parabolic systems with unbounded input: Approximation and convergence

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An abstract approximation and convergence theory for the closed-loop solution of discrete-time linear-quadratic regulator problems for parabolic systems with unbounded input is developed. Under relatively mild stabilizability and detectability assumptions, functional analytic, operator techniques are used to demonstrate the norm convergence of Galerkin-based approximations to the optimal feedback control gains. The application of the general theory to a class of abstract boundary control systems is considered. Two examples, one involving the Neumann boundary control of a one-dimensional heat equation, and the other, the vibration control of a cantilevered viscoelastic beam via shear input at the free end, are discussed.

Spectral methods for time dependent partial differential equations

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1983-01-01

The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.

Simulations of nonlinear continuous wave pressure fields in FOCUS

NASA Astrophysics Data System (ADS)

Zhao, Xiaofeng; Hamilton, Mark F.; McGough, Robert J.

2017-03-01

The Khokhlov - Zabolotskaya - Kuznetsov (KZK) equation is a parabolic approximation to the Westervelt equation that models the effects of diffraction, attenuation, and nonlinearity. Although the KZK equation is only valid in the far field of the paraxial region for mildly focused or unfocused transducers, the KZK equation is widely applied in medical ultrasound simulations. For a continuous wave input, the KZK equation is effectively modeled by the Bergen Code [J. Berntsen, Numerical Calculations of Finite Amplitude Sound Beams, in M. F. Hamilton and D. T. Blackstock, editors, Frontiers of Nonlinear Acoustics: Proceedings of 12th ISNA, Elsevier, 1990], which is a finite difference model that utilizes operator splitting. Similar C++ routines have been developed for FOCUS, the `Fast Object-Oriented C++ Ultrasound Simulator' (http://www.egr.msu.edu/˜fultras-web) to calculate nonlinear pressure fields generated by axisymmetric flat circular and spherically focused ultrasound transducers. This new routine complements an existing FOCUS program that models nonlinear ultrasound propagation with the angular spectrum approach [P. T. Christopher and K. J. Parker, J. Acoust. Soc. Am. 90, 488-499 (1991)]. Results obtained from these two nonlinear ultrasound simulation approaches are evaluated and compared for continuous wave linear simulations. The simulation results match closely in the farfield of the paraxial region, but the results differ in the nearfield. The nonlinear pressure field generated by a spherically focused transducer with a peak surface pressure of 0.2MPa radiating in a lossy medium with β = 3.5 is simulated, and the computation times are also evaluated. The nonlinear simulation results demonstrate acceptable agreement in the focal zone. These two related nonlinear simulation approaches are now included with FOCUS to enable convenient simulations of nonlinear pressure fields on desktop and laptop computers.

Coalescing neutron stars - gravitational waves from polytropic models.

NASA Astrophysics Data System (ADS)

Ruffert, M.; Rampp, M.; Janka, H.-T.

1997-05-01

The dynamics, time evolution of the mass distribution, and gravitational wave signature of coalescing neutron stars described by polytropes are compared with three simulations published previously: (a) "Run 2" of Zhuge et al. (1994PhRvD..50.6247Z), (b) "Model III" of Shibata et al. (1992, Prog, Theor. Phys. 88, 1079), and (c) "Model A64" of Ruffert et al. (1996A&A...311..532R). We aim at studying the differences due to the use of different numerical methods, different implementations of the gravitational wave backreaction, and different equations of state. We integrate the three-dimensional Newtonian equations of hydrodynamics by the Riemann-solver based "Piecewise Parabolic Method" on an equidistant Cartesian grid. Comparison (a) confronts the results of our grid-based PPM scheme with those from an SPH code. We find that due to the lower numerical viscosity of the PPM code, the post-merging oscillations and pulsations can be followed for a longer time and lead to larger secondary and tertiary maxima of the gravitational wave luminosity and to a stronger peak of the gravitational wave spectrum at a frequency of about f=~1.8KHz when compared to the results of Zhuge et al. (1994PhRvD..50.6247Z). In case (b) two grid based codes with the same backreaction formalism but differing hydrodynamic integrators and slightly different initial conditions are compared. Instead of rotationally deformed initial neutron stars we use spherically shaped stars. Satisfactory agreement of the amplitude of the gravitational wave luminosity is established, although due to the different initial conditions a small time delay develops in the onset of the dynamical instability setting in when the two stars come very close. In (c) we find that using a polytropic equation of state instead of the high-density equation of state of Lattimer & Swesty (1991, Nucl. Phys. A535, 331) employed by Ruffert et al. (1996A&A...311..532R) does not change the overall dynamical evolution of the merger and yields agreement of the gravitational wave signature to within 20% accuracy. Whereas the polytropic law describes the dynamical behaviour of the bulk of the matter at and above nuclear density sufficiently well, we, however, find clear differences of the structure and evolution of the outer layers of the neutron stars where the stiffness of the equation of state is largely overestimated. This has important implications for questions like mass loss and disk formation during the merging of binary neutron stars.

Time-Dependent Parabolic Finite Difference Formulation for Harmonic Sound Propagation in a Two-Dimensional Duct with Flow

NASA Technical Reports Server (NTRS)

Kreider, Kevin L.; Baumeister, Kenneth J.

1996-01-01

An explicit finite difference real time iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for future large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable for a harmonic monochromatic sound field, a parabolic (in time) approximation is introduced to reduce the order of the governing equation. The analysis begins with a harmonic sound source radiating into a quiescent duct. This fully explicit iteration method then calculates stepwise in time to obtain the 'steady state' harmonic solutions of the acoustic field. For stability, applications of conventional impedance boundary conditions requires coupling to explicit hyperbolic difference equations at the boundary. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for Aircraft Acoustic Nacelle Design

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1996-01-01

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

A note on the regularity of solutions of infinite dimensional Riccati equations

NASA Technical Reports Server (NTRS)

Burns, John A.; King, Belinda B.

1994-01-01

This note is concerned with the regularity of solutions of algebraic Riccati equations arising from infinite dimensional LQR and LQG control problems. We show that distributed parameter systems described by certain parabolic partial differential equations often have a special structure that smoothes solutions of the corresponding Riccati equation. This analysis is motivated by the need to find specific representations for Riccati operators that can be used in the development of computational schemes for problems where the input and output operators are not Hilbert-Schmidt. This situation occurs in many boundary control problems and in certain distributed control problems associated with optimal sensor/actuator placement.

Efficient numerical method for solving Cauchy problem for the Gamma equation

NASA Astrophysics Data System (ADS)

Koleva, Miglena N.

2011-12-01

In this work we consider Cauchy problem for the so called Gamma equation, derived by transforming the fully nonlinear Black-Scholes equation for option price into a quasilinear parabolic equation for the second derivative (Greek) Γ = VSS of the option price V. We develop an efficient numerical method for solving the model problem concerning different volatility terms. Using suitable change of variables the problem is transformed on finite interval, keeping original behavior of the solution at the infinity. Then we construct Picard-Newton algorithm with adaptive mesh step in time, which can be applied also in the case of non-differentiable functions. Results of numerical simulations are given.

Spatial complexity of solutions of higher order partial differential equations

NASA Astrophysics Data System (ADS)

Kukavica, Igor

2004-03-01

We address spatial oscillation properties of solutions of higher order parabolic partial differential equations. In the case of the Kuramoto-Sivashinsky equation ut + uxxxx + uxx + u ux = 0, we prove that for solutions u on the global attractor, the quantity card {x epsi [0, L]:u(x, t) = lgr}, where L > 0 is the spatial period, can be bounded by a polynomial function of L for all \\lambda\\in{\\Bbb R} . A similar property is proven for a general higher order partial differential equation u_t+(-1)^{s}\\partial_x^{2s}u+ \\sum_{k=0}^{2s-1}v_k(x,t)\\partial_x^k u =0 .

Efficient solution of parabolic equations by Krylov approximation methods

NASA Technical Reports Server (NTRS)

Gallopoulos, E.; Saad, Y.

1990-01-01

Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

Prediction of far-field wind turbine noise propagation with parabolic equation.

PubMed

Lee, Seongkyu; Lee, Dongjai; Honhoff, Saskia

2016-08-01

Sound propagation of wind farms is typically simulated by the use of engineering tools that are neglecting some atmospheric conditions and terrain effects. Wind and temperature profiles, however, can affect the propagation of sound and thus the perceived sound in the far field. A better understanding and application of those effects would allow a more optimized farm operation towards meeting noise regulations and optimizing energy yield. This paper presents the parabolic equation (PE) model development for accurate wind turbine noise propagation. The model is validated against analytic solutions for a uniform sound speed profile, benchmark problems for nonuniform sound speed profiles, and field sound test data for real environmental acoustics. It is shown that PE provides good agreement with the measured data, except upwind propagation cases in which turbulence scattering is important. Finally, the PE model uses computational fluid dynamics results as input to accurately predict sound propagation for complex flows such as wake flows. It is demonstrated that wake flows significantly modify the sound propagation characteristics.

Krylov Deferred Correction Accelerated Method of Lines Transpose for Parabolic Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jia, Jun; Jingfang, Huang

2008-01-01

In this paper, a new class of numerical methods for the accurate and efficient solutions of parabolic partial differential equations is presented. Unlike traditional method of lines (MoL), the new {\\bf \\it Krylov deferred correction (KDC) accelerated method of lines transpose (MoL^T)} first discretizes the temporal direction using Gaussian type nodes and spectral integration, and symbolically applies low-order time marching schemes to form a preconditioned elliptic system, which is then solved iteratively using Newton-Krylov techniques such as Newton-GMRES or Newton-BiCGStab method. Each function evaluation in the Newton-Krylov method is simply one low-order time-stepping approximation of the error by solving amore » decoupled system using available fast elliptic equation solvers. Preliminary numerical experiments show that the KDC accelerated MoL^T technique is unconditionally stable, can be spectrally accurate in both temporal and spatial directions, and allows optimal time-step sizes in long-time simulations.« less

Light propagation from fluorescent probes in biological tissues by coupled time-dependent parabolic simplified spherical harmonics equations

PubMed Central

Domínguez, Jorge Bouza; Bérubé-Lauzière, Yves

2011-01-01

We introduce a system of coupled time-dependent parabolic simplified spherical harmonic equations to model the propagation of both excitation and fluorescence light in biological tissues. We resort to a finite element approach to obtain the time-dependent profile of the excitation and the fluorescence light fields in the medium. We present results for cases involving two geometries in three-dimensions: a homogeneous cylinder with an embedded fluorescent inclusion and a realistically-shaped rodent with an embedded inclusion alike an organ filled with a fluorescent probe. For the cylindrical geometry, we show the differences in the time-dependent fluorescence response for a point-like, a spherical, and a spherically Gaussian distributed fluorescent inclusion. From our results, we conclude that the model is able to describe the time-dependent excitation and fluorescent light transfer in small geometries with high absorption coefficients and in nondiffusive domains, as may be found in small animal diffuse optical tomography (DOT) and fluorescence DOT imaging. PMID:21483606

Stability of hypersonic compression cones

NASA Astrophysics Data System (ADS)

Reed, Helen; Kuehl, Joseph; Perez, Eduardo; Kocian, Travis; Oliviero, Nicholas

2012-11-01

Our activities focus on the identification and understanding of the second-mode instability for representative configurations in hypersonic flight. These include the Langley 93-10 flared cone and the Purdue compression cone, both at 0 degrees angle of attack at Mach 6. Through application of nonlinear parabolized stability equations (NPSE) and linear parabolized stability equations (PSE) to both geometries, it is concluded that mean-flow distortion tends to amplify frequencies less than the peak frequency and stabilize those greater by modifying the boundary-layer thickness. As initial disturbance amplitude is increased and/or a broad spectrum disturbance is introduced, direct numerical simulations (DNS) or NPSE appear to be the proper choices to model the evolution, and relative evolution, because these computational tools include these nonlinear effects (mean-flow distortion). Support from AFOSR/NASA National Center for Hypersonic Research in Laminar-Turbulent Transition through Grant FA9550-09-1-0341 is gratefully acknowledged. The authors also thank Pointwise, AeroSoft, and Texas Advanced Computing Center (TACC).

Laser-modified Coulomb scattering states of an electron in the parabolic quasi-Sturmian-Floquet approach

NASA Astrophysics Data System (ADS)

Zaytsev, A. S.; Zaytsev, S. A.; Ancarani, L. U.; Kouzakov, K. A.

2018-04-01

Electron scattering states in combined Coulomb and laser fields are investigated with a nonperturbative approach based on the Hermitian Floquet theory. Taking into account the Coulomb-specific asymptotic behavior of the electron wave functions at large distances, a Lippmann-Schwinger-Floquet equation is derived in the Kramers-Henneberger frame. Such a scattering-state equation is solved numerically employing a set of parabolic quasi-Sturmian functions which have the great advantage of possessing, by construction, adequately chosen incoming or outgoing Coulomb asymptotic behaviors. Our quasi-Sturmian-Floquet approach is tested with a calculation of triple differential cross sections for a laser-assisted (e ,2 e ) process on atomic hydrogen within a first-order Born treatment of the projectile-atom interaction. Convergence with respect to the number of Floquet-Fourier expansion terms is numerically demonstrated. The illustration shows that the developed method is very efficient for the computation of light-dressed states of an electron moving in a Coulomb potential in the presence of laser radiation.

Bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations

DOE PAGES

Azunre, P.

2016-09-21

Here in this paper, two novel techniques for bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations are developed. The first provides a theorem to construct interval bounds, while the second provides a theorem to construct lower bounds convex and upper bounds concave in the parameter. The convex/concave bounds can be significantly tighter than the interval bounds because of the wrapping effect suffered by interval analysis in dynamical systems. Both types of bounds are computationally cheap to construct, requiring solving auxiliary systems twice and four times larger than the original system, respectively. An illustrative numerical examplemore » of bound construction and use for deterministic global optimization within a simple serial branch-and-bound algorithm, implemented numerically using interval arithmetic and a generalization of McCormick's relaxation technique, is presented. Finally, problems within the important class of reaction-diffusion systems may be optimized with these tools.« less

Direct Numerical Simulation of Transition Due to Traveling Crossflow Vortices

NASA Technical Reports Server (NTRS)

Li, Fei; Choudhari, Meelan M.; Duan, Lian

2016-01-01

Previous simulations of laminar breakdown mechanisms associated with stationary crossflow instability over a realistic swept-wing configuration are extended to investigate the alternate scenario of transition due to secondary instability of traveling crossflow modes. Earlier analyses based on secondary instability theory and parabolized stability equations have shown that this alternate scenario is viable when the initial amplitude of the most amplified mode of the traveling crossflow instability is greater than approximately 0.03 times the initial amplitude of the most amplified stationary mode. The linear growth predictions based on the secondary instability theory and parabolized stability equations agree well with the direct numerical simulation. Nonlinear effects are initially stabilizing but subsequently lead to a rapid growth followed by the onset of transition when the amplitude of the secondary disturbance exceeds a threshold value. Similar to the breakdown of stationary vortices, the transition zone is rather short and the boundary layer becomes completely turbulent across a distance of less than 15 times the boundary layer thickness at the completion of transition.

A diffusion model of protected population on bilocal habitat with generalized resource

NASA Astrophysics Data System (ADS)

Vasilyev, Maxim D.; Trofimtsev, Yuri I.; Vasilyeva, Natalya V.

2017-11-01

A model of population distribution in a two-dimensional area divided by an ecological barrier, i.e. the boundaries of natural reserve, is considered. Distribution of the population is defined by diffusion, directed migrations and areal resource. The exchange of specimens occurs between two parts of the habitat. The mathematical model is presented in the form of a boundary value problem for a system of non-linear parabolic equations with variable parameters of diffusion and growth function. The splitting space variables, sweep method and simple iteration methods were used for the numerical solution of a system. A set of programs was coded in Python. Numerical simulation results for the two-dimensional unsteady non-linear problem are analyzed in detail. The influence of migration flow coefficients and functions of natural birth/death ratio on the distributions of population densities is investigated. The results of the research would allow to describe the conditions of the stable and sustainable existence of populations in bilocal habitat containing the protected and non-protected zones.

Some results of recording infrasonic signals from explosions in Finland, 2009

NASA Astrophysics Data System (ADS)

Kulichkov, S.; Kremenetskaya, E.; Vinogradov, Yu.; Asming, V.; Popov, O.; Bush, G.; Golikova, E.; Drob, D.

2010-05-01

The results of recording infrasonic signals from series of explosions in Finland in 2009 are presented. The explosions were carried out by Finish militaries for destruction of outdated weapon. Explosions yield about 10 t tnt. It was performed about twenty explosions in 2009, August-September. The distance between the source and the receiver was 304 km. It was detected infrasonic waves corresponding to sound propagation along earth surface and in stratospheric and thermospheric acoustic waveguides. The significant difference in azimuths for surface, stratospheric, thermospheric arrivals of infrasound signals is obtained. These differences are due to the influence of transverse wind propagation. The theoretical calculation of the waveform of recorded infrasonic signals is produced. The calculation is done using the TDPE (Time Domain Parabolic Equation Code) method and the G2S temperature and wind profile. The temperature and wind profile are taken from balloon sounding data up to the height of 17 km. A satisfactory agreement between the results of calculations and experimental data is obtained.

Reacting Flow in the Entrance to a Channel with Surface and Gas-Phase Kinetics

NASA Astrophysics Data System (ADS)

Mikolaitis, David; Griffen, Patrick

2006-11-01

In many catalytic reactors the conversion process is most intense at the very beginning of the channel where the flow is not yet fully developed; hence there will be important interactions between the developing flow field and reaction. To study this problem we have written an object-oriented code for the analysis of reacting flow in the entrance of a channel where both surface reaction and gas-phase reaction are modeled with detailed kinetics. Fluid mechanical momentum and energy equations are modeled by parabolic ``boundary layer''-type equations where streamwise gradient terms are small and the pressure is constant in the transverse direction. Transport properties are modeled with mixture-averaging and the chemical kinetic sources terms are evaluated using Cantera. Numerical integration is done with Matlab using the function pdepe. Calculations were completed using mixtures of methane and air flowing through a channel with platinum walls held at a fixed temperature. GRI-Mech 3.0 was used to describe the gas-phase chemistry and Deutchmann's methane-air-platinum model was used for the surface chemistry. Ignition in the gas phase is predicted for high enough wall temperatures. A hot spot forms away from the walls just before ignition that is fed by radicals produced at the surface.

Development of Experimental and Computational Aeroacoustic Tools for Advanced Liner Evaluation

NASA Technical Reports Server (NTRS)

Jones, Michael G.; Watson, Willie R.; Nark, Douglas N.; Parrott, Tony L.; Gerhold, Carl H.; Brown, Martha C.

2006-01-01

Acoustic liners in aircraft engine nacelles suppress radiated noise. Therefore, as air travel increases, increasingly sophisticated tools are needed to maximize noise suppression. During the last 30 years, NASA has invested significant effort in development of experimental and computational acoustic liner evaluation tools. The Curved Duct Test Rig is a 152-mm by 381- mm curved duct that supports liner evaluation at Mach numbers up to 0.3 and source SPLs up to 140 dB, in the presence of user-selected modes. The Grazing Flow Impedance Tube is a 51- mm by 63-mm duct currently being fabricated to operate at Mach numbers up to 0.6 with source SPLs up to at least 140 dB, and will replace the existing 51-mm by 51-mm duct. Together, these test rigs allow evaluation of advanced acoustic liners over a range of conditions representative of those observed in aircraft engine nacelles. Data acquired with these test ducts are processed using three aeroacoustic propagation codes. Two are based on finite element solutions to convected Helmholtz and linearized Euler equations. The third is based on a parabolic approximation to the convected Helmholtz equation. The current status of these computational tools and their associated usage with the Langley test rigs is provided.

Modelling Bathymetric Control of Near Coastal Wave Climate: Report 3

DTIC Science & Technology

1992-02-01

complexity would occur if we were to make the full set of restrictions appropriate to the parabolic approximation of the KP equation ( Kadomtsev ... Kadomtsev , B.B. and Petviashvili , V.I., 1970, "On the stability of solitary waves in weakly dispersing media", Soy. Phys. Dokl., 15, 539-541. 24 Kirby...bar theory. Theory for Small Amplitude Bars The theory which provides the framework for analysis here is given by an extended mild-slope equation

Eulerian Dynamics with a Commutator Forcing

DTIC Science & Technology

2017-01-09

SIAM Review 56(4) (2014) 577–621. [Pes2015] J. Peszek. Discrete Cucker-Smale flocking model with a weakly singular weight. SIAM J. Math . Anal., to...viscosities in bounded domains. J. Math . Pures Appl. (9), 87(2):227– 235, 2007. [CV2010] L. Caffarelli, A. Vasseur, Drift diffusion equations with...Further time regularity for fully non-linear parabolic equations. Math . Res. Lett., 22(6):1749–1766, 2015. [CCTT2016] José A. Carrillo, Young-Pil

Cubic nonlinearity in shear wave beams with different polarizations

PubMed Central

Wochner, Mark S.; Hamilton, Mark F.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.

2008-01-01

A coupled pair of nonlinear parabolic equations is derived for the two components of the particle motion perpendicular to the axis of a shear wave beam in an isotropic elastic medium. The equations account for both quadratic and cubic nonlinearity. The present paper investigates, analytically and numerically, effects of cubic nonlinearity in shear wave beams for several polarizations: linear, elliptical, circular, and azimuthal. Comparisons are made with effects of quadratic nonlinearity in compressional wave beams. PMID:18529167

Distributed Blowing and Suction for the Purpose of Streak Control in a Boundary Layer Subjected to a Favorable Pressure Gradient

NASA Technical Reports Server (NTRS)

Forgoston, Eric; Tumin, Anatoli; Ashpis, David E.

2005-01-01

An analysis of the optimal control by blowing and suction in order to generate stream- wise velocity streaks is presented. The problem is examined using an iterative process that employs the Parabolized Stability Equations for an incompressible uid along with its adjoint equations. In particular, distributions of blowing and suction are computed for both the normal and tangential velocity perturbations for various choices of parameters.

Three dimensional PNS solutions of hypersonic internal flows with equilibrium chemistry

NASA Technical Reports Server (NTRS)

Liou, May-Fun

1989-01-01

An implicit procedure for solving parabolized Navier-Stokes equations under the assumption of a general equation of state for a gas in chemical equilibrium is given. A general and consistent approach for the evaluation of Jacobian matrices in the implicit operator avoids the use of unnecessary auxiliary quantities and approximations, and leads to a simple expression. Applications to two- and three-dimensional flow problems show efficiency in computer time and economy in storage.

Numerical evidences for the angular momentum-mass inequality for multiple axially symmetric black holes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dain, Sergio; Ortiz, Omar E.; Facultad de Matematica, Astronomia y Fisica, Universidad Nacional de Cordoba, Ciudad Universitaria

2009-07-15

We present numerical evidences for the validity of the inequality between the total mass and the total angular momentum for multiple axially symmetric (nonstationary) black holes. We use a parabolic heat flow to solve numerically the stationary axially symmetric Einstein equations. As a by-product of our method, we also give numerical evidences that there are no regular solutions of Einstein equations that describe two extreme, axially symmetric black holes in equilibrium.

The Langley Stability and Transition Analysis Code (LASTRAC) : LST, Linear and Nonlinear PSE for 2-D, Axisymmetric, and Infinite Swept Wing Boundary Layers

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan

2003-01-01

During the past two decades, our understanding of laminar-turbulent transition flow physics has advanced significantly owing to, in a large part, the NASA program support such as the National Aerospace Plane (NASP), High-speed Civil Transport (HSCT), and Advanced Subsonic Technology (AST). Experimental, theoretical, as well as computational efforts on various issues such as receptivity and linear and nonlinear evolution of instability waves take part in broadening our knowledge base for this intricate flow phenomenon. Despite all these advances, transition prediction remains a nontrivial task for engineers due to the lack of a widely available, robust, and efficient prediction tool. The design and development of the LASTRAC code is aimed at providing one such engineering tool that is easy to use and yet capable of dealing with a broad range of transition related issues. LASTRAC was written from scratch based on the state-of-the-art numerical methods for stability analysis and modem software technologies. At low fidelity, it allows users to perform linear stability analysis and N-factor transition correlation for a broad range of flow regimes and configurations by using either the linear stability theory (LST) or linear parabolized stability equations (LPSE) method. At high fidelity, users may use nonlinear PSE to track finite-amplitude disturbances until the skin friction rise. Coupled with the built-in receptivity model that is currently under development, the nonlinear PSE method offers a synergistic approach to predict transition onset for a given disturbance environment based on first principles. This paper describes the governing equations, numerical methods, code development, and case studies for the current release of LASTRAC. Practical applications of LASTRAC are demonstrated for linear stability calculations, N-factor transition correlation, non-linear breakdown simulations, and controls of stationary crossflow instability in supersonic swept wing boundary layers.

Spectral collocation methods

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Kopriva, D. A.; Patera, A. T.

1987-01-01

This review covers the theory and application of spectral collocation methods. Section 1 describes the fundamentals, and summarizes results pertaining to spectral approximations of functions. Some stability and convergence results are presented for simple elliptic, parabolic, and hyperbolic equations. Applications of these methods to fluid dynamics problems are discussed in Section 2.

Partial stabilisation of non-homogeneous bilinear systems

NASA Astrophysics Data System (ADS)

Hamidi, Z.; Ouzahra, M.

2018-06-01

In this work, we study in a Hilbert state space, the partial stabilisation of non-homogeneous bilinear systems using a bounded control. Necessary and sufficient conditions for weak and strong stabilisation are formulated in term of approximate observability like assumptions. Applications to parabolic and hyperbolic equations are presented.

Comparison of particle tracking algorithms in commercial CFD packages: sedimentation and diffusion.

PubMed

Robinson, Risa J; Snyder, Pam; Oldham, Michael J

2007-05-01

Computational fluid dynamic modeling software has enabled microdosimetry patterns of inhaled toxins and toxicants to be predicted and visualized, and is being used in inhalation toxicology and risk assessment. These predicted microdosimetry patterns in airway structures are derived from predicted airflow patterns within these airways and particle tracking algorithms used in computational fluid dynamics (CFD) software packages. Although these commercial CFD codes have been tested for accuracy under various conditions, they have not been well tested for respiratory flows in general. Nor has their particle tracking algorithm accuracy been well studied. In this study, three software packages, Fluent Discrete Phase Model (DPM), Fluent Fine Particle Model (FPM), and ANSYS CFX, were evaluated. Sedimentation and diffusion were each isolated in a straight tube geometry and tested for accuracy. A range of flow rates corresponding to adult low activity (minute ventilation = 10 L/min) and to heavy exertion (minute ventilation = 60 L/min) were tested by varying the range of dimensionless diffusion and sedimentation parameters found using the Weibel symmetric 23 generation lung morphology. Numerical results for fully developed parabolic and uniform (slip) profiles were compared respectively, to Pich (1972) and Yu (1977) analytical sedimentation solutions. Schum and Yeh (1980) equations for sedimentation were also compared. Numerical results for diffusional deposition were compared to analytical solutions of Ingham (1975) for parabolic and uniform profiles. Significant differences were found among the various CFD software packages and between numerical and analytical solutions. Therefore, it is prudent to validate CFD predictions against analytical solutions in idealized geometry before tackling the complex geometries of the respiratory tract.

Examining Changes in Radioxenon Isotope Activity Ratios during Subsurface Transport

NASA Astrophysics Data System (ADS)

Annewandter, Robert

2014-05-01

The Non-Proliferation Experiment (NPE) has demonstrated and modelled the usefulness of barometric pumping induced gas transport and subsequent soil gas sampling during On-Site inspections. Generally, gas transport has been widely studied with different numerical codes. However, gas transport of radioxenons and radioiodines in the post-detonation regime and their possible fractionation is still neglected in the open peer-reviewed literature. Atmospheric concentrations of the radioxenons Xe-135, Xe-133m, Xe-133 and Xe-131m can be used to discriminate between civilian releases (nuclear power plants or medical isotope facilities), and nuclear explosion sources. It is based on the multiple isotopic activity ratio method. Yet it is not clear whether subsurface migration of the radionuclides, with eventual release into the atmosphere, can affect the activity ratios due to fractionation. Fractionation can be caused by different mass diffusivities due to mass differences between the radionuclides. Cyclical changes in atmospheric pressure can drive subsurface gas transport. This barometric pumping phenomenon causes an oscillatoric flow in upward trending fractures or highly conductive faults which, combined with diffusion into the porous matrix, leads to a net transport of gaseous components - a so-called ratcheting effect. We use a general purpose reservoir simulator (Complex System Modelling Platform, CSMP++) which is recognized by the oil industry as leading in Discrete Fracture-Matrix (DFM) simulations. It has been applied in a range of fields such as deep geothermal systems, three-phase black oil simulations, fracture propagation in fractured, porous media, and Navier-Stokes pore-scale modelling among others. It is specifically designed to account for structurally complex geologic situation of fractured, porous media. Parabolic differential equations are solved by a continuous Galerkin finite-element method, hyperbolic differential equations by a complementary finite volume method. The parabolic and hyperbolic problem can be solved separately by operator-splitting. The resulting system of linear equations is solved by the algebraic multigrid library SAMG, developed at the Fraunhofer Institute for Algorithms and Scientific Computing, Germany. CSMP++ is developed at Montan University of Leoben, ETH Zuerich, Imperial College London and Heriot-Watt University in Edinburgh. This study examines barometric pumping-driven subsurface transport of Xe-135, Xe-133m, Xe-133, Xe-131m including I-131, I-133 and I-135 on arrival times and isotopic activity ratios. This work was funded by the CTBTO Research Award for Young Scientist and Engineers (2013).

Solution Methods for Certain Evolution Equations

NASA Astrophysics Data System (ADS)

Vega-Guzman, Jose Manuel

Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. Such explicit construction is possible due to the relation between the diffusion-type equation studied in the first part and the time-dependent Schrodinger equation. A modication of the radiation field operators for squeezed photons in a perfect cavity is also suggested with the help of a nonstandard solution of Heisenberg's equation of motion.

Analysis of band structure, transmission properties, and dispersion behavior of THz wave in one-dimensional parabolic plasma photonic crystal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Askari, Nasim; Eslami, Esmaeil, E-mail: eeslami@iust.ac.ir; Mirzaie, Reza

2015-11-15

The photonic band gap of obliquely incident terahertz electromagnetic waves in a one-dimensional plasma photonic crystal is studied. The periodic structure consists of lossless dielectric and inhomogeneous plasma with a parabolic density profile. The dispersion relation and the THz wave transmittance are analyzed based on the electromagnetic equations and transfer matrix method. The dependence of effective plasma frequency and photonic band gap characteristics on dielectric and plasma thickness, plasma density, and incident angle are discussed in detail. A theoretical calculation for effective plasma frequency is presented and compared with numerical results. Results of these two methods are in good agreement.

Nonlinear Solver Approaches for the Diffusive Wave Approximation to the Shallow Water Equations

NASA Astrophysics Data System (ADS)

Collier, N.; Knepley, M.

2015-12-01

The diffusive wave approximation to the shallow water equations (DSW) is a doubly-degenerate, nonlinear, parabolic partial differential equation used to model overland flows. Despite its challenges, the DSW equation has been extensively used to model the overland flow component of various integrated surface/subsurface models. The equation's complications become increasingly problematic when ponding occurs, a feature which becomes pervasive when solving on large domains with realistic terrain. In this talk I discuss the various forms and regularizations of the DSW equation and highlight their effect on the solvability of the nonlinear system. In addition to this analysis, I present results of a numerical study which tests the applicability of a class of composable nonlinear algebraic solvers recently added to the Portable, Extensible, Toolkit for Scientific Computation (PETSc).

A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

PubMed Central

Motsa, S. S.; Magagula, V. M.; Sibanda, P.

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252

A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

PubMed

Motsa, S S; Magagula, V M; Sibanda, P

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

On the Solutions of a 2+1-Dimensional Model for Epitaxial Growth with Axial Symmetry

NASA Astrophysics Data System (ADS)

Lu, Xin Yang

2018-04-01

In this paper, we study the evolution equation derived by Xu and Xiang (SIAM J Appl Math 69(5):1393-1414, 2009) to describe heteroepitaxial growth in 2+1 dimensions with elastic forces on vicinal surfaces is in the radial case and uniform mobility. This equation is strongly nonlinear and contains two elliptic integrals and defined via Cauchy principal value. We will first derive a formally equivalent parabolic evolution equation (i.e., full equivalence when sufficient regularity is assumed), and the main aim is to prove existence, uniqueness and regularity of strong solutions. We will extensively use techniques from the theory of evolution equations governed by maximal monotone operators in Banach spaces.

Solution of transonic flows by an integro-differential equation method

NASA Technical Reports Server (NTRS)

Ogana, W.

1978-01-01

Solutions of steady transonic flow past a two-dimensional airfoil are obtained from a singular integro-differential equation which involves a tangential derivative of the perturbation velocity potential. Subcritical flows are solved by taking central differences everywhere. For supercritical flows with shocks, central differences are taken in subsonic flow regions and backward differences in supersonic flow regions. The method is applied to a nonlifting parabolic-arc airfoil and to a lifting NACA 0012 airfoil. Results compare favorably with those of finite-difference schemes.

Hodge Numbers from Picard-Fuchs Equations

NASA Astrophysics Data System (ADS)

Doran, Charles F.; Harder, Andrew; Thompson, Alan

2017-06-01

Given a variation of Hodge structure over P^1 with Hodge numbers (1,1,\\dots,1), we show how to compute the degrees of the Deligne extension of its Hodge bundles, following Eskin-Kontsevich-Möller-Zorich, by using the local exponents of the corresponding Picard-Fuchs equation. This allows us to compute the Hodge numbers of Zucker's Hodge structure on the corresponding parabolic cohomology groups. We also apply this to families of elliptic curves, K3 surfaces and Calabi-Yau threefolds.

Low Altitude Near-the-Horizon Propagation: A Comparison Between RPO and M-Layer

DTIC Science & Technology

1993-12-01

scaling based on the assumption that a single mode contributes to the complete field strength (Ref. 31, output from M-Layer [Ref. 4, 5] in the over-the...PE. The parabolic equation approximation to the Maxwell wave equations is developed under the optical assumption that the operating frequency is so...profile data are specified (an array) capm zim profile data (modified index of refraction; an array) (a) RPO: from I to n/evs; M-Layer from 0 to nzlayr

Vector-valued Lizorkin-Triebel spaces and sharp trace theory for functions in Sobolev spaces with mixed \\pmb{L_p}-norm for parabolic problems

NASA Astrophysics Data System (ADS)

Weidemaier, P.

2005-06-01

The trace problem on the hypersurface y_n=0 is investigated for a function u=u(y,t) \\in L_q(0,T;W_{\\underline p}^{\\underline m}(\\mathbb R_+^n)) with \\partial_t u \\in L_q(0,T; L_{\\underline p}(\\mathbb R_+^n)), that is, Sobolev spaces with mixed Lebesgue norm L_{\\underline p,q}(\\mathbb R^n_+\\times(0,T))=L_q(0,T;L_{\\underline p}(\\mathbb R_+^n)) are considered; here \\underline p=(p_1,\\dots,p_n) is a vector and \\mathbb R^n_+=\\mathbb R^{n-1} \\times (0,\\infty). Such function spaces are useful in the context of parabolic equations. They allow, in particular, different exponents of summability in space and time. It is shown that the sharp regularity of the trace in the time variable is characterized by the Lizorkin-Triebel space F_{q,p_n}^{1-1/(p_nm_n)}(0,T;L_{\\widetilde{\\underline p}}(\\mathbb R^{n-1})), \\underline p=(\\widetilde{\\underline p},p_n). A similar result is established for first order spatial derivatives of u. These results allow one to determine the exact spaces for the data in the inhomogeneous Dirichlet and Neumann problems for parabolic equations of the second order if the solution is in the space L_q(0,T; W_p^2(\\Omega)) \\cap W_q^1(0,T;L_p(\\Omega)) with p \\le q.

A unified viscous theory of lift and drag of 2-D thin airfoils and 3-D thin wings

NASA Technical Reports Server (NTRS)

Yates, John E.

1991-01-01

A unified viscous theory of 2-D thin airfoils and 3-D thin wings is developed with numerical examples. The viscous theory of the load distribution is unique and tends to the classical inviscid result with Kutta condition in the high Reynolds number limit. A new theory of 2-D section induced drag is introduced with specific applications to three cases of interest: (1) constant angle of attack; (2) parabolic camber; and (3) a flapped airfoil. The first case is also extended to a profiled leading edge foil. The well-known drag due to absence of leading edge suction is derived from the viscous theory. It is independent of Reynolds number for zero thickness and varies inversely with the square root of the Reynolds number based on the leading edge radius for profiled sections. The role of turbulence in the section induced drag problem is discussed. A theory of minimum section induced drag is derived and applied. For low Reynolds number the minimum drag load tends to the constant angle of attack solution and for high Reynolds number to an approximation of the parabolic camber solution. The parabolic camber section induced drag is about 4 percent greater than the ideal minimum at high Reynolds number. Two new concepts, the viscous induced drag angle and the viscous induced separation potential are introduced. The separation potential is calculated for three 2-D cases and for a 3-D rectangular wing. The potential is calculated with input from a standard doublet lattice wing code without recourse to any boundary layer calculations. Separation is indicated in regions where it is observed experimentally. The classical induced drag is recovered in the 3-D high Reynolds number limit with an additional contribution that is Reynold number dependent. The 3-D viscous theory of minimum induced drag yields an equation for the optimal spanwise and chordwise load distribution. The design of optimal wing tip planforms and camber distributions is possible with the viscous 3-D wing theory.

Evolution of basic equations for nearshore wave field

PubMed Central

ISOBE, Masahiko

2013-01-01

In this paper, a systematic, overall view of theories for periodic waves of permanent form, such as Stokes and cnoidal waves, is described first with their validity ranges. To deal with random waves, a method for estimating directional spectra is given. Then, various wave equations are introduced according to the assumptions included in their derivations. The mild-slope equation is derived for combined refraction and diffraction of linear periodic waves. Various parabolic approximations and time-dependent forms are proposed to include randomness and nonlinearity of waves as well as to simplify numerical calculation. Boussinesq equations are the equations developed for calculating nonlinear wave transformations in shallow water. Nonlinear mild-slope equations are derived as a set of wave equations to predict transformation of nonlinear random waves in the nearshore region. Finally, wave equations are classified systematically for a clear theoretical understanding and appropriate selection for specific applications. PMID:23318680

Control of stationary crossflow modes in swept Hiemenz flows with dielectric barrier discharge plasma actuators

NASA Astrophysics Data System (ADS)

Wang, Zhefu; Wang, Liang; Fu, Song

2017-09-01

Sensitivity analyses and non-linear parabolized stability equations are solved to provide a computational assessment of the potential use of a Dielectric Barrier Discharge (DBD) plasma actuator for a prolonging laminar region in swept Hiemenz flow. The derivative of the kinetic energy with respect to the body force is deduced, and its components in different directions are defined as sensitivity functions. The results of sensitivity analyses and non-linear parabolized stability equations both indicate that the introduction of a body force as the plasma actuator at the bottom of a crossflow vortex can mitigate instability to delay flow transition. In addition, the actuator is more effective when placed more upstream until the neutral point. In fact, if the actuator is sufficiently close to the neutral point, it is likely to act as a strong disturbance over-riding the natural disturbance and dominating transition. Different operating voltages of the DBD actuators are tested, resulting in an optimal practice for transition delay. The results demonstrate that plasma actuators offer great potential for transition control.

Extremal equilibria for reaction-diffusion equations in bounded domains and applications

NASA Astrophysics Data System (ADS)

Rodríguez-Bernal, Aníbal; Vidal-López, Alejandro

We show the existence of two special equilibria, the extremal ones, for a wide class of reaction-diffusion equations in bounded domains with several boundary conditions, including non-linear ones. They give bounds for the asymptotic dynamics and so for the attractor. Some results on the existence and/or uniqueness of positive solutions are also obtained. As a consequence, several well-known results on the existence and/or uniqueness of solutions for elliptic equations are revisited in a unified way obtaining, in addition, information on the dynamics of the associated parabolic problem. Finally, we ilustrate the use of the general results by applying them to the case of logistic equations. In fact, we obtain a detailed picture of the positive dynamics depending on the parameters appearing in the equation.

Generalized heat-transport equations: parabolic and hyperbolic models

NASA Astrophysics Data System (ADS)

Rogolino, Patrizia; Kovács, Robert; Ván, Peter; Cimmelli, Vito Antonio

2018-03-01

We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some generalizations of the classical Liu and Coleman-Noll procedures. In both cases, constitutive equations for the entropy and for the entropy flux are obtained. For the second model, we consider a heat-transport equation which includes nonlocal terms and study the resulting set of balance laws, proving that the corresponding thermal perturbations propagate with finite speed.

Nonparaxial wave beams and packets with general astigmatism

NASA Astrophysics Data System (ADS)

Kiselev, A. P.; Plachenov, A. B.; Chamorro-Posada, P.

2012-04-01

We present exact solutions of the wave equation involving an arbitrary wave form with a phase closely similar to the general astigmatic phase of paraxial wave optics. Special choices of the wave form allow general astigmatic beamlike and pulselike waves with a Gaussian-type unrestricted localization in space and time. These solutions are generalizations of the known Bateman-type waves obtained from the connection existing between beamlike solutions of the paraxial parabolic equation and relatively undistorted wave solutions of the wave equation. As a technical tool, we present a full description of parametrizations of 2×2 symmetric matrices with positive imaginary part, which arise in the theory of Gaussian beams.

Traveling-Wave Solutions of the Kolmogorov-Petrovskii-Piskunov Equation

NASA Astrophysics Data System (ADS)

Pikulin, S. V.

2018-02-01

We consider quasi-stationary solutions of a problem without initial conditions for the Kolmogorov-Petrovskii-Piskunov (KPP) equation, which is a quasilinear parabolic one arising in the modeling of certain reaction-diffusion processes in the theory of combustion, mathematical biology, and other areas of natural sciences. A new efficiently numerically implementable analytical representation is constructed for self-similar plane traveling-wave solutions of the KPP equation with a special right-hand side. Sufficient conditions for an auxiliary function involved in this representation to be analytical for all values of its argument, including the endpoints, are obtained. Numerical results are obtained for model examples.

Survey of the status of finite element methods for partial differential equations

NASA Technical Reports Server (NTRS)

Temam, Roger

1986-01-01

The finite element methods (FEM) have proved to be a powerful technique for the solution of boundary value problems associated with partial differential equations of either elliptic, parabolic, or hyperbolic type. They also have a good potential for utilization on parallel computers particularly in relation to the concept of domain decomposition. This report is intended as an introduction to the FEM for the nonspecialist. It contains a survey which is totally nonexhaustive, and it also contains as an illustration, a report on some new results concerning two specific applications, namely a free boundary fluid-structure interaction problem and the Euler equations for inviscid flows.

Multigrid Relaxation of a Factorizable, Conservative Discretization of the Compressible Flow Equations

NASA Technical Reports Server (NTRS)

Roberts, Thomas W.; Sidilkover, David; Thomas, J. L.

2000-01-01

The second-order factorizable discretization of the compressible Euler equations developed by Sidilkover is extended to conservation form on general curvilinear body-fitted grids. The discrete equations are solved by symmetric collective Gauss-Seidel relaxation and FAS multigrid. Solutions for flow in a channel with Mach numbers ranging from 0.0001 to a supercritical Mach number are shown, demonstrating uniform convergence rates and no loss of accuracy in the incompressible limit. A solution for the flow around the leading edge of a semi-infinite parabolic body demonstrates that the scheme maintains rapid convergence for a flow containing a stagnation point.

Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs

NASA Astrophysics Data System (ADS)

Veneva, Milena; Ayriyan, Alexander

2018-04-01

A class of models of heat transfer processes in a multilayer domain is considered. The governing equation is a nonlinear heat-transfer equation with different temperature-dependent densities and thermal coefficients in each layer. Homogeneous Neumann boundary conditions and ideal contact ones are applied. A finite difference scheme on a special uneven mesh with a second-order approximation in the case of a piecewise constant spatial step is built. This discretization leads to a pentadiagonal system of linear equations (SLEs) with a matrix which is neither diagonally dominant, nor positive definite. Two different methods for solving such a SLE are developed - diagonal dominantization and symbolic algorithms.

Development of Multiobjective Optimization Techniques for Sonic Boom Minimization

NASA Technical Reports Server (NTRS)

Chattopadhyay, Aditi; Rajadas, John Narayan; Pagaldipti, Naryanan S.

1996-01-01

A discrete, semi-analytical sensitivity analysis procedure has been developed for calculating aerodynamic design sensitivities. The sensitivities of the flow variables and the grid coordinates are numerically calculated using direct differentiation of the respective discretized governing equations. The sensitivity analysis techniques are adapted within a parabolized Navier Stokes equations solver. Aerodynamic design sensitivities for high speed wing-body configurations are calculated using the semi-analytical sensitivity analysis procedures. Representative results obtained compare well with those obtained using the finite difference approach and establish the computational efficiency and accuracy of the semi-analytical procedures. Multidisciplinary design optimization procedures have been developed for aerospace applications namely, gas turbine blades and high speed wing-body configurations. In complex applications, the coupled optimization problems are decomposed into sublevels using multilevel decomposition techniques. In cases with multiple objective functions, formal multiobjective formulation such as the Kreisselmeier-Steinhauser function approach and the modified global criteria approach have been used. Nonlinear programming techniques for continuous design variables and a hybrid optimization technique, based on a simulated annealing algorithm, for discrete design variables have been used for solving the optimization problems. The optimization procedure for gas turbine blades improves the aerodynamic and heat transfer characteristics of the blades. The two-dimensional, blade-to-blade aerodynamic analysis is performed using a panel code. The blade heat transfer analysis is performed using an in-house developed finite element procedure. The optimization procedure yields blade shapes with significantly improved velocity and temperature distributions. The multidisciplinary design optimization procedures for high speed wing-body configurations simultaneously improve the aerodynamic, the sonic boom and the structural characteristics of the aircraft. The flow solution is obtained using a comprehensive parabolized Navier Stokes solver. Sonic boom analysis is performed using an extrapolation procedure. The aircraft wing load carrying member is modeled as either an isotropic or a composite box beam. The isotropic box beam is analyzed using thin wall theory. The composite box beam is analyzed using a finite element procedure. The developed optimization procedures yield significant improvements in all the performance criteria and provide interesting design trade-offs. The semi-analytical sensitivity analysis techniques offer significant computational savings and allow the use of comprehensive analysis procedures within design optimization studies.

Seismo-acoustic ray model benchmarking against experimental tank data.

PubMed

Camargo Rodríguez, Orlando; Collis, Jon M; Simpson, Harry J; Ey, Emanuel; Schneiderwind, Joseph; Felisberto, Paulo

2012-08-01

Acoustic predictions of the recently developed traceo ray model, which accounts for bottom shear properties, are benchmarked against tank experimental data from the EPEE-1 and EPEE-2 (Elastic Parabolic Equation Experiment) experiments. Both experiments are representative of signal propagation in a Pekeris-like shallow-water waveguide over a non-flat isotropic elastic bottom, where significant interaction of the signal with the bottom can be expected. The benchmarks show, in particular, that the ray model can be as accurate as a parabolic approximation model benchmarked in similar conditions. The results of benchmarking are important, on one side, as a preliminary experimental validation of the model and, on the other side, demonstrates the reliability of the ray approach for seismo-acoustic applications.

Fast Multilevel Solvers for a Class of Discrete Fourth Order Parabolic Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zheng, Bin; Chen, Luoping; Hu, Xiaozhe

2016-03-05

In this paper, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element methods. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to construct efficient preconditioners. We provide eigenvalue analysis for the preconditioned system and estimate the convergence rate of the preconditioned GMRes method. Furthermore, we show that these preconditioners only need to be solved inexactly by optimal multigrid algorithms. Our numerical examples indicate that the proposed preconditioners are very efficient and robust with respect to both discretization parameters and diffusion coefficients. We also investigatemore » the performance of multigrid algorithms with either collective smoothers or distributive smoothers when solving the preconditioner systems.« less

Quasi-Airy beams along tunable propagation trajectories and directions.

PubMed

Qian, Yixian; Zhang, Site

2016-05-02

We present a theoretical and experimental exhibit that accelerates quasi-Airy beams propagating along arbitrarily appointed parabolic trajectories and directions in free space. We also demonstrate that such quasi-Airy beams can be generated by a tunable phase pattern, where two disturbance factors are introduced. The topological structures of quasi-Airy beams are readily manipulated with tunable phase patterns. Quasi-Airy beams still possess the characteristics of non-diffraction, self-healing to some extent, although they are not the solutions for paraxial wave equation. The experiments show the results are consistent with theoretical predictions. It is believed that the property of propagation along arbitrarily desired parabolic trajectories will provide a broad application in trapping atom and living cell manipulation.

Krylov subspace methods - Theory, algorithms, and applications

NASA Technical Reports Server (NTRS)

Sad, Youcef

1990-01-01

Projection methods based on Krylov subspaces for solving various types of scientific problems are reviewed. The main idea of this class of methods when applied to a linear system Ax = b, is to generate in some manner an approximate solution to the original problem from the so-called Krylov subspace span. Thus, the original problem of size N is approximated by one of dimension m, typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now becoming popular for solving nonlinear equations. The main ideas in Krylov subspace methods are shown and their use in solving linear systems, eigenvalue problems, parabolic partial differential equations, Liapunov matrix equations, and nonlinear system of equations are discussed.

Nonautonomous discrete bright soliton solutions and interaction management for the Ablowitz-Ladik equation.

PubMed

Yu, Fajun

2015-03-01

We present the nonautonomous discrete bright soliton solutions and their interactions in the discrete Ablowitz-Ladik (DAL) equation with variable coefficients, which possesses complicated wave propagation in time and differs from the usual bright soliton waves. The differential-difference similarity transformation allows us to relate the discrete bright soliton solutions of the inhomogeneous DAL equation to the solutions of the homogeneous DAL equation. Propagation and interaction behaviors of the nonautonomous discrete solitons are analyzed through the one- and two-soliton solutions. We study the discrete snaking behaviors, parabolic behaviors, and interaction behaviors of the discrete solitons. In addition, the interaction management with free functions and dynamic behaviors of these solutions is investigated analytically, which have certain applications in electrical and optical systems.

Critical study of higher order numerical methods for solving the boundary-layer equations

NASA Technical Reports Server (NTRS)

Wornom, S. F.

1978-01-01

A fourth order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method, which is the natural extension of the second order box scheme to fourth order, was demonstrated with application to the incompressible, laminar and turbulent, boundary layer equations. The efficiency of the present method is compared with two point and three point higher order methods, namely, the Keller box scheme with Richardson extrapolation, the method of deferred corrections, a three point spline method, and a modified finite element method. For equivalent accuracy, numerical results show the present method to be more efficient than higher order methods for both laminar and turbulent flows.

Experimental and computational surface and flow-field results for an all-body hypersonic aircraft

NASA Technical Reports Server (NTRS)

Lockman, William K.; Lawrence, Scott L.; Cleary, Joseph W.

1990-01-01

The objective of the present investigation is to establish a benchmark experimental data base for a generic hypersonic vehicle shape for validation and/or calibration of advanced computational fluid dynamics computer codes. This paper includes results from the comprehensive test program conducted in the NASA/Ames 3.5-foot Hypersonic Wind Tunnel for a generic all-body hypersonic aircraft model. Experimental and computational results on flow visualization, surface pressures, surface convective heat transfer, and pitot-pressure flow-field surveys are presented. Comparisons of the experimental results with computational results from an upwind parabolized Navier-Stokes code developed at Ames demonstrate the capabilities of this code.

The Effect of Boundary Support and Reflector Dimensions on Inflatable Parabolic Antenna Performance

NASA Technical Reports Server (NTRS)

Coleman, Michael J.; Baginski, Frank; Romanofsky, Robert R.

2011-01-01

For parabolic antennas with sufficient surface accuracy, more power can be radiated with a larger aperture size. This paper explores the performance of antennas of various size and reflector depth. The particular focus is on a large inflatable elastic antenna reflector that is supported about its perimeter by a set of elastic tendons and is subjected to a constant hydrostatic pressure. The surface accuracy of the antenna is measured by an RMS calculation, while the reflector phase error component of the efficiency is determined by computing the power density at boresight. In the analysis, the calculation of antenna efficiency is not based on the Ruze Equation. Hence, no assumption regarding the distribution of the reflector surface distortions is presumed. The reflector surface is modeled as an isotropic elastic membrane using a linear stress-strain constitutive relation. Three types of antenna reflector construction are considered: one molded to an ideal parabolic form and two different flat panel design patterns. The flat panel surfaces are constructed by seaming together panels in a manner that the desired parabolic shape is approximately attained after pressurization. Numerical solutions of the model problem are calculated under a variety of conditions in order to estimate the accuracy and efficiency of these antenna systems. In the case of the flat panel constructions, several different cutting patterns are analyzed in order to determine an optimal cutting strategy.

Hysteresis and Phase Transitions in a Lattice Regularization of an Ill-Posed Forward-Backward Diffusion Equation

NASA Astrophysics Data System (ADS)

Helmers, Michael; Herrmann, Michael

2018-03-01

We consider a lattice regularization for an ill-posed diffusion equation with a trilinear constitutive law and study the dynamics of phase interfaces in the parabolic scaling limit. Our main result guarantees for a certain class of single-interface initial data that the lattice solutions satisfy asymptotically a free boundary problem with a hysteretic Stefan condition. The key challenge in the proof is to control the microscopic fluctuations that are inevitably produced by the backward diffusion when a particle passes the spinodal region.

Large Diffusivity and Asymptotic Behavior in Parabolic Systems.

DTIC Science & Technology

1985-01-01

interesting ones for the case in which there is an in- variant region E. Any two species Volterra - Lotka model for which the ode’s have a unique stable...qualitative results as in [9], but the rates of decay are not as sharp. Generalizations to functional differential equations are given in Section 4. 2...1, generated by the equation aw/3t = DAW in 1. ..,. ., aw/an = 0 on an. Now, fix a > 3/4. There is a constant k > 0 such that P"~~ ,r*-’ IT(t)wl

A Comparison of Some Difference Schemes for a Parabolic Problem of Zero-Coupon Bond Pricing

NASA Astrophysics Data System (ADS)

Chernogorova, Tatiana; Vulkov, Lubin

2009-11-01

This paper describes a comparison of some numerical methods for solving a convection-diffusion equation subjected by dynamical boundary conditions which arises in the zero-coupon bond pricing. The one-dimensional convection-diffusion equation is solved by using difference schemes with weights including standard difference schemes as the monotone Samarskii's scheme, FTCS and Crank-Nicolson methods. The schemes are free of spurious oscillations and satisfy the positivity and maximum principle as demanded for the financial and diffusive solution. Numerical results are compared with analytical solutions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bogatskaya, A. V., E-mail: annabogatskaya@gmail.com; Volkova, E. A.; Popov, A. M.

The time evolution of a nonequilibrium plasma channel created in a noble gas by a high-power femtosecond KrF laser pulse is investigated. It is shown that such a channel possesses specific electrodynamic properties and can be used as a waveguide for efficient transportation and amplification of microwave pulses. The propagation of microwave radiation in a plasma waveguide is analyzed by self-consistently solving (i) the Boltzmann kinetic equation for the electron energy distribution function at different spatial points and (ii) the wave equation in the parabolic approximation for a microwave pulse transported along the plasma channel.

The use of the logistic model in space motion sickness prediction

NASA Technical Reports Server (NTRS)

Lin, Karl K.; Reschke, Millard F.

1987-01-01

The one-equation and the two-equation logistic models were used to predict subjects' susceptibility to motion sickness in KC-135 parabolic flights using data from other ground-based motion sickness tests. The results show that the logistic models correctly predicted substantially more cases (an average of 13 percent) in the data subset used for model building. Overall, the logistic models ranged from 53 to 65 percent predictions of the three endpoint parameters, whereas the Bayes linear discriminant procedure ranged from 48 to 65 percent correct for the cross validation sample.

Enhanced Multiobjective Optimization Technique for Comprehensive Aerospace Design. Part A

NASA Technical Reports Server (NTRS)

Chattopadhyay, Aditi; Rajadas, John N.

1997-01-01

A multidisciplinary design optimization procedure which couples formal multiobjectives based techniques and complex analysis procedures (such as computational fluid dynamics (CFD) codes) developed. The procedure has been demonstrated on a specific high speed flow application involving aerodynamics and acoustics (sonic boom minimization). In order to account for multiple design objectives arising from complex performance requirements, multiobjective formulation techniques are used to formulate the optimization problem. Techniques to enhance the existing Kreisselmeier-Steinhauser (K-S) function multiobjective formulation approach have been developed. The K-S function procedure used in the proposed work transforms a constrained multiple objective functions problem into an unconstrained problem which then is solved using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. Weight factors are introduced during the transformation process to each objective function. This enhanced procedure will provide the designer the capability to emphasize specific design objectives during the optimization process. The demonstration of the procedure utilizes a computational Fluid dynamics (CFD) code which solves the three-dimensional parabolized Navier-Stokes (PNS) equations for the flow field along with an appropriate sonic boom evaluation procedure thus introducing both aerodynamic performance as well as sonic boom as the design objectives to be optimized simultaneously. Sensitivity analysis is performed using a discrete differentiation approach. An approximation technique has been used within the optimizer to improve the overall computational efficiency of the procedure in order to make it suitable for design applications in an industrial setting.

Application of CFD codes to the design and development of propulsion systems

NASA Technical Reports Server (NTRS)

Lord, W. K.; Pickett, G. F.; Sturgess, G. J.; Weingold, H. D.

1987-01-01

The internal flows of aerospace propulsion engines have certain common features that are amenable to analysis through Computational Fluid Dynamics (CFD) computer codes. Although the application of CFD to engineering problems in engines was delayed by the complexities associated with internal flows, many codes with different capabilities are now being used as routine design tools. This is illustrated by examples taken from the aircraft gas turbine engine of flows calculated with potential flow, Euler flow, parabolized Navier-Stokes, and Navier-Stokes codes. Likely future directions of CFD applied to engine flows are described, and current barriers to continued progress are highlighted. The potential importance of the Numerical Aerodynamic Simulator (NAS) to resolution of these difficulties is suggested.

A Simple Mathematical Model Inspired by the Purkinje Cells: From Delayed Travelling Waves to Fractional Diffusion.

PubMed

Dipierro, Serena; Valdinoci, Enrico

2018-07-01

Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurring in the Purkinje cells, whose malfunctioning is known to be related to the lack of voluntary coordination and the appearance of tremors. Also, a classical mathematical feature is that (fractional) parabolic equations possess smoothing effects, in contrast with the case of hyperbolic equations, which typically exhibit shocks and discontinuities. In this paper, we show how a simple toy-model of a highly ramified structure, somehow inspired by that of the Purkinje cells, may produce a fractional diffusion via the superposition of travelling waves that solve a hyperbolic equation. This could suggest that the high ramification of the Purkinje cells might have provided an evolutionary advantage of "smoothing" the transmission of signals and avoiding shock propagations (at the price of slowing a bit such transmission). Although an experimental confirmation of the possibility of such evolutionary advantage goes well beyond the goals of this paper, we think that it is intriguing, as a mathematical counterpart, to consider the time fractional diffusion as arising from the superposition of delayed travelling waves in highly ramified transmission media. The case of a travelling concave parabola with sufficiently small curvature is explicitly computed. The new link that we propose between time fractional diffusion and hyperbolic equation also provides a novelty with respect to the usual paradigm relating time fractional diffusion with parabolic equations in the limit. This paper is written in such a way as to be of interest to both biologists and mathematician alike. In order to accomplish this aim, both complete explanations of the objects considered and detailed lists of references are provided.

Quasi-matched propagation of an ultrashort and intense laser pulse in a plasma channel

NASA Astrophysics Data System (ADS)

Benedetti, Carlo; Schroeder, Carl; Esarey, Eric; Leemans, Wim

2011-10-01

The propagation of an ultrashort and relativistically-intense laser pulse in a preformed parabolic plasma channel is investigated. The nonlinear paraxial wave equation is solved both analytically and numerically. Numerical solutions are obtained using the 2D cylindrical, envelope, ponderomotive, hybrid PIC/fluid code INF&RNO, recently developed at LBNL. For an arbitrary laser pulse profile with a given power for each longitudinal slice (less then the critical power for self-focusing), we determine the laser intensity distribution ensuring matched propagation in the channel, neglecting non-paraxial effects (self-steepening, red-shifting, etc.). Similarly, in the case of a Gaussian pulse profile, we determine the optimal channel depth yielding a quasi-matched laser propagation, including the plasma density modification induced by the laser-pulse. The analytical results obtained for both cases in the weakly-relativistic intensity regime are presented and validated through comparison with numerical simulations. Work supported by the Office of Science, Office of High Energy Physics, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

Two dimensional analysis of low pressure flows in the annulus region between two concentric cylinders.

PubMed

Al-Kouz, Wael; Alshare, Aiman; Alkhalidi, Ammar; Kiwan, Suhil

2016-01-01

A numerical simulation of the steady two-dimensional laminar natural convection heat transfer for the gaseous low-pressure flows in the annulus region between two concentric horizontal cylinders is carried out. This type of flow occurs in "evacuated" solar collectors and in the receivers of the solar parabolic trough collectors. A finite volume code is used to solve the coupled set of governing equations. Boussinesq approximation is utilized to model the buoyancy effect. A correlation for the thermal conductivity ratio (k r = k eff/k) in terms of Knudsen number and the modified Rayleigh number is proposed for Prandtl number (Pr = 0.701). It is found that as Knudsen number increases then the thermal conductivity ratio decreases for a given Rayleigh number. Also, it is shown that the thermal conductivity ratio k r increases as Rayleigh number increases. It appears that there is no consistent trend for varying the dimensionless gap spacing between the inner and the outer cylinder ([Formula: see text]) on the thermal conductivity ratio (k r) for the considered spacing range.

The Chebyshev-Legendre method: Implementing Legendre methods on Chebyshev points

NASA Technical Reports Server (NTRS)

Don, Wai Sun; Gottlieb, David

1993-01-01

We present a new collocation method for the numerical solution of partial differential equations. This method uses the Chebyshev collocation points, but because of the way the boundary conditions are implemented, it has all the advantages of the Legendre methods. In particular, L2 estimates can be obtained easily for hyperbolic and parabolic problems.

Environmental Acoustics and Intensity Vector Acoustics with Emphasis on Shallow Water Effects and the Sea Surface

DTIC Science & Technology

2015-09-30

work of Ballard [2] in which horizontal (bathymetric) refraction is solved using a parabolic equation (PE) in Cartesian coordinates. In particular for...wedge-like ocean with penetrable ocean,” J. Acoust. Soc. Am., 82 198-210, 1987 [2] M. S. Ballard , “Modeling three-dimensional propagation in a

Shallow Water Propagation

DTIC Science & Technology

2010-02-26

bottom waveguide. The lower contour plot demonstrates that this method, unlike other parabolic equations, can treat seismic sources. 20100308162...solitons. One illustration in Figure 8 shows depth-averaged data at the Naval Research Laboratory vertical line array (VLA) [dashed blue curves...vertical line array about 15 km from the source. The right panel [blue curves] compares corresponding simulations from a three-dimensional adiabatic mode

Global solutions to random 3D vorticity equations for small initial data

NASA Astrophysics Data System (ADS)

Barbu, Viorel; Röckner, Michael

2017-11-01

One proves the existence and uniqueness in (Lp (R3)) 3, 3/2 < p < 2, of a global mild solution to random vorticity equations associated to stochastic 3D Navier-Stokes equations with linear multiplicative Gaussian noise of convolution type, for sufficiently small initial vorticity. This resembles some earlier deterministic results of T. Kato [16] and are obtained by treating the equation in vorticity form and reducing the latter to a random nonlinear parabolic equation. The solution has maximal regularity in the spatial variables and is weakly continuous in (L3 ∩L 3p/4p - 6)3 with respect to the time variable. Furthermore, we obtain the pathwise continuous dependence of solutions with respect to the initial data. In particular, one gets a locally unique solution of 3D stochastic Navier-Stokes equation in vorticity form up to some explosion stopping time τ adapted to the Brownian motion.

Lipschitz regularity for integro-differential equations with coercive Hamiltonians and application to large time behavior

NASA Astrophysics Data System (ADS)

Barles, Guy; Ley, Olivier; Topp, Erwin

2017-02-01

In this paper, we provide suitable adaptations of the ‘weak version of Bernstein method’ introduced by the first author in 1991, in order to obtain Lipschitz regularity results and Lipschitz estimates for nonlinear integro-differential elliptic and parabolic equations set in the whole space. Our interest is to obtain such Lipschitz results to possibly degenerate equations, or to equations which are indeed ‘uniformly elliptic’ (maybe in the nonlocal sense) but which do not satisfy the usual ‘growth condition’ on the gradient term allowing to use (for example) the Ishii-Lions’ method. We treat the case of a model equation with a superlinear coercivity on the gradient term which has a leading role in the equation. This regularity result together with comparison principle provided for the problem allow to obtain the ergodic large time behavior of the evolution problem in the periodic setting.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Binotti, M.; Zhu, G.; Gray, A.

An analytical approach, as an extension of one newly developed method -- First-principle OPTical Intercept Calculation (FirstOPTIC) -- is proposed to treat the geometrical impact of three-dimensional (3-D) effects on parabolic trough optical performance. The mathematical steps of this analytical approach are presented and implemented numerically as part of the suite of FirstOPTIC code. In addition, the new code has been carefully validated against ray-tracing simulation results and available numerical solutions. This new analytical approach to treating 3-D effects will facilitate further understanding and analysis of the optical performance of trough collectors as a function of incidence angle.

Experimental and computational flow-field results for an all-body hypersonic aircraft

NASA Technical Reports Server (NTRS)

Cleary, Joseph W.

1989-01-01

A comprehensive test program is defined which is being implemented in the NASA/Ames 3.5 foot Hypersonic Wind Tunnel for obtaining data on a generic all-body hypersonic vehicle for computational fluid dynamics (CFD) code validation. Computational methods (approximate inviscid methods and an upwind parabolized Navier-Stokes code) currently being applied to the all-body model are outlined. Experimental and computational results on surface pressure distributions and Pitot-pressure surveys for the basic sharp-nose model (without control surfaces) at a free-stream Mach number of 7 are presented.

On Critical Spaces for the Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Prüss, Jan; Wilke, Mathias

2017-10-01

The abstract theory of critical spaces developed in Prüss and Wilke (J Evol Equ, 2017. doi: 10.1007/s00028-017-0382-6), Prüss et al. (Critical spaces for quasilinear parabolic evolution equations and applications, 2017) is applied to the Navier-Stokes equations in bounded domains with Navier boundary conditions as well as no-slip conditions. Our approach unifies, simplifies and extends existing work in the L_p -L_q setting, considerably. As an essential step, it is shown that the strong and weak Stokes operators with Navier conditions admit an H^∞-calculus with H^∞-angle 0, and the real and complex interpolation spaces of these operators are identified.

Parabolized Navier-Stokes solutions of separation and trailing-edge flows

NASA Technical Reports Server (NTRS)

Brown, J. L.

1983-01-01

A robust, iterative solution procedure is presented for the parabolized Navier-Stokes or higher order boundary layer equations as applied to subsonic viscous-inviscid interaction flows. The robustness of the present procedure is due, in part, to an improved algorithmic formulation. The present formulation is based on a reinterpretation of stability requirements for this class of algorithms and requires only second order accurate backward or central differences for all streamwise derivatives. Upstream influence is provided for through the algorithmic formulation and iterative sweeps in x. The primary contribution to robustness, however, is the boundary condition treatment, which imposes global constraints to control the convergence path. Discussed are successful calculations of subsonic, strong viscous-inviscid interactions, including separation. These results are consistent with Navier-Stokes solutions and triple deck theory.

A Deterministic Interfacial Cyclic Oxidation Spalling Model. Part 1; Model Development and Parametric Response

NASA Technical Reports Server (NTRS)

Smialek, James L.

2002-01-01

An equation has been developed to model the iterative scale growth and spalling process that occurs during cyclic oxidation of high temperature materials. Parabolic scale growth and spalling of a constant surface area fraction have been assumed. Interfacial spallation of the only the thickest segments was also postulated. This simplicity allowed for representation by a simple deterministic summation series. Inputs are the parabolic growth rate constant, the spall area fraction, oxide stoichiometry, and cycle duration. Outputs include the net weight change behavior, as well as the total amount of oxygen and metal consumed, the total amount of oxide spalled, and the mass fraction of oxide spalled. The outputs all follow typical well-behaved trends with the inputs and are in good agreement with previous interfacial models.

Transient Growth Analysis of Compressible Boundary Layers with Parabolized Stability Equations

NASA Technical Reports Server (NTRS)

Paredes, Pedro; Choudhari, Meelan M.; Li, Fei; Chang, Chau-Lyan

2016-01-01

The linear form of parabolized linear stability equations (PSE) is used in a variational approach to extend the previous body of results for the optimal, non-modal disturbance growth in boundary layer flows. This methodology includes the non-parallel effects associated with the spatial development of boundary layer flows. As noted in literature, the optimal initial disturbances correspond to steady counter-rotating stream-wise vortices, which subsequently lead to the formation of stream-wise-elongated structures, i.e., streaks, via a lift-up effect. The parameter space for optimal growth is extended to the hypersonic Mach number regime without any high enthalpy effects, and the effect of wall cooling is studied with particular emphasis on the role of the initial disturbance location and the value of the span-wise wavenumber that leads to the maximum energy growth up to a specified location. Unlike previous predictions that used a basic state obtained from a self-similar solution to the boundary layer equations, mean flow solutions based on the full Navier-Stokes (NS) equations are used in select cases to help account for the viscous-inviscid interaction near the leading edge of the plate and also for the weak shock wave emanating from that region. These differences in the base flow lead to an increasing reduction with Mach number in the magnitude of optimal growth relative to the predictions based on self-similar mean-flow approximation. Finally, the maximum optimal energy gain for the favorable pressure gradient boundary layer near a planar stagnation point is found to be substantially weaker than that in a zero pressure gradient Blasius boundary layer.

Spatial Coding of Eye Movements Relative to Perceived Orientations During Roll Tilt with Different Gravitoinertial Loads

NASA Technical Reports Server (NTRS)

Wood, Scott; Clement, Gilles

2013-01-01

This purpose of this study was to examine the spatial coding of eye movements during roll tilt relative to perceived orientations while free-floating during the microgravity phase of parabolic flight or during head tilt in normal gravity. Binocular videographic recordings obtained in darkness from six subjects allowed us to quantify the mean deviations in gaze trajectories along both horizontal and vertical coordinates relative to the aircraft and head orientations. Both variability and curvature of gaze trajectories increased during roll tilt compared to the upright position. The saccades were less accurate during parabolic flight compared to measurements obtained in normal gravity. The trajectories of saccades along perceived horizontal orientations tended to deviate in the same direction as the head tilt, while the deviations in gaze trajectories along the perceived vertical orientations deviated in the opposite direction relative to the head tilt. Although subjects were instructed to look off in the distance while performing the eye movements, fixation distance varied with vertical gaze direction independent of whether the saccades were made along perceived aircraft or head orientations. This coupling of horizontal vergence with vertical gaze is in a consistent direction with the vertical slant of the horopter. The increased errors in gaze trajectories along both perceived orientations during microgravity can be attributed to the otolith's role in spatial coding of eye movements.

Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field

NASA Astrophysics Data System (ADS)

Moawad, S. M.; Moawad

2013-10-01

The equilibrium and stability properties of ideal magnetohydrodynamics (MHD) of compressible flow in a gravitational field with a translational symmetry are investigated. Variational principles for the steady-state equations are formulated. The MHD equilibrium equations are obtained as critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross helicity), the momentum, and the magnetic helicity. In the unperturbed case, the equilibrium states satisfy a nonlinear second-order partial differential equation (PDE) associated with hydrodynamic Bernoulli law. The PDE can be an elliptic or a parabolic equation depending on increasing the poloidal flow speed. Linear and nonlinear Lyapunov stability conditions under translational symmetric perturbations are established for the equilibrium states.

CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. II. GRAY RADIATION HYDRODYNAMICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, W.; Almgren, A.; Bell, J.

We describe the development of a flux-limited gray radiation solver for the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. The gray radiation solver is based on a mixed-frame formulation of radiation hydrodynamics. In our approach, the system is split into two parts, one part that couples the radiation and fluid in a hyperbolic subsystem, and another parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem is solved explicitly with a high-order Godunovmore » scheme, whereas the parabolic part is solved implicitly with a first-order backward Euler method.« less

Spectral methods for partial differential equations

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Streett, C. L.; Zang, T. A.

1983-01-01

Origins of spectral methods, especially their relation to the Method of Weighted Residuals, are surveyed. Basic Fourier, Chebyshev, and Legendre spectral concepts are reviewed, and demonstrated through application to simple model problems. Both collocation and tau methods are considered. These techniques are then applied to a number of difficult, nonlinear problems of hyperbolic, parabolic, elliptic, and mixed type. Fluid dynamical applications are emphasized.

Environmental Modeling Packages for the MSTDCL TDP: Review and Recommendations (Trousses de Modelisation Environnementale Pour le PDT DCLTCM: Revue et Recommendations)

DTIC Science & Technology

2009-09-01

frequency shallow water scenarios, and DRDC has ready access to a well-established PE model ( PECan ). In those spectral areas below 1 kHz, where the PE...PCs Personnel Computers PE Parabolic Equation PECan PE Model developed by DRDC SPADES/ICE Sensor Performance and Acoustic Detection Evaluation

Saha equation, single and two particle states

NASA Technical Reports Server (NTRS)

Kraeft, W. D.; Girardeau, M. D.; Strege, B.

1990-01-01

Single- and two-particle properties in a dense plasma are discussed in connection with their role in the mass action law for a partially ionized plasma. The two-particle-bound states are nearly density independent, while the continuum is essentially shifted. The single-particle states are damped, and their energy has a negative shift and a parabolic behavior for small momenta.

Laplace-Gauss and Helmholtz-Gauss paraxial modes in media with quadratic refraction index.

PubMed

Kiselev, Aleksei P; Plachenov, Alexandr B

2016-04-01

The scalar theory of paraxial wave propagation in an axisymmetric medium where the refraction index quadratically depends on transverse variables is addressed. Exact solutions of the corresponding parabolic equation are presented, generalizing the Laplace-Gauss and Helmholtz-Gauss modes earlier known for homogeneous media. Also, a generalization of a zero-order asymmetric Bessel-Gauss beam is given.

A model reduction approach to numerical inversion for a parabolic partial differential equation

NASA Astrophysics Data System (ADS)

Borcea, Liliana; Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail

2014-12-01

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss-Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments.

Thermo-electronic solar power conversion with a parabolic concentrator

NASA Astrophysics Data System (ADS)

Olukunle, Olawole C.; De, Dilip K.

2016-02-01

We consider the energy dynamics of the power generation from the sun when the solar energy is concentrated on to the emitter of a thermo-electronic converter with the help of a parabolic mirror. We use the modified Richardson-Dushman equation. The emitter cross section is assumed to be exactly equal to the focused area at a height h from the base of the mirror to prevent loss of efficiency. We report the variation of output power with solar insolation, height h, reflectivity of the mirror, and anode temperature, initially assuming that there is no space charge effect. Our methodology allows us to predict the temperature at which the anode must be cooled in order to prevent loss of efficiency of power conversion. Novel ways of tackling the space charge problem have been discussed. The space charge effect is modeled through the introduction of a parameter f (0 < f < 1) in the thermos-electron emission equation. We find that the efficiency of the power conversion depends on solar insolation, height h, apart from radii R of the concentrator aperture and emitter, and the collector material properties. We have also considered solar thermos electronic power conversion by using single atom-layer graphene as an emitter.

Dissipative tunnelling by means of scaled trajectories

NASA Astrophysics Data System (ADS)

Mousavi, S. V.; Miret-Artés, S.

2018-06-01

Dissipative quantum tunnelling through an inverted parabolic barrier is considered in the presence of an electric field. A Schrödinger-Langevin or Kostin quantum-classical transition wave equation is used and applied resulting in a scaled differential equation of motion. A Gaussian wave packet solution to the resulting scaled Kostin nonlinear equation is assumed and compared to the same solution for the scaled linear Caldirola-Kanai equation. The resulting scaled trajectories are obtained at different dynamical regimes and friction cases, showing the gradual decoherence process in this open dynamics. Theoretical results show that the transmission probabilities are always higher in the Kostin approach than in the Caldirola-Kanai approach in the presence or not of an external electric field. This discrepancy should be understood due to the presence of an environment since the corresponding open dynamics should be governed by nonlinear quantum equations, whereas the second approach is issued from an effective Hamiltonian within a linear theory.

Asymptotic behavior of degenerate logistic equations

NASA Astrophysics Data System (ADS)

Arrieta, José M.; Pardo, Rosa; Rodríguez-Bernal, Aníbal

2015-12-01

We analyze the asymptotic behavior of positive solutions of parabolic equations with a class of degenerate logistic nonlinearities of the type λu - n (x)uρ. An important characteristic of this work is that the region where the logistic term n (ṡ) vanishes, that is K0 = { x : n (x) = 0 }, may be non-smooth. We analyze conditions on λ, ρ, n (ṡ) and K0 guaranteeing that the solution starting at a positive initial condition remains bounded or blows up as time goes to infinity. The asymptotic behavior may not be the same in different parts of K0.

Fast and accurate modeling of nonlinear pulse propagation in graded-index multimode fibers.

PubMed

Conforti, Matteo; Mas Arabi, Carlos; Mussot, Arnaud; Kudlinski, Alexandre

2017-10-01

We develop a model for the description of nonlinear pulse propagation in multimode optical fibers with a parabolic refractive index profile. It consists of a 1+1D generalized nonlinear Schrödinger equation with a periodic nonlinear coefficient, which can be solved in an extremely fast and efficient way. The model is able to quantitatively reproduce recently observed phenomena like geometric parametric instability and broadband dispersive wave emission. We envisage that our equation will represent a valuable tool for the study of spatiotemporal nonlinear dynamics in the growing field of multimode fiber optics.

Asymptotically exact parabolic solutions of the generalized nonlinear Schrödinger equation with varying parameters

NASA Astrophysics Data System (ADS)

Kruglov, Vladimir I.; Harvey, John D.

2006-12-01

We present exact asymptotic similariton solutions of the generalized nonlinear Schrödinger equation (NLSE) with gain or loss terms for a normal-dispersion fiber amplifier with dispersion, nonlinearity, and gain profiles that depend on the propagation distance. Our treatment is based on the mapping of the NLSE with varying parameters to the NLSE with constant dispersion and nonlinearity coefficients and an arbitrary varying gain function. We formulate an effective procedure that leads directly, under appropriate conditions, to a wide range of exact asymptotic similariton solutions of NLSE demonstrating self-similar propagating regimes with linear chirp.

O(2) Hopf bifurcation of viscous shock waves in a channel

NASA Astrophysics Data System (ADS)

Pogan, Alin; Yao, Jinghua; Zumbrun, Kevin

2015-07-01

Extending work of Texier and Zumbrun in the semilinear non-reflection symmetric case, we study O(2) transverse Hopf bifurcation, or "cellular instability", of viscous shock waves in a channel, for a class of quasilinear hyperbolic-parabolic systems including the equations of thermoviscoelasticity. The main difficulties are to (i) obtain Fréchet differentiability of the time- T solution operator by appropriate hyperbolic-parabolic energy estimates, and (ii) handle O(2) symmetry in the absence of either center manifold reduction (due to lack of spectral gap) or (due to nonstandard quasilinear hyperbolic-parabolic form) the requisite framework for treatment by spatial dynamics on the space of time-periodic functions, the two standard treatments for this problem. The latter issue is resolved by Lyapunov-Schmidt reduction of the time- T map, yielding a four-dimensional problem with O(2) plus approximate S1 symmetry, which we treat "by hand" using direct Implicit Function Theorem arguments. The former is treated by balancing information obtained in Lagrangian coordinates with that from associated constraints. Interestingly, this argument does not apply to gas dynamics or magnetohydrodynamics (MHD), due to the infinite-dimensional family of Lagrangian symmetries corresponding to invariance under arbitrary volume-preserving diffeomorphisms.

Terawatt x-ray free-electron-laser optimization by transverse electron distribution shaping

DOE PAGES

Emma, C.; Wu, J.; Fang, K.; ...

2014-11-03

We study the dependence of the peak power of a 1.5 Å Terawatt (TW), tapered x-ray free-electron laser (FEL) on the transverse electron density distribution. Multidimensional optimization schemes for TW hard x-ray free-electron lasers are applied to the cases of transversely uniform and parabolic electron beam distributions and compared to a Gaussian distribution. The optimizations are performed for a 200 m undulator and a resonant wavelength of λ r = 1.5 Å using the fully three-dimensional FEL particle code GENESIS. The study shows that the flatter transverse electron distributions enhance optical guiding in the tapered section of the undulator andmore » increase the maximum radiation power from a maximum of 1.56 TW for a transversely Gaussian beam to 2.26 TW for the parabolic case and 2.63 TW for the uniform case. Spectral data also shows a 30%–70% reduction in energy deposited in the sidebands for the uniform and parabolic beams compared with a Gaussian. An analysis of the transverse coherence of the radiation shows the coherence area to be much larger than the beam spotsize for all three distributions, making coherent diffraction imaging experiments possible.« less

Influence of Tooth Spacing Error on Gears With and Without Profile Modifications

NASA Technical Reports Server (NTRS)

Padmasolala, Giri; Lin, Hsiang H.; Oswald, Fred B.

2000-01-01

A computer simulation was conducted to investigate the effectiveness of profile modification for reducing dynamic loads in gears with different tooth spacing errors. The simulation examined varying amplitudes of spacing error and differences in the span of teeth over which the error occurs. The modification considered included both linear and parabolic tip relief. The analysis considered spacing error that varies around most of the gear circumference (similar to a typical sinusoidal error pattern) as well as a shorter span of spacing errors that occurs on only a few teeth. The dynamic analysis was performed using a revised version of a NASA gear dynamics code, modified to add tooth spacing errors to the analysis. Results obtained from the investigation show that linear tip relief is more effective in reducing dynamic loads on gears with small spacing errors but parabolic tip relief becomes more effective as the amplitude of spacing error increases. In addition, the parabolic modification is more effective for the more severe error case where the error is spread over a longer span of teeth. The findings of this study can be used to design robust tooth profile modification for improving dynamic performance of gear sets with different tooth spacing errors.

Angular spectral framework to test full corrections of paraxial solutions.

PubMed

Mahillo-Isla, R; González-Morales, M J

2015-07-01

Different correction methods for paraxial solutions have been used when such solutions extend out of the paraxial regime. The authors have used correction methods guided by either their experience or some educated hypothesis pertinent to the particular problem that they were tackling. This article provides a framework so as to classify full wave correction schemes. Thus, for a given solution of the paraxial wave equation, we can select the best correction scheme of those available. Some common correction methods are considered and evaluated under the proposed scope. Another remarkable contribution is obtained by giving the necessary conditions that two solutions of the Helmholtz equation must accomplish to accept a common solution of the parabolic wave equation as a paraxial approximation of both solutions.

Numerical simulation of transverse fuel injection

NASA Technical Reports Server (NTRS)

Mao, Marlon; Riggins, David W.; Mcclinton, Charles R.

1991-01-01

A review of recent work at NASA Langley Research Center to compare the predictions of transverse fuel injector flow fields and mixing performance with experimental results is presented. Various cold (non-reactive) mixing studies were selected for code calibration which include the effects of boundary layer thickness and injection angle for sonic hydrogen injection into supersonic air. Angled injection of helium is also included. This study was performed using both the three-dimensional elliptic and the parabolized Navier-Stokes (PNS) versions of SPARK. Axial solution planes were passed from PNS to elliptic and elliptic to PNS in order to efficiently generate solutions. The PNS version is used both upstream and far downstream of the injector where the flow can be considered parabolic in nature. The comparisons are used to identify experimental deficiencies and computational procedures to improve agreement.

A modified Dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.; Dwoyer, D. M.

1983-01-01

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow has been developed. The revision incorporates balancing of massflow rates on each marching step in order to maintain front-to-back continuity during the calculation. Qualitative agreement with analytical predictions and experimental results has been obtained for some flows with well-known solutions.

FIBER OPTICS: Method of calculation of the propagation constant for guided modes

NASA Astrophysics Data System (ADS)

Ardasheva, L. I.; Sadykov, Nail R.; Chernyakov, V. E.

1992-09-01

A new method of calculating the propagation constants and wave eigenfunctions of guided modes is proposed for axisymmetric translationally invariant fiber-optic waveguides with arbitrary refractive index profiles. The method is based on solving a parabolic scalar wave equation. A comparison is made between the numerical solution under steady-state conditions and the eigenfunctions of single-mode and multimode waveguides.

MURI: Impact of Oceanographic Variability on Acoustic Communications

DTIC Science & Technology

2012-09-30

ACSSC.2010.5757934 (2010). [published] [50] K. Tu, T.M. Duman, J.G. Proakis, and M. Stojanovic, “Cooperative MIMO - OFDM communications: Receiver...considered across bands of frequencies in the range 1-50 kHz. Multiple source and receiver cases ( MIMO ) will be of particular interest. Validating...Parabolic Equation (PE) acoustic models. Communication receiver design has included processors for orthogonal frequency division multiplexing ( OFDM

High Field Transport of Free Carriers at the SI-SIO2 Interface.

DTIC Science & Technology

1983-10-27

nuotbor) - Investigations of interface transport, ballistic transport and generally speaking high field transport in silicon and III-V compounds are...Tang and K. Hess, "Energy Diffusion Equation for an Electron Gas Interacting with Polar Optical Phonons: Non- Parabolic Case," Solid State...deformation potential electron-phonon scattering coeffi- cents is preented for elemental and compound semiconductors. Explesions for t acoustical defonoation

A Numerical Model for Trickle Bed Reactors

NASA Astrophysics Data System (ADS)

Propp, Richard M.; Colella, Phillip; Crutchfield, William Y.; Day, Marcus S.

2000-12-01

Trickle bed reactors are governed by equations of flow in porous media such as Darcy's law and the conservation of mass. Our numerical method for solving these equations is based on a total-velocity splitting, sequential formulation which leads to an implicit pressure equation and a semi-implicit mass conservation equation. We use high-resolution finite-difference methods to discretize these equations. Our solution scheme extends previous work in modeling porous media flows in two ways. First, we incorporate physical effects due to capillary pressure, a nonlinear inlet boundary condition, spatial porosity variations, and inertial effects on phase mobilities. In particular, capillary forces introduce a parabolic component into the recast evolution equation, and the inertial effects give rise to hyperbolic nonconvexity. Second, we introduce a modification of the slope-limiting algorithm to prevent our numerical method from producing spurious shocks. We present a numerical algorithm for accommodating these difficulties, show the algorithm is second-order accurate, and demonstrate its performance on a number of simplified problems relevant to trickle bed reactor modeling.

Numerical solution of Space Shuttle Orbiter flow field including real gas effects

NASA Technical Reports Server (NTRS)

Prabhu, D. K.; Tannehill, J. C.

1984-01-01

The hypersonic, laminar flow around the Space Shuttle Orbiter has been computed for both an ideal gas (gamma = 1.2) and equilibrium air using a real-gas, parabolized Navier-Stokes code. This code employs a generalized coordinate transformation; hence, it places no restrictions on the orientation of the solution surfaces. The initial solution in the nose region was computed using a 3-D, real-gas, time-dependent Navier-Stokes code. The thermodynamic and transport properties of equilibrium air were obtained from either approximate curve fits or a table look-up procedure. Numerical results are presented for flight conditions corresponding to the STS-3 trajectory. The computed surface pressures and convective heating rates are compared with data from the STS-3 flight.

Combined Numerical/Analytical Perturbation Solutions of the Navier-Stokes Equations for Aerodynamic (Ejector Nozzle) Flows

NASA Technical Reports Server (NTRS)

DeChant, Lawrence J.

1997-01-01

In spite of the rapid advances in both scalar and parallel computational tools, the large number and breadth of variables involved in aerodynamic systems make the use of parabolized or even boundary layer fluid flow models impractical for both preliminary design and inverse design problems. Given this restriction, we have concluded that reduced or approximate models are an important family of tools for design purposes. This study of a combined perturbation/numerical modeling methodology with an application to ejector-mixer nozzles (shown schematically in the following figure) is nearing completion. The work is being funded by a grant from the NASA Lewis Research Center to Texas A&M University. These ejector-mixer nozzle models are designed to be of use to the High Speed Civil Transport Program and may be adopted by both NASA and industry. A computer code incorporating the ejector-mixer models is under development. This code, the Differential Reduced Ejector/Mixer Analysis (DREA), can be run fast enough to be used as a subroutine or to be called by a design optimization routine. Simplified conservation equations--x-momentum, energy, and mass conservation--are used to define the model. Unlike other preliminary design models, DREA requires minimal empirical input and includes vortical mixing and a fully compressible formulation among other features. DREA is being validated by comparing it with results obtained from open literature and proprietary industry data. Preliminary results for a subsonic ejector and a supersonic ejector are shown. In addition, dedicated experiments have been performed at Texas A&M. These experiments use a hydraulic/gas flow analog to provide information about the inviscid mixing interface structure. Final validation and documentation of this work is expected by May of 1997. However, preliminary versions of DREA can be expected in early 1997. In summary, DREA provides a sufficiently detailed and realistic ejector-mixer nozzle model at a computational cost compatible with preliminary design applications.

Computational Methods for Control and Estimation of Distributed System

DTIC Science & Technology

1988-08-01

prey example. [1987, August] Estimation of Nonlinearities in Parabolic Models for Growth, Predation and Dispersal of Populations. S a ON A VARIATIONAL ...NOTATION 17. COSATI CODES 18. SUBJECT TERMS (Continue on reverse if necessary and identify by block number) FIELD GROUP SUB-GROUP 19. ABSTRACT (Continue...techniques for infinite dimensional systems. (v) Control and stabilization of visco-elastic structures. (vi) Approximation in delay and Volterra type

A theoretical and experimental investigation of nonlinear propagation of ultrasound through tissue mimicking media

NASA Astrophysics Data System (ADS)

Rielly, Matthew Robert

An existing numerical model (known as the Bergen code) is used to investigate finite amplitude ultrasound propagation through multiple layers of tissue-like media. This model uses a finite difference method to solve the nonlinear parabolic KZK wave equation. The code is modified to include an arbitrary frequency dependence of absorption and transmission effects for wave propagation across a plane interface at normal incidence. In addition the code is adapted to calculate the total intensity loss associated with the absorption of the fundamental and nonlinearly generated harmonics. Measurements are also taken of the axial nonlinear pressure field generated from a circular focused, 2.25 MHz source, through single and multiple layered tissue mimicking fluids, for source pressures in the range from 13 kPa to 310 kPa. Two tissue mimicking fluids are developed to provide acoustic properties similar to amniotic fluid and a typical soft tissue. The values of the nonlinearity parameter, sound velocity and frequency dependence of attenuation for both fluids are presented, and the measurement procedures employed to obtain these characteristics are described in detail. These acoustic parameters, together with the measured source conditions are used as input to the numerical model, allowing the experimental conditions to be simulated. Extensive comparisons are made between the model's predictions and the axial pressure field measurements. Results are presented in the frequency domain showing the fundamental and three subsequent harmonic amplitudes on axis, as a function of axial distance. These show that significant nonlinear distortion can occur through media with characteristics typical of tissue. Time domain waveform comparisons are also made. An excellent agreement is found between theory and experiment indicating that the model can be used to predict nonlinear ultrasound propagation through multiple layers of tissue-like media. The numerical code is also used to model the intensity loss through layered tissue mimics and results are presented illustrating the effects of altering the layered medium on the magnitude and spatial distribution of intensity loss.

On the Representation of Aquifer Compressibility in General Subsurface Flow Codes: How an Alternate Definition of Aquifer Compressibility Matches Results from the Groundwater Flow Equation

NASA Astrophysics Data System (ADS)

Birdsell, D.; Karra, S.; Rajaram, H.

2016-12-01

The governing equations for subsurface flow codes in deformable porous media are derived from the fluid mass balance equation. One class of these codes, which we call general subsurface flow (GSF) codes, does not explicitly track the motion of the solid porous media but does accept general constitutive relations for porosity, density, and fluid flux. Examples of GSF codes include PFLOTRAN, FEHM, STOMP, and TOUGH2. Meanwhile, analytical and numerical solutions based on the groundwater flow equation have assumed forms for porosity, density, and fluid flux. We review the derivation of the groundwater flow equation, which uses the form of Darcy's equation that accounts for the velocity of fluids with respect to solids and defines the soil matrix compressibility accordingly. We then show how GSF codes have a different governing equation if they use the form of Darcy's equation that is written only in terms of fluid velocity. The difference is seen in the porosity change, which is part of the specific storage term in the groundwater flow equation. We propose an alternative definition of soil matrix compressibility to correct for the untracked solid velocity. Simulation results show significantly less error for our new compressibility definition than the traditional compressibility when compared to analytical solutions from the groundwater literature. For example, the error in one calculation for a pumped sandstone aquifer goes from 940 to <70 Pa when the new compressibility is used. Code users and developers need to be aware of assumptions in the governing equations and constitutive relations in subsurface flow codes, and our newly-proposed compressibility function should be incorporated into GSF codes.

On the Representation of Aquifer Compressibility in General Subsurface Flow Codes: How an Alternate Definition of Aquifer Compressibility Matches Results from the Groundwater Flow Equation

NASA Astrophysics Data System (ADS)

Birdsell, D.; Karra, S.; Rajaram, H.

2017-12-01

The governing equations for subsurface flow codes in deformable porous media are derived from the fluid mass balance equation. One class of these codes, which we call general subsurface flow (GSF) codes, does not explicitly track the motion of the solid porous media but does accept general constitutive relations for porosity, density, and fluid flux. Examples of GSF codes include PFLOTRAN, FEHM, STOMP, and TOUGH2. Meanwhile, analytical and numerical solutions based on the groundwater flow equation have assumed forms for porosity, density, and fluid flux. We review the derivation of the groundwater flow equation, which uses the form of Darcy's equation that accounts for the velocity of fluids with respect to solids and defines the soil matrix compressibility accordingly. We then show how GSF codes have a different governing equation if they use the form of Darcy's equation that is written only in terms of fluid velocity. The difference is seen in the porosity change, which is part of the specific storage term in the groundwater flow equation. We propose an alternative definition of soil matrix compressibility to correct for the untracked solid velocity. Simulation results show significantly less error for our new compressibility definition than the traditional compressibility when compared to analytical solutions from the groundwater literature. For example, the error in one calculation for a pumped sandstone aquifer goes from 940 to <70 Pa when the new compressibility is used. Code users and developers need to be aware of assumptions in the governing equations and constitutive relations in subsurface flow codes, and our newly-proposed compressibility function should be incorporated into GSF codes.

Subsonic and Supersonic Jet Noise Calculations Using PSE and DNS

NASA Technical Reports Server (NTRS)

Balakumar, P.; Owis, Farouk

1999-01-01

Noise radiated from a supersonic jet is computed using the Parabolized Stability Equations (PSE) method. The evolution of the instability waves inside the jet is computed using the PSE method and the noise radiated to the far field from these waves is calculated by solving the wave equation using the Fourier transform method. We performed the computations for a cold supersonic jet of Mach number 2.1 which is excited by disturbances with Strouhal numbers St=.2 and .4 and the azimuthal wavenumber m=l. Good agreement in the sound pressure level are observed between the computed and the measured (Troutt and McLaughlin 1980) results.

On a strong solution of the non-stationary Navier-Stokes equations under slip or leak boundary conditions of friction type

NASA Astrophysics Data System (ADS)

Kashiwabara, Takahito

Strong solutions of the non-stationary Navier-Stokes equations under non-linearized slip or leak boundary conditions are investigated. We show that the problems are formulated by a variational inequality of parabolic type, to which uniqueness is established. Using Galerkin's method and deriving a priori estimates, we prove global and local existence for 2D and 3D slip problems respectively. For leak problems, under no-leak assumption at t=0 we prove local existence in 2D and 3D cases. Compatibility conditions for initial states play a significant role in the estimates.

SAGUARO: a finite-element computer program for partially saturated porous flow problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eaton, R.R.; Gartling, D.K.; Larson, D.E.

1983-06-01

SAGUARO is a finite element computer program designed to calculate two-dimensional flow of mass and energy through porous media. The media may be saturated or partially saturated. SAGUARO solves the parabolic time-dependent mass transport equation which accounts for the presence of partially saturated zones through the use of highly non-linear material characteristic curves. The energy equation accounts for the possibility of partially saturated regions by adjusting the thermal capacitances and thermal conductivities according to the volume fraction of water present in the local pores. Program capabilities, user instructions and a sample problem are presented in this manual.

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

NASA Technical Reports Server (NTRS)

Burns, John A.; Marrekchi, Hamadi

1993-01-01

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

Quantum deformations of conformal algebras with mass-like deformation parameters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frydryszak, Andrzej; Lukierski, Jerzy; Mozrzymas, Marek

1998-12-15

We recall the mathematical apparatus necessary for the quantum deformation of Lie algebras, namely the notions of coboundary Lie algebras, classical r-matrices, classical Yang-Baxter equations (CYBE), Froebenius algebras and parabolic subalgebras. Then we construct the quantum deformation of D=1, D=2 and D=3 conformal algebras, showing that this quantization introduce fundamental mass parameters. Finally we consider with more details the quantization of D=4 conformal algebra. We build three classes of sl(4,C) classical r-matrices, satisfying CYBE and depending respectively on 8, 10 and 12 generators of parabolic subalgebras. We show that only the 8-dimensional r-matrices allow to impose the D=4 conformal o(4,2){approx_equal}su(2,2)more » reality conditions. Weyl reflections and Dynkin diagram automorphisms for o(4,2) define the class of admissible bases for given classical r-matrices.« less

On asymptotic behavior and energy distribution for some one-dimensional non-parabolic diffusion problems

NASA Astrophysics Data System (ADS)

Kim, Seonghak; Yan, Baisheng

2018-06-01

We study some non-parabolic diffusion problems in one space dimension, where the diffusion flux exhibits forward and backward nature of the Perona–Malik, Höllig or non-Fourier type. Classical weak solutions to such problems are constructed in a way to capture some expected and unexpected properties, including anomalous asymptotic behaviors and energy dissipation or allocation. Specific properties of solutions will depend on the type of the diffusion flux, but the primary method of our study relies on reformulating diffusion equations involved as an inhomogeneous partial differential inclusion and on constructing solutions from the differential inclusion by a combination of the convex integration and Baire’s category methods. In doing so, we introduce the appropriate notion of subsolutions of the partial differential inclusion and their transition gauge, which plays a pivotal role in dealing with some specific features of the constructed weak solutions.

Enhanced Particle Swarm Optimization Algorithm: Efficient Training of ReaxFF Reactive Force Fields.

PubMed

Furman, David; Carmeli, Benny; Zeiri, Yehuda; Kosloff, Ronnie

2018-06-12

Particle swarm optimization (PSO) is a powerful metaheuristic population-based global optimization algorithm. However, when it is applied to nonseparable objective functions, its performance on multimodal landscapes is significantly degraded. Here we show that a significant improvement in the search quality and efficiency on multimodal functions can be achieved by enhancing the basic rotation-invariant PSO algorithm with isotropic Gaussian mutation operators. The new algorithm demonstrates superior performance across several nonlinear, multimodal benchmark functions compared with the rotation-invariant PSO algorithm and the well-established simulated annealing and sequential one-parameter parabolic interpolation methods. A search for the optimal set of parameters for the dispersion interaction model in the ReaxFF- lg reactive force field was carried out with respect to accurate DFT-TS calculations. The resulting optimized force field accurately describes the equations of state of several high-energy molecular crystals where such interactions are of crucial importance. The improved algorithm also presents better performance compared to a genetic algorithm optimization method in the optimization of the parameters of a ReaxFF- lg correction model. The computational framework is implemented in a stand-alone C++ code that allows the straightforward development of ReaxFF reactive force fields.

Simulation of electromagnetic ion cyclotron triggered emissions in the Earth's inner magnetosphere

NASA Astrophysics Data System (ADS)

Shoji, Masafumi; Omura, Yoshiharu

2011-05-01

In a recent observation by the Cluster spacecraft, emissions triggered by electromagnetic ion cyclotron (EMIC) waves were discovered in the inner magnetosphere. We perform hybrid simulations to reproduce the EMIC triggered emissions. We develop a self-consistent one-dimensional hybrid code with a cylindrical geometry of the background magnetic field. We assume a parabolic magnetic field to model the dipole magnetic field in the equatorial region of the inner magnetosphere. Triggering EMIC waves are driven by a left-handed polarized external current assumed at the magnetic equator in the simulation model. Cold proton, helium, and oxygen ions, which form branches of the dispersion relation of the EMIC waves, are uniformly distributed in the simulation space. Energetic protons with a loss cone distribution function are also assumed as resonant particles. We reproduce rising tone emissions in the simulation space, finding a good agreement with the nonlinear wave growth theory. In the energetic proton velocity distribution we find formation of a proton hole, which is assumed in the nonlinear wave growth theory. A substantial amount of the energetic protons are scattered into the loss cone, while some of the resonant protons are accelerated to higher pitch angles, forming a pancake velocity distribution.

Numerical Solution of the Kzk Equation for Pulsed Finite Amplitude Sound Beams in Thermoviscous Fluids

NASA Astrophysics Data System (ADS)

Lee, Yang-Sub

A time-domain numerical algorithm for solving the KZK (Khokhlov-Zabolotskaya-Kuznetsov) nonlinear parabolic wave equation is developed for pulsed, axisymmetric, finite amplitude sound beams in thermoviscous fluids. The KZK equation accounts for the combined effects of diffraction, absorption, and nonlinearity at the same order of approximation. The accuracy of the algorithm is established via comparison with analytical solutions for several limiting cases, and with numerical results obtained from a widely used algorithm for solving the KZK equation in the frequency domain. The time domain algorithm is used to investigate waveform distortion and shock formation in directive sound beams radiated by pulsed circular piston sources. New results include predictions for the entire process of self-demodulation, and for the effect of frequency modulation on pulse envelope distortion. Numerical results are compared with measurements, and focused sources are investigated briefly.

Dynamic contact problem with adhesion and damage between thermo-electro-elasto-viscoplastic bodies

NASA Astrophysics Data System (ADS)

Hadj ammar, Tedjani; Saïdi, Abdelkader; Azeb Ahmed, Abdelaziz

2017-05-01

We study of a dynamic contact problem between two thermo-electro-elasto-viscoplastic bodies with damage and adhesion. The contact is frictionless and is modeled with normal compliance condition. We derive variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of evolutionary variational inequalities, parabolic inequalities, differential equations, and fixed point theorem.

Local regularity for time-dependent tug-of-war games with varying probabilities

NASA Astrophysics Data System (ADS)

Parviainen, Mikko; Ruosteenoja, Eero

2016-07-01

We study local regularity properties of value functions of time-dependent tug-of-war games. For games with constant probabilities we get local Lipschitz continuity. For more general games with probabilities depending on space and time we obtain Hölder and Harnack estimates. The games have a connection to the normalized p (x , t)-parabolic equation ut = Δu + (p (x , t) - 2) Δ∞N u.

3D Gaussian Beam Modeling

DTIC Science & Technology

2011-09-01

optimized building blocks such as a parallelized tri-diagonal linear solver (used in the “implicit finite differences ” and split-step Pade PE models...and Ding Lee. “A finite - difference treatment of interface conditions for the parabolic wave equation: The horizontal interface.” The Journal of the...Acoustical Society of America, 71(4):855, 1982. 3. Ding Lee and Suzanne T. McDaniel. “A finite - difference treatment of interface conditions for

Deep Water Ocean Acoustics

DTIC Science & Technology

2015-10-19

and has a large number of hydroacoustic signals generated by seismic events. Results Many of these results were reported in the previous July 15...noise, under-ice scattering, bathymetric diffraction and the application of the ocean acoustic Parabolic Equation to infrasound . 2. Tasks a. Task...of long-range signals is a seismic event on the Kerguelen Plateau (-53°S 71°E) in the southern ocean. This region of the world, which includes Heard

Elastic Bottom Propagation Mechanisms Investigated by Parabolic Equation Methods

DTIC Science & Technology

2014-09-30

channel propagation of oceanic T waves from seismic sources in the presence of intervening seamounts or coral reef barriers is established using elastic PE...environments in the form of scattering at an elastic interface, oceanic T - waves , and Scholte waves . OBJECTIVES To implement explosive and earthquake...oceanic T - waves , which are acoustic waves that result from earthquake or buried explosive sources, and Rayleigh-type waves along the ocean floor, whose

Numerical approach to optimal portfolio in a power utility regime-switching model

NASA Astrophysics Data System (ADS)

Gyulov, Tihomir B.; Koleva, Miglena N.; Vulkov, Lubin G.

2017-12-01

We consider a system of weakly coupled degenerate semi-linear parabolic equations of optimal portfolio in a regime-switching with power utility function, derived by A.R. Valdez and T. Vargiolu [14]. First, we discuss some basic properties of the solution of this system. Then, we develop and analyze implicit-explicit, flux limited finite difference schemes for the differential problem. Numerical experiments are discussed.

Improved Estimates of Thermodynamic Parameters

NASA Technical Reports Server (NTRS)

Lawson, D. D.

1982-01-01

Techniques refined for estimating heat of vaporization and other parameters from molecular structure. Using parabolic equation with three adjustable parameters, heat of vaporization can be used to estimate boiling point, and vice versa. Boiling points and vapor pressures for some nonpolar liquids were estimated by improved method and compared with previously reported values. Technique for estimating thermodynamic parameters should make it easier for engineers to choose among candidate heat-exchange fluids for thermochemical cycles.

Deep Water Ocean Acoustics

DTIC Science & Technology

2015-07-17

under- ice scattering, bathymetric diffraction and the application of the ocean acoustic Parabolic Equation to infrasound. 2. Tasks a. Task 1...and Climate of the Ocean, Phase II (ECCO2): High-Resolution Global-Ocean and Sea- Ice Data Synthesis) model re- analysis for the years 1992 and 1993...The ECCO2 model is a state estimation based upon data syntheses obtained by least squares fitting of the global ocean and sea- ice configuration of

Parabolized Stability Equations analysis of nonlinear interactions with forced eigenmodes to control subsonic jet instabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Itasse, Maxime, E-mail: Maxime.Itasse@onera.fr; Brazier, Jean-Philippe, E-mail: Jean-Philippe.Brazier@onera.fr; Léon, Olivier, E-mail: Olivier.Leon@onera.fr

2015-08-15

Nonlinear evolution of disturbances in an axisymmetric, high subsonic, high Reynolds number hot jet with forced eigenmodes is studied using the Parabolized Stability Equations (PSE) approach to understand how modes interact with one another. Both frequency and azimuthal harmonic interactions are analyzed by setting up one or two modes at higher initial amplitudes and various phases. While single mode excitation leads to harmonic growth and jet noise amplification, controlling the evolution of a specific mode has been made possible by forcing two modes (m{sub 1}, n{sub 1}), (m{sub 2}, n{sub 2}), such that the difference in azimuth and in frequencymore » matches the desired “target” mode (m{sub 1} − m{sub 2}, n{sub 1} − n{sub 2}). A careful setup of the initial amplitudes and phases of the forced modes, defined as the “killer” modes, has allowed the minimizing of the initially dominant instability in the near pressure field, as well as its estimated radiated noise with a 15 dB loss. Although an increase of the overall sound pressure has been found in the range of azimuth and frequency analyzed, the present paper reveals the possibility to make the initially dominant instability ineffective acoustically using nonlinear interactions with forced eigenmodes.« less

Modeling propagation of infrasound signals observed by a dense seismic network.

PubMed

Chunchuzov, I; Kulichkov, S; Popov, O; Hedlin, M

2014-01-01

The long-range propagation of infrasound from a surface explosion with an explosive yield of about 17.6 t TNT that occurred on June 16, 2008 at the Utah Test and Training Range (UTTR) in the western United States is simulated using an atmospheric model that includes fine-scale layered structure of the wind velocity and temperature fields. Synthetic signal parameters (waveforms, amplitudes, and travel times) are calculated using parabolic equation and ray-tracing methods for a number of ranges between 100 and 800 km from the source. The simulation shows the evolution of several branches of stratospheric and thermospheric signals with increasing range from the source. Infrasound signals calculated using a G2S (ground-to-space) atmospheric model perturbed by small-scale layered wind velocity and temperature fluctuations are shown to agree well with recordings made by the dense High Lava Plains seismic network located at an azimuth of 300° from UTTR. The waveforms of calculated infrasound arrivals are compared with those of seismic recordings. This study illustrates the utility of dense seismic networks for mapping an infrasound field with high spatial resolution. The parabolic equation calculations capture both the effect of scattering of infrasound into geometric acoustic shadow zones and significant temporal broadening of the arrivals.

Investigate the shock focusing under a single vortex disturbance using 2D Saint-Venant equations with a shock-capturing scheme

NASA Astrophysics Data System (ADS)

Zhao, Jiaquan; Li, Renfu; Wu, Haiyan

2018-02-01

In order to characterize the flow structure and the effect of acoustic waves caused by the shock-vortex interaction on the performance of the shock focusing, the incident plane shock wave with a single disturbance vortex focusing in a parabolic cavity is simulated systematically through solving the two-dimensional, unsteady Saint-Venant equations with the two order HLL scheme of Riemann solvers. The simulations show that the dilatation effect to be dominant in the net vorticity generation, while the baroclinic effect is dominate in the absence of initial vortex disturbance. Moreover, the simulations show that the time evolution of maximum focusing pressure with initial vortex is more complicate than that without initial vortex, which has a lot of relevance with the presence of quadrupolar acoustic wave structure induced by shock-vortex interaction and its propagation in the cavity. Among shock and other disturbance parameters, the shock Mach number, vortex Mach number and the shape of parabolic reflector proved to play a critical role in the focusing of shock waves and the strength of viscous dissipation, which in turn govern the evolution of maximum focusing pressure due to the gas dynamic focus, the change in dissipation rate and the coincidence of motion disturbance vortex with aerodynamic focus point.

A permutation characterization of Sturm global attractors of Hamiltonian type

NASA Astrophysics Data System (ADS)

Fiedler, Bernold; Rocha, Carlos; Wolfrum, Matthias

We consider Neumann boundary value problems of the form u=u+f on the interval 0⩽x⩽π for dissipative nonlinearities f=f(u). A permutation characterization for the global attractors of the semiflows generated by these equations is well known, even in the much more general case f=f(x,u,u). We present a permutation characterization for the global attractors in the restrictive class of nonlinearities f=f(u). In this class the stationary solutions of the parabolic equation satisfy the second order ODE v+f(v)=0 and we obtain the permutation characterization from a characterization of the set of 2 π-periodic orbits of this planar Hamiltonian system. Our results are based on a diligent discussion of this mere pendulum equation.

Factors influencing the thermally-induced strength degradation of B/Al composites

NASA Technical Reports Server (NTRS)

Dicarlo, J. A.

1982-01-01

Literature data related to the thermally-induced strength degradation of B/Al composites were examined in the light of fracture theories based on reaction-controlled fiber weakening. Under the assumption of a parabolic time-dependent growth for the interfacial reaction product, a Griffith-type fracture model was found to yield simple equations whose predictions were in good agreement with data for boron fiber average strength and for B/Al axial fracture strain. The only variables in these equations were the time and temperature of the thermal exposure and an empirical factor related to fiber surface smoothness prior to composite consolidation. Such variables as fiber diameter and aluminum alloy composition were found to have little influence. The basic and practical implications of the fracture model equations are discussed.

Transformed Fourier and Fick equations for the control of heat and mass diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guenneau, S.; Petiteau, D.; Zerrad, M.

We review recent advances in the control of diffusion processes in thermodynamics and life sciences through geometric transforms in the Fourier and Fick equations, which govern heat and mass diffusion, respectively. We propose to further encompass transport properties in the transformed equations, whereby the temperature is governed by a three-dimensional, time-dependent, anisotropic heterogeneous convection-diffusion equation, which is a parabolic partial differential equation combining the diffusion equation and the advection equation. We perform two dimensional finite element computations for cloaks, concentrators and rotators of a complex shape in the transient regime. We precise that in contrast to invisibility cloaks for waves,more » the temperature (or mass concentration) inside a diffusion cloak crucially depends upon time, its distance from the source, and the diffusivity of the invisibility region. However, heat (or mass) diffusion outside cloaks, concentrators and rotators is unaffected by their presence, whatever their shape or position. Finally, we propose simplified designs of layered cylindrical and spherical diffusion cloaks that might foster experimental efforts in thermal and biochemical metamaterials.« less

Overview of the ArbiTER edge plasma eigenvalue code

NASA Astrophysics Data System (ADS)

Baver, Derek; Myra, James; Umansky, Maxim

2011-10-01

The Arbitrary Topology Equation Reader, or ArbiTER, is a flexible eigenvalue solver that is currently under development for plasma physics applications. The ArbiTER code builds on the equation parser framework of the existing 2DX code, extending it to include a topology parser. This will give the code the capability to model problems with complicated geometries (such as multiple X-points and scrape-off layers) or model equations with arbitrary numbers of dimensions (e.g. for kinetic analysis). In the equation parser framework, model equations are not included in the program's source code. Instead, an input file contains instructions for building a matrix from profile functions and elementary differential operators. The program then executes these instructions in a sequential manner. These instructions may also be translated into analytic form, thus giving the code transparency as well as flexibility. We will present an overview of how the ArbiTER code is to work, as well as preliminary results from early versions of this code. Work supported by the U.S. DOE.

Computations of the Magnus effect for slender bodies in supersonic flow

NASA Technical Reports Server (NTRS)

Sturek, W. B.; Schiff, L. B.

1980-01-01

A recently reported Parabolized Navier-Stokes code has been employed to compute the supersonic flow field about spinning cone, ogive-cylinder, and boattailed bodies of revolution at moderate incidence. The computations were performed for flow conditions where extensive measurements for wall pressure, boundary layer velocity profiles and Magnus force had been obtained. Comparisons between the computational results and experiment indicate excellent agreement for angles of attack up to six degrees. The comparisons for Magnus effects show that the code accurately predicts the effects of body shape and Mach number for the selected models for Mach numbers in the range of 2-4.

Examining Changes in Radioxenon Isotope Activity Ratios during Subsurface Transport

NASA Astrophysics Data System (ADS)

Annewandter, R.

2013-12-01

The Non-Proliferation Experiment (NPE) has demonstrated and modelled the usefulness of barometric pumping induced soil gas sampling during On-Site inspections. Gas transport has been widely studied with different numerical codes. However, gas transport of all radioxenons in the post-detonation regime and their possible fractionation is still neglected in the open literature. Atmospheric concentrations of the radioxenons Xe-135, Xe-133m, Xe-133 and Xe-131m can be used to discriminate between civilian releases (nuclear power plants or medical isotope facilities), and nuclear explosion sources. It is based on the isotopic activity ratio method. Yet it is not clear whether subsurface migration of the radioxenons, with eventual release into the atmosphere, can affect the activity ratios due to fractionation. Fractionation can be caused by different diffusivities due to mass differences between the radioxenons. A previous study showed surface arrival time of a chemically inert gaseous tracer is affected by its diffusivity. They observed detectable amount for SF6 50 days after detonation and 375 days for He-3. They predict 50 and 80 days for Xe-133 and Ar-37 respectively. Cyclical changes in atmospheric pressure can drive subsurface gas transport. This barometric pumping phenomenon causes an oscillatoric flow in upward trending fractures which, combined with diffusion into the porous matrix, leads to a net transport of gaseous components - a ratcheting effect. We use a general purpose reservoir simulator (Complex System Modelling Platform, CSMP++) which has been applied in a range of fields such as deep geothermal systems, three-phase black oil simulations , fracture propagation in fractured, porous media, Navier-Stokes pore-scale modelling among others. It is specifically designed to account for structurally complex geologic situation of fractured, porous media. Parabolic differential equations are solved by a continuous Galerkin finite-element method, hyperbolic differential equations by a complementary finite volume method. The parabolic and hyperbolic problem can be solved separately using the operator-splitting method (Implicit Pressure Explicit Saturation, IMPES). The resulting system of linear equations is solved by the algebraic multigrid library SAMG, developed at the Fraunhofer Institute for Algorithms and Scientific Computing. CSMP++ is developed at Montan University of Leoben, ETH Zuerich, Imperial College London and Heriot-Watt University in Edinburgh. To date, there has been no research investigating how subsurface transport impacts isotope activity ratios. The isotopic activity ratio method can be used to discriminate between civil release or nuclear explosion sources. This study examines possible fractionation of Xe-135, Xe-133m, Xe-133, Xe-131m during barometric pumping-driven subsurface migration, which can affect surface arrival times and isotopic activity ratios. Surface arrival times for the Noble gases Kr-81, Kr-85 and Ar-39 are also calculated.

APL-UW Deep Water Propagation 2015-2017: Philippine Sea Data Analysis

DTIC Science & Technology

independent Monte Carlo parabolic equation simulations . The autospectrum of normalized intensity had an excellent match to that of a time-dependent Monte...ambient noise; systems along the Aleutian chain have either no significant trendor a slight increasing trend; systems in the central Pacific Ocean...At the end of the grant, it was determined that the Kauai cable had suffered a break in the shallow near-shore region. Additional contractual

Well-Posedness Results for a Class of Toxicokinetic Models

DTIC Science & Technology

2001-07-24

estimation. The main result that we establish here regarding well-posedness of solutions is based on ideas presented in [5] and [1]. Banks and Musante [5...necessary regularity required for the model to t into the second class of abstract problems discussed by Banks and Musante . Transport models for other...upon the results of Banks and Musante by achieving well-posedness for a more general class of abstract nonlinear parabolic equations. Ackleh, Banks and

PE Workshop II. Proceedings of the Second Parabolic Equation Workshop

DTIC Science & Technology

1993-01-01

13) The values for the Padd coefficients tabulated in [8] were generated using the same accuracy and stability constraints used to generate the Pad6...singly to that subject. With the expectation that such a workshop would soon occur, the general topic of underwater acoustic scattering was minimized...were not generated for all of the test cases. The available reference solutions were forwarded to the participants on 23 April 1991. Since the workshop

Design, Integration and Flight Test of a Pair of Autonomous Spacecraft Flying in Formation

DTIC Science & Technology

2013-05-01

representatives from the Air Force Research Laboratory, NASA’s Goddard Space Flight Center, the Jet Propulsion Laboratory, Boeing, Lockheed Martin, as...categories: elliptical , hyperbolic and parabolic (known as “Keplerian orbits”), each with their own characteristics and applications. These equations...of M-SAT’s operation is that of an elliptical nature, or more precisely a near-circular orbit. The primary method of determining the orbital elements

Accelerated Simulation of Kinetic Transport Using Variational Principles and Sparsity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Caflisch, Russel

This project is centered on the development and application of techniques of sparsity and compressed sensing for variational principles, PDEs and physics problems, in particular for kinetic transport. This included derivation of sparse modes for elliptic and parabolic problems coming from variational principles. The research results of this project are on methods for sparsity in differential equations and their applications and on application of sparsity ideas to kinetic transport of plasmas.

Development of Vector Parabolic Equation Technique for Propagation in Urban and Tunnel Environments

DTIC Science & Technology

2010-09-01

relativistic quantum mechanics J. Phys. A: Math. Gen. 16 1869–84 [8] Nottale L 1995 Scale relativity, fractal space- time and quantum mechanics Quantum...proportional to the “ time ” elapsed. By performing various approximations to the transfer function, several approximate absorbing boundary condi- tions...The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing

3-D Acoustic Scattering from 2-D Rough Surfaces Using A Parabolic Equation Model

DTIC Science & Technology

2013-12-01

Frequency Acoustic Propagation in Shallow Water.” Journal of Oceanic Engineering, September 2011: 1–10. Liu, Jin Yuan, Chen Fen Huang, and Ping Chang...loss values at a constant depth. .............................52  xi LIST OF ACRONYMS AND ABBREVIATIONS FD Finite Difference MMPE Monterey...2013). First, at each range step ( xi ), the 3-D field is transformed from cross-range spatial variable (y) to cross-range wavenumber variable (ky

EM Propagation & Atmospheric Effects Assessment

DTIC Science & Technology

2008-09-30

The split-step Fourier parabolic equation ( SSPE ) algorithm provides the complex amplitude and phase (group delay) of the continuous wave (CW) signal...the APM is based on the SSPE , we are implementing the more efficient Fourier synthesis technique to determine the transfer function. To this end a...needed in order to sample H(f) via the SSPE , and indeed with the proper parameters chosen, the two pulses can be resolved in the time window shown in

A moving mesh finite difference method for equilibrium radiation diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

Finite element analysis of low speed viscous and inviscid aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1977-01-01

A weak interaction solution algorithm was established for aerodynamic flow about an isolated airfoil. Finite element numerical methodology was applied to solution of each of differential equations governing potential flow, and viscous and turbulent boundary layer and wake flow downstream of the sharp trailing edge. The algorithm accounts for computed viscous displacement effects on the potential flow. Closure for turbulence was accomplished using both first and second order models. The COMOC finite element fluid mechanics computer program was modified to solve the identified equation systems for two dimensional flows. A numerical program was completed to determine factors affecting solution accuracy, convergence and stability for the combined potential, boundary layer, and parabolic Navier-Stokes equation systems. Good accuracy and convergence are demonstrated. Each solution is obtained within the identical finite element framework of COMOC.

Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations.

PubMed

Bell, John B; Garcia, Alejandro L; Williams, Sarah A

2007-07-01

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS solver are compared with theory, when available, and with molecular simulations using a direct simulation Monte Carlo algorithm.

Accessible solitons of fractional dimension

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhong, Wei-Ping, E-mail: zhongwp6@126.com; Texas A&M University at Qatar, P.O. Box 23874, Doha; Belić, Milivoj

We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential.more » •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.« less

On the solution of evolution equations based on multigrid and explicit iterative methods

NASA Astrophysics Data System (ADS)

Zhukov, V. T.; Novikova, N. D.; Feodoritova, O. B.

2015-08-01

Two schemes for solving initial-boundary value problems for three-dimensional parabolic equations are studied. One is implicit and is solved using the multigrid method, while the other is explicit iterative and is based on optimal properties of the Chebyshev polynomials. In the explicit iterative scheme, the number of iteration steps and the iteration parameters are chosen as based on the approximation and stability conditions, rather than on the optimization of iteration convergence to the solution of the implicit scheme. The features of the multigrid scheme include the implementation of the intergrid transfer operators for the case of discontinuous coefficients in the equation and the adaptation of the smoothing procedure to the spectrum of the difference operators. The results produced by these schemes as applied to model problems with anisotropic discontinuous coefficients are compared.

Factors influencing the thermally-induced strength degradation of B/Al composites

NASA Technical Reports Server (NTRS)

Dicarlo, J. A.

1983-01-01

Literature data related to the thermally-induced strength degradation of B/Al composites were examined in the light of fracture theories based on reaction-controlled fiber weakening. Under the assumption of a parabolic time-dependent growth for the interfacial reaction product, a Griffith-type fracture model was found to yield simple equations whose predictions were in good agreement with data for boron fiber average strength and for B/Al axial fracture strain. The only variables in these equations were the time and temperature of the thermal exposure and an empirical factor related to fiber surface smoothness prior to composite consolidation. Such variables as fiber diameter and aluminum alloy composition were found to have little influence. The basic and practical implications of the fracture model equations are discussed. Previously announced in STAR as N82-24297

Higher and lowest order mixed finite element approximation of subsurface flow problems with solutions of low regularity

NASA Astrophysics Data System (ADS)

Bause, Markus

2008-02-01

In this work we study mixed finite element approximations of Richards' equation for simulating variably saturated subsurface flow and simultaneous reactive solute transport. Whereas higher order schemes have proved their ability to approximate reliably reactive solute transport (cf., e.g. [Bause M, Knabner P. Numerical simulation of contaminant biodegradation by higher order methods and adaptive time stepping. Comput Visual Sci 7;2004:61-78]), the Raviart- Thomas mixed finite element method ( RT0) with a first order accurate flux approximation is popular for computing the underlying water flow field (cf. [Bause M, Knabner P. Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods. Adv Water Resour 27;2004:565-581, Farthing MW, Kees CE, Miller CT. Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow. Adv Water Resour 26;2003:373-394, Starke G. Least-squares mixed finite element solution of variably saturated subsurface flow problems. SIAM J Sci Comput 21;2000:1869-1885, Younes A, Mosé R, Ackerer P, Chavent G. A new formulation of the mixed finite element method for solving elliptic and parabolic PDE with triangular elements. J Comp Phys 149;1999:148-167, Woodward CS, Dawson CN. Analysis of expanded mixed finite element methods for a nonlinear parabolic equation modeling flow into variably saturated porous media. SIAM J Numer Anal 37;2000:701-724]). This combination might be non-optimal. Higher order techniques could increase the accuracy of the flow field calculation and thereby improve the prediction of the solute transport. Here, we analyse the application of the Brezzi- Douglas- Marini element ( BDM1) with a second order accurate flux approximation to elliptic, parabolic and degenerate problems whose solutions lack the regularity that is assumed in optimal order error analyses. For the flow field calculation a superiority of the BDM1 approach to the RT0 one is observed, which however is less significant for the accompanying solute transport.

The Early Development of Indian Radio Astronomy: A Personal Perspective

NASA Astrophysics Data System (ADS)

Swarup, Govind

In this chapter I recall my initiation into the field of radio astronomy during 1953-1955 at CSIRO, Australia; the transfer of thirty-two 6-feet (1.8-m) diameter parabolic dishes from Potts Hill, Sydney, to India in 1958; and their erection at Kalyan, near Bombay (Mumbai), in 1963-1965. The Kalyan Radio Telescope was the first modern radio telescope built in India. This led to the establishment of a very active radio astronomy group at the Tata Institute of Fundamental Research, which subsequently built two world-class radio telescopes during the last 50 years and also contributed to the development of an indigenous microwave antenna industry in India. The Ooty Radio Telescope, built during 1965-1970, has an ingenious design which takes advantage of India's location near the Earth's Equator. The long axis of this 530-m × 30-m parabolic cylinder was made parallel to the Equator, by placing it on a hill with the same slope as the geographic latitude ( 11°), thus allowing it to track celestial sources continuously for 9.5 h every day. By utilizing lunar occultations, the telescope was able to measure the angular sizes of a large number of faint radio galaxies and quasars with arc-second resolution for the first time. Subsequently, during the 1990s, the group set up the Giant Metrewave Radio Telescope (GMRT) near Pune in western India, in order to investigate certain astrophysical phenomena which are best studied at decimetre and metre wavelengths. The GMRT is an array of 30 fully steerable 45-m diameter parabolic dishes, which operates at several frequencies below 1.43 GHz. These efforts have also contributed to the international proposal to construct the Square Kilometre Array (SKA). This chapter is a revised version of Swarup (Journal of Astronomical History and Heritage, 9: 21-33, 2006).

Energy Decay and Boundary Control for Distributed Parameter Systems with Viscoelastic Damping

DTIC Science & Technology

1989-07-24

for the evolution variational 2 inequality for a rigid-visco-plastic (Bingham) fluid [4, 11-13J. Other work involved numerical and theoretical analysis...dimensional parabolic -elliptic interface problem, submitted to Quart. Appl. Math. 16. W. Desch and R. K. Miller, Exponential Stabilization of Volterra ...17 16. SUPPLEMENTARY NOTATION 17, COSATI CODES 18. SUBJECT TERMS (Continue an revemu of necessay and kdeftOi by block number) FIELD IGROUP ISUB-GROUP

Generalized Forchheimer Flows of Isentropic Gases

NASA Astrophysics Data System (ADS)

Celik, Emine; Hoang, Luan; Kieu, Thinh

2018-03-01

We consider generalized Forchheimer flows of either isentropic gases or slightly compressible fluids in porous media. By using Muskat's and Ward's general form of the Forchheimer equations, we describe the fluid dynamics by a doubly nonlinear parabolic equation for the appropriately defined pseudo-pressure. The volumetric flux boundary condition is converted to a time-dependent Robin-type boundary condition for this pseudo-pressure. We study the corresponding initial boundary value problem, and estimate the L^∞ and W^{1,2-a} (with 0

On the exploration of effect of critical beam power on the propagation of Gaussian laser beam in collisionless magnetized plasma

NASA Astrophysics Data System (ADS)

Urunkar, T. U.; Valkunde, A. T.; Vhanmore, B. D.; Gavade, K. M.; Patil, S. D.; Takale, M. V.

2018-05-01

It is quite known that critical power of the laser plays vital role in the propagation of Gaussian laser beam in collisionless plasma. The nonlinearity in dielectric constant considered herein is due to the ponderomotive force. In the present analysis, the interval of critical beam power has been explored to sustain the competition between diffraction and self-focusing of Gaussian laser beam during propagation in collisionless magnetized plasma. Differential equation for beam-width parameter has been established by using WKB and paraxial approximations under parabolic equation approach. The effect of critical power on the propagation of Gaussian laser beam has been presented graphically and discussed.

Ponderomotive and weakly relativistic self-focusing of Gaussian laser beam in plasma: Effect of light absorption

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patil, S. D., E-mail: sdpatilphy@gmail.com; Takale, M. V.

2016-05-06

This paper presents an influence of light absorption on self-focusing of laser beam propagation in plasma. The differential equation for beam-width parameter is obtained using the Wentzel-Kramers-Brillouin and paraxial approximations through parabolic equation approach. The nonlinearity in dielectric function is assumed to be aroused due to the combined effect of weakly relativistic and ponderomotive regime. To highlight the nature of propagation, behavior of beam-width parameter with dimensionless distance of propagation is presented graphically and discussed. The present work is helpful to understand issues related to the beam propagation in laser plasma interaction experiments where light absorption plays a vital role.

N-Soliton Solution and Soliton Resonances for the (2+1)-Dimensional Inhomogeneous Gardner Equation

NASA Astrophysics Data System (ADS)

Wang, Xin; Geng, Xian-Guo

2017-08-01

We derive the Lax pair and Darboux transformation for the (2+1)-dimensional inhomogeneous Gardner equation via the two-singular manifold method from Painlevé analysis. N-soliton solution in a compact determinant representation of Grammian type is presented. As an application, dynamic properties of the bright and dark soliton solutions under periodic and parabolic oscillations up to second order are shown. Resonant behaviors of two bright and two dark solitons are studied, and asymptotic analysis of the corresponding resonant bright and dark two-soliton solutions are performed, respectively. Supported by National Natural Science Foundation of China under Grant No. 11331008 and China Postdoctoral Science Foundation Funded Sixtieth Batches (2016M602252)

Slender-Body Theory Based On Approximate Solution of the Transonic Flow Equation

NASA Technical Reports Server (NTRS)

Spreiter, John R.; Alksne, Alberta Y.

1959-01-01

Approximate solution of the nonlinear equations of the small disturbance theory of transonic flow are found for the pressure distribution on pointed slender bodies of revolution for flows with free-stream, Mach number 1, and for flows that are either purely subsonic or purely supersonic. These results are obtained by application of a method based on local linearization that was introduced recently in the analysis of similar problems in two-dimensional flows. The theory is developed for bodies of arbitrary shape, and specific results are given for cone-cylinders and for parabolic-arc bodies at zero angle of attack. All results are compared either with existing theoretical results or with experimental data.

Fick's second law transformed: one path to cloaking in mass diffusion.

PubMed

Guenneau, S; Puvirajesinghe, T M

2013-06-06

Here, we adapt the concept of transformational thermodynamics, whereby the flux of temperature is controlled via anisotropic heterogeneous diffusivity, for the diffusion and transport of mass concentration. The n-dimensional, time-dependent, anisotropic heterogeneous Fick's equation is considered, which is a parabolic partial differential equation also applicable to heat diffusion, when convection occurs, for example, in fluids. This theory is illustrated with finite-element computations for a liposome particle surrounded by a cylindrical multi-layered cloak in a water-based environment, and for a spherical multi-layered cloak consisting of layers of fluid with an isotropic homogeneous diffusivity, deduced from an effective medium approach. Initial potential applications could be sought in bioengineering.

Spectral methods in time for a class of parabolic partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ierley, G.; Spencer, B.; Worthing, R.

1992-09-01

In this paper, we introduce a fully spectral solution for the partial differential equation u[sub t] + uu[sub x] + vu[sub xx] + [mu]u[sub xxx] + [lambda]u[sub xxxx] = O. For periodic boundary conditions in space, the use of a Fourier expansion in x admits of a particularly efficient algorithm with respect to expansion of the time dependence in a Chebyshev series. Boundary conditions other than periodic may still be treated with reasonable, though lesser, efficiency. for all cases, very high accuracy is attainable at moderate computational cost relative to the expense of variable order finite difference methods in time.more » 14 refs., 9 figs.« less

xRage Equation of State

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grove, John W.

2016-08-16

The xRage code supports a variety of hydrodynamic equation of state (EOS) models. In practice these are generally accessed in the executing code via a pressure-temperature based table look up. This document will describe the various models supported by these codes and provide details on the algorithms used to evaluate the equation of state.

Pulsed fusion space propulsion: Computational Magneto-Hydro Dynamics of a multi-coil parabolic reaction chamber

NASA Astrophysics Data System (ADS)

Romanelli, Gherardo; Mignone, Andrea; Cervone, Angelo

2017-10-01

Pulsed fusion propulsion might finally revolutionise manned space exploration by providing an affordable and relatively fast access to interplanetary destinations. However, such systems are still in an early development phase and one of the key areas requiring further investigations is the operation of the magnetic nozzle, the device meant to exploit the fusion energy and generate thrust. One of the last pulsed fusion magnetic nozzle design is the so called multi-coil parabolic reaction chamber: the reaction is thereby ignited at the focus of an open parabolic chamber, enclosed by a series of coaxial superconducting coils that apply a magnetic field. The field, beside confining the reaction and preventing any contact between hot fusion plasma and chamber structure, is also meant to reflect the explosion and push plasma out of the rocket. Reflection is attained thanks to electric currents induced in conductive skin layers that cover each of the coils, the change of plasma axial momentum generates thrust in reaction. This working principle has yet to be extensively verified and computational Magneto-Hydro Dynamics (MHD) is a viable option to achieve that. This work is one of the first detailed ideal-MHD analysis of a multi-coil parabolic reaction chamber of this kind and has been completed employing PLUTO, a freely distributed computational code developed at the Physics Department of the University of Turin. The results are thus a preliminary verification of the chamber's performance. Nonetheless, plasma leakage through the chamber structure has been highlighted. Therefore, further investigations are required to validate the chamber design. Implementing a more accurate physical model (e.g. Hall-MHD or relativistic-MHD) is thus mandatory, and PLUTO shows the capabilities to achieve that.

On purpose simulation model for molten salt CSP parabolic trough

NASA Astrophysics Data System (ADS)

Caranese, Carlo; Matino, Francesca; Maccari, Augusto

2017-06-01

The utilization of computer codes and simulation software is one of the fundamental aspects for the development of any kind of technology and, in particular, in CSP sector for researchers, energy institutions, EPC and others stakeholders. In that extent, several models for the simulation of CSP plant have been developed with different main objectives (dynamic simulation, productivity analysis, techno economic optimization, etc.), each of which has shown its own validity and suitability. Some of those models have been designed to study several plant configurations taking into account different CSP plant technologies (Parabolic trough, Linear Fresnel, Solar Tower or Dish) and different settings for the heat transfer fluid, the thermal storage systems and for the overall plant operating logic. Due to a lack of direct experience of Molten Salt Parabolic Trough (MSPT) commercial plant operation, most of the simulation tools do not foresee a suitable management of the thermal energy storage logic and of the solar field freeze protection system, but follow standard schemes. ASSALT, Ase Software for SALT csp plants, has been developed to improve MSPT plant's simulations, by exploiting the most correct operational strategies in order to provide more accurate technical and economical results. In particular, ASSALT applies MSPT specific control logics for the electric energy production and delivery strategy as well as the operation modes of the Solar Field in off-normal sunshine condition. With this approach, the estimated plant efficiency is increased and the electricity consumptions required for the plant operation and management is drastically reduced. Here we present a first comparative study on a real case 55 MWe Molten Salt Parabolic Trough CSP plant placed in the Tibetan highlands, using ASSALT and SAM (System Advisor Model), which is a commercially available simulation tool.

Application of advanced computational codes in the design of an experiment for a supersonic throughflow fan rotor

NASA Technical Reports Server (NTRS)

Wood, Jerry R.; Schmidt, James F.; Steinke, Ronald J.; Chima, Rodrick V.; Kunik, William G.

1987-01-01

Increased emphasis on sustained supersonic or hypersonic cruise has revived interest in the supersonic throughflow fan as a possible component in advanced propulsion systems. Use of a fan that can operate with a supersonic inlet axial Mach number is attractive from the standpoint of reducing the inlet losses incurred in diffusing the flow from a supersonic flight Mach number to a subsonic one at the fan face. The design of the experiment using advanced computational codes to calculate the components required is described. The rotor was designed using existing turbomachinery design and analysis codes modified to handle fully supersonic axial flow through the rotor. A two-dimensional axisymmetric throughflow design code plus a blade element code were used to generate fan rotor velocity diagrams and blade shapes. A quasi-three-dimensional, thin shear layer Navier-Stokes code was used to assess the performance of the fan rotor blade shapes. The final design was stacked and checked for three-dimensional effects using a three-dimensional Euler code interactively coupled with a two-dimensional boundary layer code. The nozzle design in the expansion region was analyzed with a three-dimensional parabolized viscous code which corroborated the results from the Euler code. A translating supersonic diffuser was designed using these same codes.

Numerical simulation of steady supersonic flow over spinning bodies of revolution

NASA Technical Reports Server (NTRS)

Sturek, W. B.; Schiff, L. B.

1982-01-01

A recently reported parabolized Navier-Stokes code has been employed to compute the supersonic flowfield about a spinning cone and spinning and nonspinning ogive cylinder and boattailed bodies of revolution at moderate incidence. The computations were performed for flow conditions where extensive measurements for wall pressure, boundary-layer velocity profiles, and Magnus force had been obtained. Comparisons between the computational results and experiment indicate excellent agreement for angles of attack up to 6 deg. At angles greater than 6 deg discrepancies are noted which are tentatively attributed to turbulence modeling errors. The comparisons for Magnus effects show that the code accurately predicts the effects of body shape for the selected models.

Block Iterative Methods for Elliptic and Parabolic Difference Equations.

DTIC Science & Technology

1981-09-01

S V PARTER, M STEUERWALT N0OO14-7A-C-0341 UNCLASSIFIED CSTR -447 NL ENN.EEEEEN LLf SCOMPUTER SCIENCES c~DEPARTMENT SUniversity of Wisconsin- SMadison...suggests that iterative algorithms that solve for several points at once will converge more rapidly than point algorithms . The Gaussian elimination... algorithm is seen in this light to converge in one step. Frankel [14], Young [34], Arms, Gates, and Zondek [1], and Varga [32], using the algebraic structure

Numerical Methods of Parameter Identification for Problems Arising in Elasticity.

DTIC Science & Technology

1982-06-01

Theorem 2.21 remains essentially unchanged by the inclusion of this new term . We now turn to a concrete realization of the approximate identification...cost if it had been accomplished under contract or if it had been done in-house in terms of manpower and/or dollars? ( ) a. MAN-YEARS ( ) b. $ 4...eigenfunction) state approximations were applied to a class of hyperbolic and parabolic equations, and also used in [7 ], where spline-based state

Simulation and Design Methods for Free-electron Laser Systems

DTIC Science & Technology

2009-12-01

the transverse Laplacian symbol ( 2 ) denotes differentiation only in the x and y coordinates. In this new parabolic form of the wave equation... compounded over a longer time and has a greater effect. In an oscillator, each pass an optical pulse makes through the resonator is a new interaction with...phosphor screen in the beam’s path and observing the spot(s) illuminated upon it. The phosphor screen can also serve as a charge collector , with

Properties of Differential Equations through Different Measures.

DTIC Science & Technology

1980-03-01

34 Parabolic differential inequalities in cones". Appl. Ana l., 9 (1979), 257-266. 8O =3𔄀-1i74 2 Lakshmikantham, V., and Vaughn, R. "Reaction-diffusion...Gronwall type inequalities , existence of extremal solutions, a comparison prin- ciple, and Peano’s type of existence result (for the Volterra ...differential systems with impulsive perturbations in terms of two measures." Nonlinear Analysis 1 (1977), 667-677. Leela, S., and Moauro, V. "Existence of

Approximations of Thermoelastic and Viscoelastic Control Systems

DTIC Science & Technology

1990-06-01

parabolic partial differential equations. The development of computational algorithms for designing controllers for such systems is an Immenselv complex...hereditary differential system on Rr , then approximate the "’historv" or -’memory- term (i.e.. the integral term in i.S)). In this paper we will use a... variation introduced by Fabiano and Ito ([FI]) of the averaging scheme considered by Banks and Burns ([BB]) for the second stage. The idea of the "’AVE

Numerical artifacts in the Generalized Porous Medium Equation: Why harmonic averaging itself is not to blame

NASA Astrophysics Data System (ADS)

Maddix, Danielle C.; Sampaio, Luiz; Gerritsen, Margot

2018-05-01

The degenerate parabolic Generalized Porous Medium Equation (GPME) poses numerical challenges due to self-sharpening and its sharp corner solutions. For these problems, we show results for two subclasses of the GPME with differentiable k (p) with respect to p, namely the Porous Medium Equation (PME) and the superslow diffusion equation. Spurious temporal oscillations, and nonphysical locking and lagging have been reported in the literature. These issues have been attributed to harmonic averaging of the coefficient k (p) for small p, and arithmetic averaging has been suggested as an alternative. We show that harmonic averaging is not solely responsible and that an improved discretization can mitigate these issues. Here, we investigate the causes of these numerical artifacts using modified equation analysis. The modified equation framework can be used for any type of discretization. We show results for the second order finite volume method. The observed problems with harmonic averaging can be traced to two leading error terms in its modified equation. This is also illustrated numerically through a Modified Harmonic Method (MHM) that can locally modify the critical terms to remove the aforementioned numerical artifacts.

A scale-entropy diffusion equation to describe the multi-scale features of turbulent flames near a wall

NASA Astrophysics Data System (ADS)

Queiros-Conde, D.; Foucher, F.; Mounaïm-Rousselle, C.; Kassem, H.; Feidt, M.

2008-12-01

Multi-scale features of turbulent flames near a wall display two kinds of scale-dependent fractal features. In scale-space, an unique fractal dimension cannot be defined and the fractal dimension of the front is scale-dependent. Moreover, when the front approaches the wall, this dependency changes: fractal dimension also depends on the wall-distance. Our aim here is to propose a general geometrical framework that provides the possibility to integrate these two cases, in order to describe the multi-scale structure of turbulent flames interacting with a wall. Based on the scale-entropy quantity, which is simply linked to the roughness of the front, we thus introduce a general scale-entropy diffusion equation. We define the notion of “scale-evolutivity” which characterises the deviation of a multi-scale system from the pure fractal behaviour. The specific case of a constant “scale-evolutivity” over the scale-range is studied. In this case, called “parabolic scaling”, the fractal dimension is a linear function of the logarithm of scale. The case of a constant scale-evolutivity in the wall-distance space implies that the fractal dimension depends linearly on the logarithm of the wall-distance. We then verified experimentally, that parabolic scaling represents a good approximation of the real multi-scale features of turbulent flames near a wall.

Spin polarization of two-dimensional electron system in parabolic potential

NASA Astrophysics Data System (ADS)

Miyake, Takashi; Totsuji, Chieko; Nakanishi, Kenta; Tsuruta, Kenji; Totsuji, Hiroo

2008-09-01

We analyze the ground state of the two-dimensional quantum system of electrons confined in a parabolic potential with the system size around 100 at 0 K. We map the system onto a classical system on the basis of the classical-map hypernetted-chain (CHNC) method which has been proven to work in the integral-equation-based analyses of uniform systems and apply classical Monte Carlo and molecular dynamics simulations. We find that, when we decrease the strength of confinement keeping the number of confined electrons fixed, the energy of the spin-polarized state with somewhat lower average density becomes smaller than that of the spin-unpolarized state with somewhat higher average density. This system thus undergoes the transition from the spin-unpolarized state to the spin polarized state and the corresponding critical value of r estimated from the average density is as low as r∼0.4 which is much smaller than the r value for the Wigner lattice formation. When we compare the energies of spin-unpolarized and spin-polarized states for given average density, our data give the critical r value for the transition between unpolarized and polarized states around 10 which is close to but still smaller than the known possibility of polarization at r∼27. The advantage of our method is a direct applicability to geometrically complex systems which are difficult to analyze by integral equations and this is an example.

A high order accurate finite element algorithm for high Reynolds number flow prediction

NASA Technical Reports Server (NTRS)

Baker, A. J.

1978-01-01

A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.

An ill-posed problem for the Black-Scholes equation for a profitable forecast of prices of stock options on real market data

NASA Astrophysics Data System (ADS)

Klibanov, Michael V.; Kuzhuget, Andrey V.; Golubnichiy, Kirill V.

2016-01-01

A new empirical mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock, new initial and new boundary conditions. Conventional notions of maturity time and strike prices are not used. The Black-Scholes equation is solved as a parabolic equation with the reversed time, which is an ill-posed problem. Thus, a regularization method is used to solve it. To verify the validity of our model, real market data for 368 randomly selected liquid options are used. A new trading strategy is proposed. Our results indicates that our method is profitable on those options. Furthermore, it is shown that the performance of two simple extrapolation-based techniques is much worse. We conjecture that our method might lead to significant profits of those financial insitutions which trade large amounts of options. We caution, however, that further studies are necessary to verify this conjecture.

Weakly Nonlinear Analysis of Vortex Formation in a Dissipative Variant of the Gross--Pitaevskii Equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tzou, J. C.; Kevrekidis, P. G.; Kolokolnikov, T.

2016-05-10

For a dissipative variant of the two-dimensional Gross--Pitaevskii equation with a parabolic trap under rotation, we study a symmetry breaking process that leads to the formation of vortices. The first symmetry breaking leads to the formation of many small vortices distributed uniformly near the Thomas$-$Fermi radius. The instability occurs as a result of a linear instability of a vortex-free steady state as the rotation is increased above a critical threshold. We focus on the second subsequent symmetry breaking, which occurs in the weakly nonlinear regime. At slightly above threshold, we derive a one-dimensional amplitude equation that describes the slow evolutionmore » of the envelope of the initial instability. Here, we show that the mechanism responsible for initiating vortex formation is a modulational instability of the amplitude equation. We also illustrate the role of dissipation in the symmetry breaking process. All analyses are confirmed by detailed numerical computations« less

Global boundary flattening transforms for acoustic propagation under rough sea surfaces.

PubMed

Oba, Roger M

2010-07-01

This paper introduces a conformal transform of an acoustic domain under a one-dimensional, rough sea surface onto a domain with a flat top. This non-perturbative transform can include many hundreds of wavelengths of the surface variation. The resulting two-dimensional, flat-topped domain allows direct application of any existing, acoustic propagation model of the Helmholtz or wave equation using transformed sound speeds. Such a transform-model combination applies where the surface particle velocity is much slower than sound speed, such that the boundary motion can be neglected. Once the acoustic field is computed, the bijective (one-to-one and onto) mapping permits the field interpolation in terms of the original coordinates. The Bergstrom method for inverse Riemann maps determines the transform by iterated solution of an integral equation for a surface matching term. Rough sea surface forward scatter test cases provide verification of the method using a particular parabolic equation model of the Helmholtz equation.

Characterization of Lorenz number with Seebeck coefficient measurement

DOE PAGES

Kim, Hyun -Sik; Gibbs, Zachary M.; Tang, Yinglu; ...

2015-04-01

In analyzing zT improvements due to lattice thermal conductivity (κ L ) reduction, electrical conductivity (σ) and total thermal conductivity (κ Total ) are often used to estimate the electronic component of the thermal conductivity (κ E ) and in turn κ L from κ L = ~ κ Total - LσT. The Wiedemann-Franz law, κ E = LσT, where L is Lorenz number, is widely used to estimate κ E from σ measurements. It is a common practice to treat L as a universal factor with 2.44 × 10⁻⁸ WΩK⁻² (degenerate limit). However, significant deviations from the degenerate limitmore » (approximately 40% or more for Kane bands) are known to occur for non-degenerate semiconductors where L converges to 1.5 × 10⁻⁸ WΩK⁻² for acoustic phonon scattering. The decrease in L is correlated with an increase in thermopower (absolute value of Seebeck coefficient (S)). Thus, a first order correction to the degenerate limit of L can be based on the measured thermopower, |S|, independent of temperature or doping. We propose the equation: (where L is in 10⁻⁸ WΩK⁻² and S in μV/K) as a satisfactory approximation for L. This equation is accurate within 5% for single parabolic band/acoustic phonon scattering assumption and within 20% for PbSe, PbS, PbTe, Si₀.₈Ge₀.₂ where more complexity is introduced, such as non-parabolic Kane bands, multiple bands, and/or alternate scattering mechanisms. The use of this equation for L rather than a constant value (when detailed band structure and scattering mechanism is not known) will significantly improve the estimation of lattice thermal conductivity. L = 1.5 + exp [-|S|116]« less

An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids

NASA Astrophysics Data System (ADS)

English, R. Elliot; Qiu, Linhai; Yu, Yue; Fedkiw, Ronald

2013-12-01

We present a novel method for discretizing the incompressible Navier-Stokes equations on a multitude of moving and overlapping Cartesian grids each with an independently chosen cell size to address adaptivity. Advection is handled with first and second order accurate semi-Lagrangian schemes in order to alleviate any time step restriction associated with small grid cell sizes. Likewise, an implicit temporal discretization is used for the parabolic terms including Navier-Stokes viscosity which we address separately through the development of a method for solving the heat diffusion equations. The most intricate aspect of any such discretization is the method used in order to solve the elliptic equation for the Navier-Stokes pressure or that resulting from the temporal discretization of parabolic terms. We address this by first removing any degrees of freedom which duplicately cover spatial regions due to overlapping grids, and then providing a discretization for the remaining degrees of freedom adjacent to these regions. We observe that a robust second order accurate symmetric positive definite readily preconditioned discretization can be obtained by constructing a local Voronoi region on the fly for each degree of freedom in question in order to obtain both its stencil (logically connected neighbors) and stencil weights. Internal curved boundaries such as at solid interfaces are handled using a simple immersed boundary approach which is directly applied to the Voronoi mesh in both the viscosity and pressure solves. We independently demonstrate each aspect of our approach on test problems in order to show efficacy and convergence before finally addressing a number of common test cases for incompressible flow with stationary and moving solid bodies.

Physical effect of a variable magnetic field on the heat transfer of a nanofluid-based concentrating parabolic solar collector

NASA Astrophysics Data System (ADS)

Tahari, M.; Ghorbanian, A.; Hatami, M.; Jing, D.

2017-12-01

In this paper, the physical effect of a variable magnetic field on a nanofluid-based concentrating parabolic solar collector (NCPSC) is demonstrated. A section of reservoir is modeled as a semi-circular cavity under the solar radiation with the magnetic source located in the center or out of the cavity and the governing equations were solved by the FlexPDE numerical software. The effect of four physical parameters, i.e., Hartmann Number (Ha), nanoparticles volume fraction ( φ, magnetic field strength ( γ and magnetic source location ( b, on the Nusselt number is discussed. To find the interaction of these parameters and its effect on the heat transfer, a central composite design (CCD) is used and analysis is performed on the 25 experiments proposed by CCD. Analysis of variance (ANOVA) of the results reveals that increasing the Hartmann number decreases the Nusselt number due to the Lorentz force resulting from the presence of stronger magnetic field.

Oxidation of 304 stainless steel in high-temperature steam

NASA Astrophysics Data System (ADS)

Ishida, Toshihisa; Harayama, Yasuo; Yaguchi, Sinnosuke

1986-08-01

An experiment on oxidation of 304 stainless steel was performed in steam between 900°C and 1350°C, using the spare cladding of the reactor of the nuclear-powered ship Mutsu. The temperature range was appropriate for a postulated loss of coolant accident (LOCA) analysis of a LWR. The oxidation kinetics were found to obey the parabolic law during the first period of 8 min. After the first period, the parabolic reaction rate constant decreased in the case of heating temperatures between 1100°C and 1250°C. At 1250°C, especially, a marked decrease was observed in the oxide scale-forming kinetics when the surface treated initially by mechanical polishing and given a residual stress. This enhanced oxidation resistance was attributed to the presence of a chromium-enriched layer which was detected by use of an X-ray microanalyzer. The oxidation kinetics equation obtained for the first 8 min is applicable to the model calculation of a hypothetical LOCA in a LWR, employing 304 stainless steel cladding.

Combustion of hydrogen injected into a supersonic airstream (the SHIP computer program)

NASA Technical Reports Server (NTRS)

Markatos, N. C.; Spalding, D. B.; Tatchell, D. G.

1977-01-01

The mathematical and physical basis of the SHIP computer program which embodies a finite-difference, implicit numerical procedure for the computation of hydrogen injected into a supersonic airstream at an angle ranging from normal to parallel to the airstream main flow direction is described. The physical hypotheses built into the program include: a two-equation turbulence model, and a chemical equilibrium model for the hydrogen-oxygen reaction. Typical results for equilibrium combustion are presented and exhibit qualitatively plausible behavior. The computer time required for a given case is approximately 1 minute on a CDC 7600 machine. A discussion of the assumption of parabolic flow in the injection region is given which suggests that improvement in calculation in this region could be obtained by use of the partially parabolic procedure of Pratap and Spalding. It is concluded that the technique described herein provides the basis for an efficient and reliable means for predicting the effects of hydrogen injection into supersonic airstreams and of its subsequent combustion.

On the global well-posedness theory for a class of PDE models for criminal activity

NASA Astrophysics Data System (ADS)

Rodríguez, N.

2013-10-01

We study a class of ‘reaction-advection-diffusion’ system of partial differential equations, which can be taken as basic models for criminal activity. This class of models are based on routine activity theory and other theories, such as the ‘repeat and near-repeat victimization effect’ and were first introduced in Short et al. (2008) [11]. In these models the criminal density is advected by a velocity field that depends on a scalar field, which measures the appeal to commit a crime. We refer to this scalar field as the attractiveness field. We prove local well-posedness of solutions for the general class of models. Furthermore, we prove global well-posedness of solutions to a fully-parabolic system with a velocity field that depends logarithmically on the attractiveness field. Our final result is the global well-posedness of solutions the fully-parabolic system with velocity field that depends linearly on the attractiveness field for small initial mass.

Prediction of the space adaptation syndrome

NASA Technical Reports Server (NTRS)

Reschke, M. F.; Homick, J. L.; Ryan, P.; Moseley, E. C.

1984-01-01

The univariate and multivariate relationships of provocative measures used to produce motion sickness symptoms were described. Normative subjects were used to develop and cross-validate sets of linear equations that optimally predict motion sickness in parabolic flights. The possibility of reducing the number of measurements required for prediction was assessed. After describing the variables verbally and statistically for 159 subjects, a factor analysis of 27 variables was completed to improve understanding of the relationships between variables and to reduce the number of measures for prediction purposes. The results of this analysis show that none of variables are significantly related to the responses to parabolic flights. A set of variables was selected to predict responses to KC-135 flights. A series of discriminant analyses were completed. Results indicate that low, moderate, or severe susceptibility could be correctly predicted 64 percent and 53 percent of the time on original and cross-validation samples, respectively. Both the factor analysis and the discriminant analysis provided no basis for reducing the number of tests.

TEMPEST II--A NEUTRON THERMALIZATION CODE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shudde, R.H.; Dyer, J.

The TEMPEST II neutron thermalization code in Fortran for IBM 709 or 7090 calculates thermal neutron flux spectra based upon the Wigner-Wilkins equation, the Wilkins equation, or the Maxwellian distribution. When a neutron spectrum is obtained, TEMPEST II provides microscopic and macroscopic cross section averages over that spectrum. Equations used by the code and sample input and output data are given. (auth)

Solution of the Burnett equations for hypersonic flows near the continuum limit

NASA Technical Reports Server (NTRS)

Imlay, Scott T.

1992-01-01

The INCA code, a three-dimensional Navier-Stokes code for analysis of hypersonic flowfields, was modified to analyze the lower reaches of the continuum transition regime, where the Navier-Stokes equations become inaccurate and Monte Carlo methods become too computationally expensive. The two-dimensional Burnett equations and the three-dimensional rotational energy transport equation were added to the code and one- and two-dimensional calculations were performed. For the structure of normal shock waves, the Burnett equations give consistently better results than Navier-Stokes equations and compare reasonably well with Monte Carlo methods. For two-dimensional flow of Nitrogen past a circular cylinder the Burnett equations predict the total drag reasonably well. Care must be taken, however, not to exceed the range of validity of the Burnett equations.

Reciprocity relationships in vector acoustics and their application to vector field calculations.

PubMed

Deal, Thomas J; Smith, Kevin B

2017-08-01

The reciprocity equation commonly stated in underwater acoustics relates pressure fields and monopole sources. It is often used to predict the pressure measured by a hydrophone for multiple source locations by placing a source at the hydrophone location and calculating the field everywhere for that source. A similar equation that governs the orthogonal components of the particle velocity field is needed to enable this computational method to be used for acoustic vector sensors. This paper derives a general reciprocity equation that accounts for both monopole and dipole sources. This vector-scalar reciprocity equation can be used to calculate individual components of the received vector field by altering the source type used in the propagation calculation. This enables a propagation model to calculate the received vector field components for an arbitrary number of source locations with a single model run for each vector field component instead of requiring one model run for each source location. Application of the vector-scalar reciprocity principle is demonstrated with analytic solutions for a range-independent environment and with numerical solutions for a range-dependent environment using a parabolic equation model.

Optimal trajectories based on linear equations

NASA Technical Reports Server (NTRS)

Carter, Thomas E.

1990-01-01

The Principal results of a recent theory of fuel optimal space trajectories for linear differential equations are presented. Both impulsive and bounded-thrust problems are treated. A new form of the Lawden Primer vector is found that is identical for both problems. For this reason, starting iteratives from the solution of the impulsive problem are highly effective in the solution of the two-point boundary-value problem associated with bounded thrust. These results were applied to the problem of fuel optimal maneuvers of a spacecraft near a satellite in circular orbit using the Clohessy-Wiltshire equations. For this case two-point boundary-value problems were solved using a microcomputer, and optimal trajectory shapes displayed. The results of this theory can also be applied if the satellite is in an arbitrary Keplerian orbit through the use of the Tschauner-Hempel equations. A new form of the solution of these equations has been found that is identical for elliptical, parabolic, and hyperbolic orbits except in the way that a certain integral is evaluated. For elliptical orbits this integral is evaluated through the use of the eccentric anomaly. An analogous evaluation is performed for hyperbolic orbits.

Linear and nonlinear stability of the Blasius boundary layer

NASA Technical Reports Server (NTRS)

Bertolotti, F. P.; Herbert, TH.; Spalart, P. R.

1992-01-01

Two new techniques for the study of the linear and nonlinear instability in growing boundary layers are presented. The first technique employs partial differential equations of parabolic type exploiting the slow change of the mean flow, disturbance velocity profiles, wavelengths, and growth rates in the streamwise direction. The second technique solves the Navier-Stokes equation for spatially evolving disturbances using buffer zones adjacent to the inflow and outflow boundaries. Results of both techniques are in excellent agreement. The linear and nonlinear development of Tollmien-Schlichting (TS) waves in the Blasius boundary layer is investigated with both techniques and with a local procedure based on a system of ordinary differential equations. The results are compared with previous work and the effects of non-parallelism and nonlinearity are clarified. The effect of nonparallelism is confirmed to be weak and, consequently, not responsible for the discrepancies between measurements and theoretical results for parallel flow.

Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations

NASA Technical Reports Server (NTRS)

Osher, Stanley; Sethian, James A.

1987-01-01

New numerical algorithms are devised (PSC algorithms) for following fronts propagating with curvature-dependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These algorithms approximate the equations of motion, which resemble Hamilton-Jacobi equations with parabolic right-hand-sides, by using techniques from the hyperbolic conservation laws. Non-oscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps in the moving fronts. The algorithms handle topological merging and breaking naturally, work in any number of space dimensions, and do not require that the moving surface be written as a function. The methods can be used also for more general Hamilton-Jacobi-type problems. The algorithms are demonstrated by computing the solution to a variety of surface motion problems.

Dark solitons for a variable-coefficient higher-order nonlinear Schrödinger equation in the inhomogeneous optical fiber

NASA Astrophysics Data System (ADS)

Sun, Yan; Tian, Bo; Wu, Xiao-Yu; Liu, Lei; Yuan, Yu-Qiang

2017-04-01

Under investigation in this paper is a variable-coefficient higher-order nonlinear Schrödinger equation, which has certain applications in the inhomogeneous optical fiber communication. Through the Hirota method, bilinear forms, dark one- and two-soliton solutions for such an equation are obtained. We graphically study the solitons with d1(z), d2(z) and d3(z), which represent the variable coefficients of the group-velocity dispersion, third-order dispersion and fourth-order dispersion, respectively. With the different choices of the variable coefficients, we obtain the parabolic, periodic and V-shaped dark solitons. Head-on and overtaking collisions are depicted via the dark two soliton solutions. Velocities of the dark solitons are linearly related to d1(z), d2(z) and d3(z), respectively, while the amplitudes of the dark solitons are not related to such variable coefficients.

An approximation theory for the identification of linear thermoelastic systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Su, Chien-Hua Frank

1990-01-01

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

OFFSET - RAY TRACING OPTICAL ANALYSIS OF OFFSET SOLAR COLLECTOR FOR SPACE STATION SOLAR DYNAMIC POWER SYSTEM

NASA Technical Reports Server (NTRS)

Jefferies, K.

1994-01-01

OFFSET is a ray tracing computer code for optical analysis of a solar collector. The code models the flux distributions within the receiver cavity produced by reflections from the solar collector. It was developed to model the offset solar collector of the solar dynamic electric power system being developed for Space Station Freedom. OFFSET has been used to improve the understanding of the collector-receiver interface and to guide the efforts of NASA contractors also researching the optical components of the power system. The collector for Space Station Freedom consists of 19 hexagonal panels each containing 24 triangular, reflective facets. Current research is geared toward optimizing flux distribution inside the receiver via changes in collector design and receiver orientation. OFFSET offers many options for experimenting with the design of the system. The offset parabolic collector model configuration is determined by an input file of facet corner coordinates. The user may choose other configurations by changing this file, but to simulate collectors that have other than 19 groups of 24 triangular facets would require modification of the FORTRAN code. Each of the roughly 500 facets in the assembled collector may be independently aimed to smooth out, or tailor, the flux distribution on the receiver's wall. OFFSET simulates the effects of design changes such as in receiver aperture location, tilt angle, and collector facet contour. Unique features of OFFSET include: 1) equations developed to pseudo-randomly select ray originating sources on the Sun which appear evenly distributed and include solar limb darkening; 2) Cone-optics technique used to add surface specular error to the ray originating sources to determine the apparent ray sources of the reflected sun; 3) choice of facet reflective surface contour -- spherical, ideal parabolic, or toroidal; 4) Gaussian distributions of radial and tangential components of surface slope error added to the surface normals at the ten nodal points on each facet; and 5) color contour plots of receiver incident flux distribution generated by PATRAN processing of FORTRAN computer code output. OFFSET output includes a file of input data for confirmation, a PATRAN results file containing the values necessary to plot the flux distribution at the receiver surface, a PATRAN results file containing the intensity distribution on a 40 x 40 cm area of the receiver aperture plane, a data file containing calculated information on the system configuration, a file including the X-Y coordinates of the target points of each collector facet on the aperture opening, and twelve P/PLOT input data files to allow X-Y plotting of various results data. OFFSET is written in FORTRAN (70%) for the IBM VM operating system. The code contains PATRAN statements (12%) and P/PLOT statements (18%) for generating plots. Once the program has been run on VM (or an equivalent system), the PATRAN and P/PLOT files may be transferred to a DEC VAX (or equivalent system) with access to PATRAN for PATRAN post processing. OFFSET was written in 1988 and last updated in 1989. PATRAN is a registered trademark of PDA Engineering. IBM is a registered trademark of International Business Machines Corporation. DEC VAX is a registered trademark of Digital Equipment Corporation.

Numerical Treatment of Degenerate Diffusion Equations via Feller's Boundary Classification, and Applications

NASA Technical Reports Server (NTRS)

Cacio, Emanuela; Cohn, Stephen E.; Spigler, Renato

2011-01-01

A numerical method is devised to solve a class of linear boundary-value problems for one-dimensional parabolic equations degenerate at the boundaries. Feller theory, which classifies the nature of the boundary points, is used to decide whether boundary conditions are needed to ensure uniqueness, and, if so, which ones they are. The algorithm is based on a suitable preconditioned implicit finite-difference scheme, grid, and treatment of the boundary data. Second-order accuracy, unconditional stability, and unconditional convergence of solutions of the finite-difference scheme to a constant as the time-step index tends to infinity are further properties of the method. Several examples, pertaining to financial mathematics, physics, and genetics, are presented for the purpose of illustration.

Influence of light absorption on relativistic self-focusing of Gaussian laser beam in cold quantum plasma

NASA Astrophysics Data System (ADS)

Patil, S. D.; Valkunde, A. T.; Vhanmore, B. D.; Urunkar, T. U.; Gavade, K. M.; Takale, M. V.

2018-05-01

When inter particle distance is comparable to the de Broglies wavelength of charged particles, quantum effects in plasmas are unavoidable. We have exploited an influence of light absorption on self-focusing of Gaussian laser beam in cold quantum plasma by considering relativistic nonlinearity. Nonlinear differential equation governing beam-width parameter has been established by using parabolic equation approach under paraxial and WKB approximations. The effect of light absorption on variation of beam-width parameter with dimensionless distance of propagation is presented graphically and discussed. It is found that light absorption plays vital role in weakening the relativistic self-focusing of laser beam during propagation in cold quantum plasma and gives reasonably interesting results.

Towards developing robust algorithms for solving partial differential equations on MIMD machines

NASA Technical Reports Server (NTRS)

Saltz, Joel H.; Naik, Vijay K.

1988-01-01

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

Towards developing robust algorithms for solving partial differential equations on MIMD machines

NASA Technical Reports Server (NTRS)

Saltz, J. H.; Naik, V. K.

1985-01-01

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

An intrinsic approach in the curved n-body problem: The negative curvature case

NASA Astrophysics Data System (ADS)

Diacu, Florin; Pérez-Chavela, Ernesto; Reyes Victoria, J. Guadalupe

We consider the motion of n point particles of positive masses that interact gravitationally on the 2-dimensional hyperbolic sphere, which has negative constant Gaussian curvature. Using the stereographic projection, we derive the equations of motion of this curved n-body problem in the Poincaré disk, where we study the elliptic relative equilibria. Then we obtain the equations of motion in the Poincaré upper half plane in order to analyze the hyperbolic and parabolic relative equilibria. Using techniques of Riemannian geometry, we characterize each of the above classes of periodic orbits. For n=2 and n=3 we recover some previously known results and find new qualitative results about relative equilibria that were not apparent in an extrinsic setting.

Convergence of Weak Kähler-Ricci Flows on Minimal Models of Positive Kodaira Dimension

NASA Astrophysics Data System (ADS)

Eyssidieux, Phylippe; Guedj, Vincent; Zeriahi, Ahmed

2018-02-01

Studying the behavior of the Kähler-Ricci flow on mildly singular varieties, one is naturally lead to study weak solutions of degenerate parabolic complex Monge-Ampère equations. In this article, the third of a series on this subject, we study the long term behavior of the normalized Kähler-Ricci flow on mildly singular varieties of positive Kodaira dimension, generalizing results of Song and Tian who dealt with smooth minimal models.

An Adaptive Method of Lines with Error Control for Parabolic Equations of the Reaction-Diffusion Type.

DTIC Science & Technology

1984-06-01

space discretization error . 1. I 3 1. INTRODUCTION Reaction- diffusion processes occur in many branches of biology and physical chemistry. Examples...to model reaction- diffusion phenomena. The primary goal of this adaptive method is to keep a particular norm of the space discretization error less...AD-A142 253 AN ADAPTIVE MET6 OFD LNES WITH ERROR CONTROL FOR 1 INST FOR PHYSICAL SCIENCE AND TECH. I BABUSKAAAO C7 EA OH S UMR AN UNVC EEP R

The Numerical Calculation of Traveling Wave Solutions of Nonlinear Parabolic Equations on the Line.

DTIC Science & Technology

1984-02-01

kc(i~~ +’~ which can be rewrittenw W (T is) Ic (sic) - (+ Using the convolution formulas and the expression for the inverse transform of-I (se e.g...2i 2f 1 2 c) + 4f1 1- f 3] 1 We now have: f ) (0,0,4) ; (2.17) f2 3(U) (0,0,0*) x 3 -, (0,,) . 3u ’ The inverse transform of (2.15) is given by: E

Regularization and Approximation of a Class of Evolution Problems in Applied Mathematics

DTIC Science & Technology

1991-01-01

8217 DT)IG AD-A242 223 FINAL REPORT Nov61991:ti -ll IN IImI 1OV1 Ml99 1 REGULARIZATION AND APPROXIMATION OF A-CLASS OF EVOLUTION -PROBLEMS IN APPLIED...The University of Texas at Austin Austin, TX 78712 91 10 30 050 FINAL REPORT "Regularization and Approximation of a Class of Evolution Problems in...micro-structured parabolic system. A mathematical analysis of the regularized equations-has been developed to support our approach. Supporting

Numerical calculation of transonic flow about slender bodies of revolution

NASA Technical Reports Server (NTRS)

Bailey, F. R.

1971-01-01

A relaxation method is described for the numerical solution of the transonic small disturbance equation for flow about a slender body of revolution. Results for parabolic arc bodies, both with and without an attached sting, are compared with wind-tunnel measurements for a free-stream Mach number range from 0.90 to 1.20. The method is also used to show the effects of wind-tunnel wall interference by including boundary conditions representing porous-wall and open-jet wind-tunnel test sections.

The transition prediction toolkit: LST, SIT, PSE, DNS, and LES

NASA Technical Reports Server (NTRS)

Zang, Thomas A.; Chang, Chau-Lyan; Ng, Lian L.

1992-01-01

The e(sup N) method for predicting transition onset is an amplitude ratio criterion that is on the verge of full maturation for three-dimensional, compressible, real gas flows. Many of the components for a more sophisticated, absolute amplitude criterion are now emerging: receptivity theory, secondary instability theory, parabolized stability equations approaches, direct numerical simulation and large-eddy simulation. This paper will provide a description of each of these new theoretical tools and provide indications of their current status.

Time-domain theory of gyrotron traveling wave amplifiers operating at grazing incidence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ginzburg, N. S., E-mail: ginzburg@appl.sci-nnov.ru; Nizhny Novgorod State University, Gagarin Ave., 23, 603950 Nizhny Novgorod; Sergeev, A. S.

Time-domain theory of the gyrotron traveling wave tube (gyro-TWT) operating at grazing incidence has been developed. The theory is based on a description of wave propagation by a parabolic equation. The results of the simulations are compared with experimental results of the observation of subnanosecond pulse amplification in a gyro-TWT consisting of three gain sections separated by severs. The theory developed can also be used successfully for a description of amplification of monochromatic signals.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luo, Yousong, E-mail: yousong.luo@rmit.edu.au

This paper deals with a class of optimal control problems governed by an initial-boundary value problem of a parabolic equation. The case of semi-linear boundary control is studied where the control is applied to the system via the Wentzell boundary condition. The differentiability of the state variable with respect to the control is established and hence a necessary condition is derived for the optimal solution in the case of both unconstrained and constrained problems. The condition is also sufficient for the unconstrained convex problems. A second order condition is also derived.

GridMan: A grid manipulation system

NASA Technical Reports Server (NTRS)

Eiseman, Peter R.; Wang, Zhu

1992-01-01

GridMan is an interactive grid manipulation system. It operates on grids to produce new grids which conform to user demands. The input grids are not constrained to come from any particular source. They may be generated by algebraic methods, elliptic methods, hyperbolic methods, parabolic methods, or some combination of methods. The methods are included in the various available structured grid generation codes. These codes perform the basic assembly function for the various elements of the initial grid. For block structured grids, the assembly can be quite complex due to a large number of clock corners, edges, and faces for which various connections and orientations must be properly identified. The grid generation codes are distinguished among themselves by their balance between interactive and automatic actions and by their modest variations in control. The basic form of GridMan provides a much more substantial level of grid control and will take its input from any of the structured grid generation codes. The communication link to the outside codes is a data file which contains the grid or section of grid.

Non-linear hydrodynamical evolution of rotating relativistic stars: numerical methods and code tests

NASA Astrophysics Data System (ADS)

Font, José A.; Stergioulas, Nikolaos; Kokkotas, Kostas D.

2000-04-01

We present numerical hydrodynamical evolutions of rapidly rotating relativistic stars, using an axisymmetric, non-linear relativistic hydrodynamics code. We use four different high-resolution shock-capturing (HRSC) finite-difference schemes (based on approximate Riemann solvers) and compare their accuracy in preserving uniformly rotating stationary initial configurations in long-term evolutions. Among these four schemes, we find that the third-order piecewise parabolic method scheme is superior in maintaining the initial rotation law in long-term evolutions, especially near the surface of the star. It is further shown that HRSC schemes are suitable for the evolution of perturbed neutron stars and for the accurate identification (via Fourier transforms) of normal modes of oscillation. This is demonstrated for radial and quadrupolar pulsations in the non-rotating limit, where we find good agreement with frequencies obtained with a linear perturbation code. The code can be used for studying small-amplitude or non-linear pulsations of differentially rotating neutron stars, while our present results serve as testbed computations for three-dimensional general-relativistic evolution codes.

Regularized Moment Equations and Shock Waves for Rarefied Granular Gas

NASA Astrophysics Data System (ADS)

Reddy, Lakshminarayana; Alam, Meheboob

2016-11-01

It is well-known that the shock structures predicted by extended hydrodynamic models are more accurate than the standard Navier-Stokes model in the rarefied regime, but they fail to predict continuous shock structures when the Mach number exceeds a critical value. Regularization or parabolization is one method to obtain smooth shock profiles at all Mach numbers. Following a Chapman-Enskog-like method, we have derived the "regularized" version 10-moment equations ("R10" moment equations) for inelastic hard-spheres. In order to show the advantage of R10 moment equations over standard 10-moment equations, the R10 moment equations have been employed to solve the Riemann problem of plane shock waves for both molecular and granular gases. The numerical results are compared between the 10-moment and R10-moment models and it is found that the 10-moment model fails to produce continuous shock structures beyond an upstream Mach number of 1 . 34 , while the R10-moment model predicts smooth shock profiles beyond the upstream Mach number of 1 . 34 . The density and granular temperature profiles are found to be asymmetric, with their maxima occurring within the shock-layer.

Solving the Coupled System Improves Computational Efficiency of the Bidomain Equations

PubMed Central

Southern, James A.; Plank, Gernot; Vigmond, Edward J.; Whiteley, Jonathan P.

2017-01-01

The bidomain equations are frequently used to model the propagation of cardiac action potentials across cardiac tissue. At the whole organ level the size of the computational mesh required makes their solution a significant computational challenge. As the accuracy of the numerical solution cannot be compromised, efficiency of the solution technique is important to ensure that the results of the simulation can be obtained in a reasonable time whilst still encapsulating the complexities of the system. In an attempt to increase efficiency of the solver, the bidomain equations are often decoupled into one parabolic equation that is computationally very cheap to solve and an elliptic equation that is much more expensive to solve. In this study the performance of this uncoupled solution method is compared with an alternative strategy in which the bidomain equations are solved as a coupled system. This seems counter-intuitive as the alternative method requires the solution of a much larger linear system at each time step. However, in tests on two 3-D rabbit ventricle benchmarks it is shown that the coupled method is up to 80% faster than the conventional uncoupled method — and that parallel performance is better for the larger coupled problem. PMID:19457741

GCKP84-general chemical kinetics code for gas-phase flow and batch processes including heat transfer effects

NASA Technical Reports Server (NTRS)

Bittker, D. A.; Scullin, V. J.

1984-01-01

A general chemical kinetics code is described for complex, homogeneous ideal gas reactions in any chemical system. The main features of the GCKP84 code are flexibility, convenience, and speed of computation for many different reaction conditions. The code, which replaces the GCKP code published previously, solves numerically the differential equations for complex reaction in a batch system or one dimensional inviscid flow. It also solves numerically the nonlinear algebraic equations describing the well stirred reactor. A new state of the art numerical integration method is used for greatly increased speed in handling systems of stiff differential equations. The theory and the computer program, including details of input preparation and a guide to using the code are given.

A critical analysis of the accuracy of several numerical techniques for combustion kinetic rate equations

NASA Technical Reports Server (NTRS)

Radhadrishnan, Krishnan

1993-01-01

A detailed analysis of the accuracy of several techniques recently developed for integrating stiff ordinary differential equations is presented. The techniques include two general-purpose codes EPISODE and LSODE developed for an arbitrary system of ordinary differential equations, and three specialized codes CHEMEQ, CREK1D, and GCKP4 developed specifically to solve chemical kinetic rate equations. The accuracy study is made by application of these codes to two practical combustion kinetics problems. Both problems describe adiabatic, homogeneous, gas-phase chemical reactions at constant pressure, and include all three combustion regimes: induction, heat release, and equilibration. To illustrate the error variation in the different combustion regimes the species are divided into three types (reactants, intermediates, and products), and error versus time plots are presented for each species type and the temperature. These plots show that CHEMEQ is the most accurate code during induction and early heat release. During late heat release and equilibration, however, the other codes are more accurate. A single global quantity, a mean integrated root-mean-square error, that measures the average error incurred in solving the complete problem is used to compare the accuracy of the codes. Among the codes examined, LSODE is the most accurate for solving chemical kinetics problems. It is also the most efficient code, in the sense that it requires the least computational work to attain a specified accuracy level. An important finding is that use of the algebraic enthalpy conservation equation to compute the temperature can be more accurate and efficient than integrating the temperature differential equation.

Stability of the parabolic Poincaré bundle

NASA Astrophysics Data System (ADS)

Basu, Suratno; Biswas, Indranil; Dan, Krishanu

Given a compact Riemann surface X and a moduli space Mα(Λ) of parabolic stable bundles on it of fixed determinant of complete parabolic flags, we prove that the Poincaré parabolic bundle on X × Mα(Λ) is parabolic stable with respect to a natural polarization on X × Mα(Λ).

RAZORBACK - A Research Reactor Transient Analysis Code Version 1.0 - Volume 3: Verification and Validation Report.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Talley, Darren G.

2017-04-01

This report describes the work and results of the verification and validation (V&V) of the version 1.0 release of the Razorback code. Razorback is a computer code designed to simulate the operation of a research reactor (such as the Annular Core Research Reactor (ACRR)) by a coupled numerical solution of the point reactor kinetics equations, the energy conservation equation for fuel element heat transfer, the equation of motion for fuel element thermal expansion, and the mass, momentum, and energy conservation equations for the water cooling of the fuel elements. This V&V effort was intended to confirm that the code showsmore » good agreement between simulation and actual ACRR operations.« less

Traveling waves in Hall-magnetohydrodynamics and the ion-acoustic shock structure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hagstrom, George I.; Hameiri, Eliezer

Hall-magnetohydrodynamics (HMHD) is a mixed hyperbolic-parabolic partial differential equation that describes the dynamics of an ideal two fluid plasma with massless electrons. We study the only shock wave family that exists in this system (the other discontinuities being contact discontinuities and not shocks). We study planar traveling wave solutions and we find solutions with discontinuities in the hydrodynamic variables, which arise due to the presence of real characteristics in Hall-MHD. We introduce a small viscosity into the equations and use the method of matched asymptotic expansions to show that solutions with a discontinuity satisfying the Rankine-Hugoniot conditions and also anmore » entropy condition have continuous shock structures. The lowest order inner equations reduce to the compressible Navier-Stokes equations, plus an equation which implies the constancy of the magnetic field inside the shock structure. We are able to show that the current is discontinuous across the shock, even as the magnetic field is continuous, and that the lowest order outer equations, which are the equations for traveling waves in inviscid Hall-MHD, are exactly integrable. We show that the inner and outer solutions match, which allows us to construct a family of uniformly valid continuous composite solutions that become discontinuous when the diffusivity vanishes.« less

Excitation of a Parallel Plate Waveguide by an Array of Rectangular Waveguides

NASA Technical Reports Server (NTRS)

Rengarajan, Sembiam

2011-01-01

This work addresses the problem of excitation of a parallel plate waveguide by an array of rectangular waveguides that arises in applications such as the continuous transverse stub (CTS) antenna and dual-polarized parabolic cylindrical reflector antennas excited by a scanning line source. In order to design the junction region between the parallel plate waveguide and the linear array of rectangular waveguides, waveguide sizes have to be chosen so that the input match is adequate for the range of scan angles for both polarizations. Electromagnetic wave scattered by the junction of a parallel plate waveguide by an array of rectangular waveguides is analyzed by formulating coupled integral equations for the aperture electric field at the junction. The integral equations are solved by the method of moments. In order to make the computational process efficient and accurate, the method of weighted averaging was used to evaluate rapidly oscillating integrals encountered in the moment matrix. In addition, the real axis spectral integral is evaluated in a deformed contour for speed and accuracy. The MoM results for a large finite array have been validated by comparing its reflection coefficients with corresponding results for an infinite array generated by the commercial finite element code, HFSS. Once the aperture electric field is determined by MoM, the input reflection coefficients at each waveguide port, and coupling for each polarization over the range of useful scan angles, are easily obtained. Results for the input impedance and coupling characteristics for both the vertical and horizontal polarizations are presented over a range of scan angles. It is shown that the scan range is limited to about 35 for both polarizations and therefore the optimum waveguide is a square of size equal to about 0.62 free space wavelength.

An evaluation of three two-dimensional computational fluid dynamics codes including low Reynolds numbers and transonic Mach numbers

NASA Technical Reports Server (NTRS)

Hicks, Raymond M.; Cliff, Susan E.

1991-01-01

Full-potential, Euler, and Navier-Stokes computational fluid dynamics (CFD) codes were evaluated for use in analyzing the flow field about airfoils sections operating at Mach numbers from 0.20 to 0.60 and Reynolds numbers from 500,000 to 2,000,000. The potential code (LBAUER) includes weakly coupled integral boundary layer equations for laminar and turbulent flow with simple transition and separation models. The Navier-Stokes code (ARC2D) uses the thin-layer formulation of the Reynolds-averaged equations with an algebraic turbulence model. The Euler code (ISES) includes strongly coupled integral boundary layer equations and advanced transition and separation calculations with the capability to model laminar separation bubbles and limited zones of turbulent separation. The best experiment/CFD correlation was obtained with the Euler code because its boundary layer equations model the physics of the flow better than the other two codes. An unusual reversal of boundary layer separation with increasing angle of attack, following initial shock formation on the upper surface of the airfoil, was found in the experiment data. This phenomenon was not predicted by the CFD codes evaluated.

Un-collided-flux preconditioning for the first order transport equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rigley, M.; Koebbe, J.; Drumm, C.

2013-07-01

Two codes were tested for the first order neutron transport equation using finite element methods. The un-collided-flux solution is used as a preconditioner for each of these methods. These codes include a least squares finite element method and a discontinuous finite element method. The performance of each code is shown on problems in one and two dimensions. The un-collided-flux preconditioner shows good speedup on each of the given methods. The un-collided-flux preconditioner has been used on the second-order equation, and here we extend those results to the first order equation. (authors)

Gene expression analysis of WRKY transcription factors in Arabidopsis thaliana cell cultures during a parabolic flight

NASA Astrophysics Data System (ADS)

Babbick, Maren; Barjaktarović, Žarko; Hampp, Ruediger

Plants sense gravity by specialized cells (statocytes) and adjust growth and development accordingly. It has, however, also been shown that plant cells which are not part of specialized tissues are also able to sense gravitational forces. Therefore we used undifferentiated, homogeneous cell cultures of Arabidopsis thaliana (cv. Columbia) in order to identify early alterations in gene expression as a response to altered gravitational field strengths. In this contribution we report on cell cultures exposed to parabolic flights (approximately 20 sec of microgravity). For this short-term exposure study, we specifically checked for genes at the beginning of signal transduction chains, such as those coding for transcription factors (TFs). TFs are small proteins that regulate expression of their target genes by binding to specific promoter sequences. Our main focus were members of the so-called WRKY TF family. WRKY TFs are known to be involved in various physiological processes like senescence and pathogen defense. By quantifying transcriptional changes of these genes by real-time RT-PCR, we wanted to find out, how gene expression is affected by both hyperand microgravity conditions during a parabolic flight. For this purpose Arabidopsis thaliana callus cultures were metabolically quenched by the injection of RNAlater at the end of the microgravity-phase of each parabola. The data we present will show how fast changes in amounts of transcripts will occur, and to what degree the expression profiles are comparable with data obtained from exposures to hypergravity and simulated microgravity.

Ring-Sheared Drop (RSD): Microgravity Module for Containerless Flow Studies

NASA Astrophysics Data System (ADS)

Gulati, Shreyash; Raghunandan, Aditya; Rasheed, Fayaz; McBride, Samantha A.; Hirsa, Amir H.

2017-02-01

Microgravity is potentially a powerful tool for investigating processes that are sensitive to the presence of solid walls, since fluid containment can be achieved by surface tension. One such process is the transformation of protein in solution into amyloid fibrils; these are protein aggregates associated with neurodegenerative diseases such as Alzheimer's and Parkinson's. In addition to solid walls, experiments with gravity are also subject to influences from sedimentation of aggregates and buoyancy-driven convection. The ring-sheared drop (RSD) module is a flow apparatus currently under development to study formation of amyloid fibrils aboard the International Space Station (ISS). A 25 mm diameter drop of protein solution will be contained by surface tension and constrained by a pair of sharp-edged tubes, forming two contact rings. Shear can be imparted by rotating one ring with the other ring kept stationary. Here we report on parabolic flights conducted to test the growth and pinning of 10 mm diameter drops of water in under 10 s of microgravity. Finite element method (FEM) based fluid dynamics computations using a commercial package (COMSOL) assisted in the design of the parabolic flight experiments. Prior to the parabolic flights, the code was validated against experiments in the lab (1 g), on the growth of sessile and pendant droplets. The simulations show good agreement with the experiments. This modeling capability will enable the development of the RSD at the 25 mm scale for the ISS.

Computation of asymmetric supersonic flows around cones at large incidence

NASA Technical Reports Server (NTRS)

Degani, David

1987-01-01

The Schiff-Steger parabolized Navier-Stokes (PNS) code has been modified to allow computation of conical flowfields around cones at high incidence. The improved algorithm of Degani and Schiff has been incorporated with the PNS code. This algorithm adds the cross derivative and circumferential viscous terms to the original PNS code and modifies the algebraic eddy viscosity turbulence model to take into account regions of so called cross-flow separation. Assuming the flowfield is conical (but not necessarily symmetric) a marching stepback procedure is used: the solution is marched one step downstream using improved PNS code and the flow variables are then scaled to place the solution back to the original station. The process is repeated until no change in the flow variables is observed with further marching. The flow variables are then constant along rays of the flowfield. The experiments obtained by Bannik and Nebbeling were chosen as a test case. In these experiments a cone of 7.5 deg. half angle at Mach number 2.94 and Reynolds number 1.372 x 10(7) was tested up 34 deg. angle of attack. At high angle of attack nonconical asymmetric leeward side vortex patterns were observed. In the first set of computations, using an earlier obtained solution of the above cone for angle of attack of 22.6 deg. and at station x=0.5 as a starting solution, the angle of attack was gradually increased up to 34 deg. During this procedure the grid was carfully adjusted to capture the bow shock. A stable, converged symmetric solution was obtained. Since the numerical code converged to a symmetric solution which is not the physical one, the stability was tested by a random perturbation at each point. The possible effect of surface roughness or non perfect body shape was also investigated. It was concluded that although the assumption of conical viscous flows can be very useful for certain cases, it can not be used for the present case. Thus the second part of the investigation attempted to obtain a marching (in space) solution with the PNS method using the conical solution as initial data. Finally, the solution of the full Navier-Stokes equations was carried out.

Fully-coupled analysis of jet mixing problems. Part 1. Shock-capturing model, SCIPVIS

NASA Technical Reports Server (NTRS)

Dash, S. M.; Wolf, D. E.

1984-01-01

A computational model, SCIPVIS, is described which predicts the multiple cell shock structure in imperfectly expanded, turbulent, axisymmetric jets. The model spatially integrates the parabolized Navier-Stokes jet mixing equations using a shock-capturing approach in supersonic flow regions and a pressure-split approximation in subsonic flow regions. The regions are coupled using a viscous-characteristic procedure. Turbulence processes are represented via the solution of compressibility-corrected two-equation turbulence models. The formation of Mach discs in the jet and the interactive analysis of the wake-like mixing process occurring behind Mach discs is handled in a rigorous manner. Calculations are presented exhibiting the fundamental interactive processes occurring in supersonic jets and the model is assessed via comparisons with detailed laboratory data for a variety of under- and overexpanded jets.

Strong convergence and convergence rates of approximating solutions for algebraic Riccati equations in Hilbert spaces

NASA Technical Reports Server (NTRS)

Ito, Kazufumi

1987-01-01

The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.

Nonresonant Faraday rotation in glassy semiconductors

NASA Astrophysics Data System (ADS)

van den Keybus, P.; Grevendonk, W.

1986-06-01

Nonresonant interband Faraday rotation in amorphous semiconductors, as a function of photon energy, may be described by an equation derived for direct transitions in crystalline semiconductors. In this paper it is shown how this equation may be obtained for the former case also, assuming a parabolic density of states function N(E) and a correlation between valence- and conduction-band states. The analysis of experiments on chalcogenide glasses reveals a Faraday-rotation energy gap EFRg that is significantly larger than the optical gap Eoptg. The effect is attributed to transitions between extended states, so that it is meaningful to compare EFRg with the mobility gap Eμg. For oxide glasses both gaps are comparable but for chalcogenide glasses EFRg is too large by a few tenths of 1 eV.

Laser dynamics in transversely inhomogeneous plasma and its relevance to wakefield acceleration

NASA Astrophysics Data System (ADS)

Pathak, V. B.; Vieira, J.; Silva, L. O.; Nam, Chang Hee

2018-05-01

We present full set of coupled equations describing the weakly relativistic dynamics of a laser in a plasma with transverse inhomogeneity. We apply variational principle approach to obtain these coupled equations governing laser spot-size, transverse wavenumber, curvature, transverse centroid, etc. We observe that such plasma inhomogeneity can lead to stronger self-focusing. We further discuss the guiding conditions of laser in parabolic plasma channels. With the help of multi-dimensional particle in cell simulations the study is extended to the blowout regime of laser wakefield acceleration to show laser as well as self-injected electron bunch steering in plasma to generate unconventional particle trajectories. Our simulation results demonstrate that such transverse inhomogeneities due to asymmetric self focusing lead to asymmetric bubble excitation, thus inducing off-axis self-injection.

An almost symmetric Strang splitting scheme for nonlinear evolution equations.

PubMed

Einkemmer, Lukas; Ostermann, Alexander

2014-07-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.

Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods. Appendix 2

NASA Technical Reports Server (NTRS)

Prudhomme, C.; Rovas, D. V.; Veroy, K.; Machiels, L.; Maday, Y.; Patera, A. T.; Turinici, G.; Zang, Thomas A., Jr. (Technical Monitor)

2002-01-01

We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced basis approximations, Galerkin projection onto a space W(sub N) spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation, relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures, methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage, in which, given a new parameter value, we calculate the output of interest and associated error bound, depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.

Investigating the use of a rational Runge Kutta method for transport modelling

NASA Astrophysics Data System (ADS)

Dougherty, David E.

An unconditionally stable explicit time integrator has recently been developed for parabolic systems of equations. This rational Runge Kutta (RRK) method, proposed by Wambecq 1 and Hairer 2, has been applied by Liu et al.3 to linear heat conduction problems in a time-partitioned solution context. An important practical question is whether the method has application for the solution of (nearly) hyperbolic equations as well. In this paper the RRK method is applied to a nonlinear heat conduction problem, the advection-diffusion equation, and the hyperbolic Buckley-Leverett problem. The method is, indeed, found to be unconditionally stable for the linear heat conduction problem and performs satisfactorily for the nonlinear heat flow case. A heuristic limitation on the utility of RRK for the advection-diffusion equation arises in the Courant number; for the second-order accurate one-step two-stage RRK method, a limiting Courant number of 2 applies. First order upwinding is not as effective when used with RRK as with Euler one-step methods. The method is found to perform poorly for the Buckley-Leverett problem.

CFORM- LINEAR CONTROL SYSTEM DESIGN AND ANALYSIS: CLOSED FORM SOLUTION AND TRANSIENT RESPONSE OF THE LINEAR DIFFERENTIAL EQUATION

NASA Technical Reports Server (NTRS)

Jamison, J. W.

1994-01-01

CFORM was developed by the Kennedy Space Center Robotics Lab to assist in linear control system design and analysis using closed form and transient response mechanisms. The program computes the closed form solution and transient response of a linear (constant coefficient) differential equation. CFORM allows a choice of three input functions: the Unit Step (a unit change in displacement); the Ramp function (step velocity); and the Parabolic function (step acceleration). It is only accurate in cases where the differential equation has distinct roots, and does not handle the case for roots at the origin (s=0). Initial conditions must be zero. Differential equations may be input to CFORM in two forms - polynomial and product of factors. In some linear control analyses, it may be more appropriate to use a related program, Linear Control System Design and Analysis (KSC-11376), which uses root locus and frequency response methods. CFORM was written in VAX FORTRAN for a VAX 11/780 under VAX VMS 4.7. It has a central memory requirement of 30K. CFORM was developed in 1987.

An interaction algorithm for prediction of mean and fluctuating velocities in two-dimensional aerodynamic wake flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Orzechowski, J. A.

1980-01-01

A theoretical analysis is presented yielding sets of partial differential equations for determination of turbulent aerodynamic flowfields in the vicinity of an airfoil trailing edge. A four phase interaction algorithm is derived to complete the analysis. Following input, the first computational phase is an elementary viscous corrected two dimensional potential flow solution yielding an estimate of the inviscid-flow induced pressure distribution. Phase C involves solution of the turbulent two dimensional boundary layer equations over the trailing edge, with transition to a two dimensional parabolic Navier-Stokes equation system describing the near-wake merging of the upper and lower surface boundary layers. An iteration provides refinement of the potential flow induced pressure coupling to the viscous flow solutions. The final phase is a complete two dimensional Navier-Stokes analysis of the wake flow in the vicinity of a blunt-bases airfoil. A finite element numerical algorithm is presented which is applicable to solution of all partial differential equation sets of inviscid-viscous aerodynamic interaction algorithm. Numerical results are discussed.

Localized light waves: Paraxial and exact solutions of the wave equation (a review)

NASA Astrophysics Data System (ADS)

Kiselev, A. P.

2007-04-01

Simple explicit localized solutions are systematized over the whole space of a linear wave equation, which models the propagation of optical radiation in a linear approximation. Much attention has been paid to exact solutions (which date back to the Bateman findings) that describe wave beams (including Bessel-Gauss beams) and wave packets with a Gaussian localization with respect to the spatial variables and time. Their asymptotics with respect to free parameters and at large distances are presented. A similarity between these exact solutions and harmonic in time fields obtained in the paraxial approximation based on the Leontovich-Fock parabolic equation has been studied. Higher-order modes are considered systematically using the separation of variables method. The application of the Bateman solutions of the wave equation to the construction of solutions to equations with dispersion and nonlinearity and their use in wavelet analysis, as well as the summation of Gaussian beams, are discussed. In addition, solutions localized at infinity known as the Moses-Prosser “acoustic bullets”, as well as their harmonic in time counterparts, “ X waves”, waves from complex sources, etc., have been considered. Everywhere possible, the most elementary mathematical formalism is used.

Monge-Ampére simulation of fourth order PDEs in two dimensions with application to elastic-electrostatic contact problems

NASA Astrophysics Data System (ADS)

DiPietro, Kelsey L.; Lindsay, Alan E.

2017-11-01

We present an efficient moving mesh method for the simulation of fourth order nonlinear partial differential equations (PDEs) in two dimensions using the Parabolic Monge-Ampére (PMA) equation. PMA methods have been successfully applied to the simulation of second order problems, but not on systems with higher order equations which arise in many topical applications. Our main application is the resolution of fine scale behavior in PDEs describing elastic-electrostatic interactions. The PDE system considered has multiple parameter dependent singular solution modalities, including finite time singularities and sharp interface dynamics. We describe how to construct a dynamic mesh algorithm for such problems which incorporates known self similar or boundary layer scalings of the underlying equation to locate and dynamically resolve fine scale solution features in these singular regimes. We find a key step in using the PMA equation for mesh generation in fourth order problems is the adoption of a high order representation of the transformation from the computational to physical mesh. We demonstrate the efficacy of the new method on a variety of examples and establish several new results and conjectures on the nature of self-similar singularity formation in higher order PDEs.

Electromagnetism on anisotropic fractal media

NASA Astrophysics Data System (ADS)

Ostoja-Starzewski, Martin

2013-04-01

Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green-Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampère laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

HYDRA-II: A hydrothermal analysis computer code: Volume 2, User's manual

DOE Office of Scientific and Technical Information (OSTI.GOV)

McCann, R.A.; Lowery, P.S.; Lessor, D.L.

1987-09-01

HYDRA-II is a hydrothermal computer code capable of three-dimensional analysis of coupled conduction, convection, and thermal radiation problems. This code is especially appropriate for simulating the steady-state performance of spent fuel storage systems. The code has been evaluated for this application for the US Department of Energy's Commercial Spent Fuel Management Program. HYDRA-II provides a finite-difference solution in cartesian coordinates to the equations governing the conservation of mass, momentum, and energy. A cylindrical coordinate system may also be used to enclose the cartesian coordinate system. This exterior coordinate system is useful for modeling cylindrical cask bodies. The difference equations formore » conservation of momentum incorporate directional porosities and permeabilities that are available to model solid structures whose dimensions may be smaller than the computational mesh. The equation for conservation of energy permits modeling of orthotropic physical properties and film resistances. Several automated methods are available to model radiation transfer within enclosures and from fuel rod to fuel rod. The documentation of HYDRA-II is presented in three separate volumes. Volume 1 - Equations and Numerics describes the basic differential equations, illustrates how the difference equations are formulated, and gives the solution procedures employed. This volume, Volume 2 - User's Manual, contains code flow charts, discusses the code structure, provides detailed instructions for preparing an input file, and illustrates the operation of the code by means of a sample problem. The final volume, Volume 3 - Verification/Validation Assessments, provides a comparison between the analytical solution and the numerical simulation for problems with a known solution. 6 refs.« less

A standard description and costing methodology for the balance-of-plant items of a solar thermal electric power plant. Report of a multi-institutional working group

NASA Technical Reports Server (NTRS)

1983-01-01

Standard descriptions for solar thermal power plants are established and uniform costing methodologies for nondevelopmental balance of plant (BOP) items are developed. The descriptions and methodologies developed are applicable to the major systems. These systems include the central receiver, parabolic dish, parabolic trough, hemispherical bowl, and solar pond. The standard plant is defined in terms of four categories comprising (1) solar energy collection, (2) power conversion, (3) energy storage, and (4) balance of plant. Each of these categories is described in terms of the type and function of components and/or subsystems within the category. A detailed description is given for the BOP category. BOP contains a number of nondevelopmental items that are common to all solar thermal systems. A standard methodology for determining the costs of these nondevelopmental BOP items is given. The methodology is presented in the form of cost equations involving cost factors such as unit costs. A set of baseline values for the normalized cost factors is also given.

Investigating the possibility of a turning point in the dark energy equation of state

NASA Astrophysics Data System (ADS)

Hu, YaZhou; Li, Miao; Li, XiaoDong; Zhang, ZhenHui

2014-08-01

We investigate a second order parabolic parametrization, w( a) = w t + w a ( a t - a)2, which is a direct characterization of a possible turning in w. The cosmological consequence of this parametrization is explored by using the observational data of the SNLS3 type Ia supernovae sample, the CMB measurements from WMAP9 and Planck, the Hubble parameter measurement from HST, and the baryon acoustic oscillation (BAO) measurements from 6dFGS, BOSS DR11 and improved WiggleZ. We found the existence of a turning point in w at a ˜ 0.7 is favored at 1 σ CL. In the epoch 0.55 < a < 0.9, w < -1 is favored at 1 σ CL, and this significance increases near a = 0.8, reaching a 2 σ CL. The parabolic parametrization achieve equivalent performance to the ΛCDM and Chevallier-Polarski-Linder (CPL) models when the Akaike information criterion was used to assess them. Our analysis shows the value of considering high order parametrizations when studying the cosmological constraints on w.

Estimation of the Thermal Process in the Honeycomb Panel by a Monte Carlo Method

NASA Astrophysics Data System (ADS)

Gusev, S. A.; Nikolaev, V. N.

2018-01-01

A new Monte Carlo method for estimating the thermal state of the heat insulation containing honeycomb panels is proposed in the paper. The heat transfer in the honeycomb panel is described by a boundary value problem for a parabolic equation with discontinuous diffusion coefficient and boundary conditions of the third kind. To obtain an approximate solution, it is proposed to use the smoothing of the diffusion coefficient. After that, the obtained problem is solved on the basis of the probability representation. The probability representation is the expectation of the functional of the diffusion process corresponding to the boundary value problem. The process of solving the problem is reduced to numerical statistical modelling of a large number of trajectories of the diffusion process corresponding to the parabolic problem. It was used earlier the Euler method for this object, but that requires a large computational effort. In this paper the method is modified by using combination of the Euler and the random walk on moving spheres methods. The new approach allows us to significantly reduce the computation costs.

Application of a multi-level grid method to transonic flow calculations

NASA Technical Reports Server (NTRS)

South, J. C., Jr.; Brandt, A.

1976-01-01

A multi-level grid method was studied as a possible means of accelerating convergence in relaxation calculations for transonic flows. The method employs a hierarchy of grids, ranging from very coarse to fine. The coarser grids are used to diminish the magnitude of the smooth part of the residuals. The method was applied to the solution of the transonic small disturbance equation for the velocity potential in conservation form. Nonlifting transonic flow past a parabolic arc airfoil is studied with meshes of both constant and variable step size.

Time-domain model of gyroklystrons with diffraction power input and output

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ginzburg, N. S., E-mail: ginzburg@appl.sci-nnov.ru; Rozental, R. M.; Sergeev, A. S.

A time-domain theory of gyroklystrons with diffraction input and output has been developed. The theory is based on the description of the wave excitation and propagation by a parabolic equation. The results of the simulations are in good agreement with the experimental studies of two-cavity gyroklystrons operating at the first and second cyclotron harmonics. Along with the basic characteristics of the amplification regimes, such as the gain and efficiency, the developed method makes it possible to define the conditions of spurious self-excitation and frequency-locking by an external signal.

The Linear Quadratic Optimal Control Problem for Infinite Dimensional Systems with Unbounded Input and Output Operators.

DTIC Science & Technology

1984-01-01

5.5) respectively (5.3) and (5.8) which means that u(t) - 0 respectively v(t) - 0 for t > o. The evolution of the systems (5.1) and (5.3) in terms ...input/output delays; and b) the general theory is presented in such a way that it applies to both . . ... ..- Lr parabolic and hyperbolic I P9es as...particular emphasis is placed on the development of the duality theory by means of two different state concepts. The resulting evolution equations

RANDOM EVOLUTIONS, MARKOV CHAINS, AND SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS

PubMed Central

Griego, R. J.; Hersh, R.

1969-01-01

Several authors have considered Markov processes defined by the motion of a particle on a fixed line with a random velocity1, 6, 8, 10 or a random diffusivity.5, 12 A “random evolution” is a natural but apparently new generalization of this notion. In this note we hope to show that this concept leads to simple and powerful applications of probabilistic tools to initial-value problems of both parabolic and hyperbolic type. We obtain existence theorems, representation theorems, and asymptotic formulas, both old and new. PMID:16578690

Coherent reflection from surface gravity water waves during reciprocal acoustic transmissions.

PubMed

Badiey, Mohsen; Song, Aijun; Smith, Kevin B

2012-10-01

During a recent experiment in Kauai, Hawaii, reciprocal transmissions were conducted between two acoustic transceivers mounted on the seafloor at a depth of 100 m. The passage of moving surface wave crests was shown to generate focused and intense coherent acoustic returns, which had increasing or decreasing delay depending on the direction of propagation relative to the direction of surface wave crests. It is shown that a rough surface two-dimensional parabolic equation model with an evolving sea surface can produce qualitative agreement with data for the dynamic surface returns.

Microscopic Theory and Simulation of Quantum-Well Intersubband Absorption

NASA Technical Reports Server (NTRS)

Li, Jianzhong; Ning, C. Z.

2004-01-01

We study the linear intersubband absorption spectra of a 15 nm InAs quantum well using the intersubband semiconductor Bloch equations with a three-subband model and a constant dephasing rate. We demonstrate the evolution of intersubband absorption spectral line shape as a function of temperature and electron density. Through a detailed examination of various contributions, such as the phase space filling effects, the Coulomb many-body effects and the non-parabolicity effect, we illuminate the underlying physics that shapes the spectra. Keywords: Intersubband transition, linear absorption, semiconductor heterostructure, InAs quantum well

Verification and Validation of the k-kL Turbulence Model in FUN3D and CFL3D Codes

NASA Technical Reports Server (NTRS)

Abdol-Hamid, Khaled S.; Carlson, Jan-Renee; Rumsey, Christopher L.

2015-01-01

The implementation of the k-kL turbulence model using multiple computational uid dy- namics (CFD) codes is reported herein. The k-kL model is a two-equation turbulence model based on Abdol-Hamid's closure and Menter's modi cation to Rotta's two-equation model. Rotta shows that a reliable transport equation can be formed from the turbulent length scale L, and the turbulent kinetic energy k. Rotta's equation is well suited for term-by-term mod- eling and displays useful features compared to other two-equation models. An important di erence is that this formulation leads to the inclusion of higher-order velocity derivatives in the source terms of the scale equations. This can enhance the ability of the Reynolds- averaged Navier-Stokes (RANS) solvers to simulate unsteady ows. The present report documents the formulation of the model as implemented in the CFD codes Fun3D and CFL3D. Methodology, veri cation and validation examples are shown. Attached and sepa- rated ow cases are documented and compared with experimental data. The results show generally very good comparisons with canonical and experimental data, as well as matching results code-to-code. The results from this formulation are similar or better than results using the SST turbulence model.

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. The governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models are described in detail.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D has been developed to solve the three dimensional, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort has been to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation have been emphasized. The governing equations are solved in generalized non-orthogonal body-fitted coordinates by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. It describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

Algorithm and code development for unsteady three-dimensional Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru

1994-01-01

Aeroelastic tests require extensive cost and risk. An aeroelastic wind-tunnel experiment is an order of magnitude more expensive than a parallel experiment involving only aerodynamics. By complementing the wind-tunnel experiments with numerical simulations, the overall cost of the development of aircraft can be considerably reduced. In order to accurately compute aeroelastic phenomenon it is necessary to solve the unsteady Euler/Navier-Stokes equations simultaneously with the structural equations of motion. These equations accurately describe the flow phenomena for aeroelastic applications. At ARC a code, ENSAERO, is being developed for computing the unsteady aerodynamics and aeroelasticity of aircraft, and it solves the Euler/Navier-Stokes equations. The purpose of this cooperative agreement was to enhance ENSAERO in both algorithm and geometric capabilities. During the last five years, the algorithms of the code have been enhanced extensively by using high-resolution upwind algorithms and efficient implicit solvers. The zonal capability of the code has been extended from a one-to-one grid interface to a mismatching unsteady zonal interface. The geometric capability of the code has been extended from a single oscillating wing case to a full-span wing-body configuration with oscillating control surfaces. Each time a new capability was added, a proper validation case was simulated, and the capability of the code was demonstrated.

Adaptive focusing of laser radiation onto a rough reflecting surface through the turbulent and nonlinear atmosphere

NASA Astrophysics Data System (ADS)

Vorontsov, Mikhail A.; Kolosov, Valeriy V.

2004-12-01

Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related with maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing outgoing wave propagation, and the equation describing evolution of the mutual coherence function (MCF) for the backscattered (returned) wave. The resulting evolution equation for the MCF is further simplified by the use of the smooth refractive index approximation. This approximation enables derivation of the transport equation for the returned wave brightness function, analyzed here using method characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wavefront sensors that perform sensing of speckle-averaged characteristics of the wavefront phase (TIL sensors). Analysis of the wavefront phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric turbulence-related phase aberrations. We also show that wavefront sensing results depend on the extended target shape, surface roughness, and the outgoing beam intensity distribution on the target surface.

Analysis of wave propagation and wavefront sensing in target-in-the-loop beam control systems

NASA Astrophysics Data System (ADS)

Vorontsov, Mikhail A.; Kolosov, Valeri V.

2004-10-01

Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related with maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing outgoing wave propagation, and the equation describing evolution of the mutual intensity function (MIF) for the backscattered (returned) wave. The resulting evolution equation for the MIF is further simplified by the use of the smooth refractive index approximation. This approximation enables derivation of the transport equation for the returned wave brightness function, analyzed here using method characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wavefront sensors that perform sensing of speckle-averaged characteristics of the wavefront phase (TIL sensors). Analysis of the wavefront phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric turbulence-related phase aberrations. We also show that wavefront sensing results depend on the extended target shape, surface roughness, and the outgoing beam intensity distribution on the target surface.

Femtosecond parabolic pulse shaping in normally dispersive optical fibers.

PubMed

Sukhoivanov, Igor A; Iakushev, Sergii O; Shulika, Oleksiy V; Díez, Antonio; Andrés, Miguel

2013-07-29

Formation of parabolic pulses at femtosecond time scale by means of passive nonlinear reshaping in normally dispersive optical fibers is analyzed. Two approaches are examined and compared: the parabolic waveform formation in transient propagation regime and parabolic waveform formation in the steady-state propagation regime. It is found that both approaches could produce parabolic pulses as short as few hundred femtoseconds applying commercially available fibers, specially designed all-normal dispersion photonic crystal fiber and modern femtosecond lasers for pumping. The ranges of parameters providing parabolic pulse formation at the femtosecond time scale are found depending on the initial pulse duration, chirp and energy. Applicability of different fibers for femtosecond pulse shaping is analyzed. Recommendation for shortest parabolic pulse formation is made based on the analysis presented.

Non linear shock wave propagation in heterogeneous fluids: a numerical approach beyond the parabolic approximation with application to sonic boom.

NASA Astrophysics Data System (ADS)

Dagrau, Franck; Coulouvrat, François; Marchiano, Régis; Héron, Nicolas

2008-06-01

Dassault Aviation as a civil aircraft manufacturer is studying the feasibility of a supersonic business jet with the target of an "acceptable" sonic boom at the ground level, and in particular in case of focusing. A sonic boom computational process has been performed, that takes into account meteorological effects and aircraft manoeuvres. Turn manoeuvres and aircraft acceleration create zones of convergence of rays (caustics) which are the place of sound amplification. Therefore two elements have to be evaluated: firstly the geometrical position of the caustics, and secondly the noise level in the neighbourhood of the caustics. The modelling of the sonic boom propagation is based essentially on the assumptions of geometrical acoustics. Ray tracing is obtained according to Fermat's principle as paths that minimise the propagation time between the source (the aircraft) and the receiver. Wave amplitude and time waveform result from the solution of the inviscid Burgers' equation written along each individual ray. The "age variable" measuring the cumulative nonlinear effects is linked to the ray tube area. Caustics are located as the place where the ray tube area vanishes. Since geometrical acoustics does not take into account diffraction effects, it breaks down in the neighbourhood of caustics where it would predict unphysical infinite pressure amplitude. The aim of this study is to describe an original method for computing the focused noise level. The approach involves three main steps that can be summarised as follows. The propagation equation is solved by a forward marching procedure split into three successive steps: linear propagation in a homogeneous medium, linear perturbation due to the weak heterogeneity of the medium, and non-linear effects. The first step is solved using an "exact" angular spectrum algorithm. Parabolic approximation is applied only for the weak perturbation due to the heterogeneities. Finally, non linear effects are performed by solving the in-viscid Burgers' equation. As this one is valid for a plane wave, the direction of this last one is not prescribed a priori, but is computed in a self-adaptative way using an efficient numerical solver of the non-linear eikonal equation (Fast Marching Method).

The small community solar thermal power experiment. Parabolic dish technology for industrial process heat application

NASA Technical Reports Server (NTRS)

Polzien, R. E.; Rodriguez, D.

1981-01-01

Aspects of incorporating a thermal energy transport system (ETS) into a field of parabolic dish collectors for industrial process heat (IPH) applications were investigated. Specific objectives are to: (1) verify the mathematical optimization of pipe diameters and insulation thicknesses calculated by a computer code; (2) verify the cost model for pipe network costs using conventional pipe network construction; (3) develop a design and the associated production costs for incorporating risers and downcomers on a low cost concentrator (LCC); (4) investigate the cost reduction of using unconventional pipe construction technology. The pipe network design and costs for a particular IPH application, specifically solar thermally enhanced oil recovery (STEOR) are analyzed. The application involves the hybrid operation of a solar powered steam generator in conjunction with a steam generator using fossil fuels to generate STEOR steam for wells. It is concluded that the STEOR application provides a baseline pipe network geometry used for optimization studies of pipe diameter and insulation thickness, and for development of comparative cost data, and operating parameters for the design of riser/downcomer modifications to the low cost concentrator.

Design of a high-efficiency train headlamp with low power consumption using dual half-parabolic aluminized reflectors.

PubMed

Liang, Wei-Lun; Su, Guo-Dung J

2018-02-20

We propose a train headlamp system using dual half-circular parabolic aluminized reflectors. Each half-circular reflector contains five high-efficiency and small-package light-emitting diode (LED) chips, and the halves are 180° rotationally symmetric. For traffic safety, the headlamp satisfies the Code of Federal Regulations. To predict the pattern of illumination, an analytical derivation is developed for the optical path of a ray that is perpendicular to and emitted from the center of an LED chip. This ray represents the main ray emitted from the LED chip and is located at the maximum illuminance of the spot projected by the LED source onto a screen. We then analyze the design systematically to determine the locations of the LED chips in the reflector that minimize electricity consumption while satisfying reliability constraints associated with traffic safety. Compared to a typical train headlamp system with an incandescent or halogen lamp needing several hundred watts, the proposed system only uses 20.18 W to achieve the luminous intensity requirements.

The Use of a Code-generating System for the Derivation of the Equations for Wind Turbine Dynamics

NASA Astrophysics Data System (ADS)

Ganander, Hans

2003-10-01

For many reasons the size of wind turbines on the rapidly growing wind energy market is increasing. Relations between aeroelastic properties of these new large turbines change. Modifications of turbine designs and control concepts are also influenced by growing size. All these trends require development of computer codes for design and certification. Moreover, there is a strong desire for design optimization procedures, which require fast codes. General codes, e.g. finite element codes, normally allow such modifications and improvements of existing wind turbine models. This is done relatively easy. However, the calculation times of such codes are unfavourably long, certainly for optimization use. The use of an automatic code generating system is an alternative for relevance of the two key issues, the code and the design optimization. This technique can be used for rapid generation of codes of particular wind turbine simulation models. These ideas have been followed in the development of new versions of the wind turbine simulation code VIDYN. The equations of the simulation model were derived according to the Lagrange equation and using Mathematica®, which was directed to output the results in Fortran code format. In this way the simulation code is automatically adapted to an actual turbine model, in terms of subroutines containing the equations of motion, definitions of parameters and degrees of freedom. Since the start in 1997, these methods, constituting a systematic way of working, have been used to develop specific efficient calculation codes. The experience with this technique has been very encouraging, inspiring the continued development of new versions of the simulation code as the need has arisen, and the interest for design optimization is growing.

The fractional diffusion limit of a kinetic model with biochemical pathway

NASA Astrophysics Data System (ADS)

Perthame, Benoît; Sun, Weiran; Tang, Min

2018-06-01

Kinetic-transport equations that take into account the intracellular pathways are now considered as the correct description of bacterial chemotaxis by run and tumble. Recent mathematical studies have shown their interest and their relations to more standard models. Macroscopic equations of Keller-Segel type have been derived using parabolic scaling. Due to the randomness of receptor methylation or intracellular chemical reactions, noise occurs in the signaling pathways and affects the tumbling rate. Then comes the question to understand the role of an internal noise on the behavior of the full population. In this paper we consider a kinetic model for chemotaxis which includes biochemical pathway with noises. We show that under proper scaling and conditions on the tumbling frequency as well as the form of noise, fractional diffusion can arise in the macroscopic limits of the kinetic equation. This gives a new mathematical theory about how long jumps can be due to the internal noise of the bacteria.

Diffraction of a Gaussian beam in a three-dimensional smoothly inhomogeneous medium: an eikonal-based complex geometrical-optics approach.

PubMed

Berczynski, Pawel; Bliokh, Konstantin Yu; Kravtsov, Yuri A; Stateczny, Andrzej

2006-06-01

We present an ab initio account of the paraxial complex geometrical optics (CGO) in application to scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of the Riccati type. This substantially simplifies the description of Gaussian beam diffraction as compared with full-wave or parabolic (quasi-optics) equations. For a Gaussian beam propagating in a homogeneous medium or along the symmetry axis in a lenslike medium, the CGO equations possess analytical solutions; otherwise, they can be readily solved numerically. As a nontrivial example we consider Gaussian beam propagation and diffraction along a helical ray in an axially symmetric waveguide medium. It is shown that the major axis of the beam's elliptical cross section grows unboundedly; it is oriented predominantly in the azimuthal (binormal) direction and does not obey the parallel-transport law.

Direct simulation for the instability and breakup of laminar liquid jets

NASA Technical Reports Server (NTRS)

Chuech, S. G.; Przekwas, A. J.; Yang, H. Q.; Gross, K. W.

1990-01-01

A direct numerical simulation method is described for predicting the deformation of laminar liquid jets. In the present nonlinear direct simulation, the convective term, which has been discarded in past linear analyses by Rayleigh and others, is included in the hydrodynamic equations. It is shown that only by maintaining full complexity of the nonlinear surface tension term accurate drop formation can be predicted. The continuity and momentum equations in the transient form are integrated on an adaptive grid, conforming the jet and surface wave shape. The equations, which are parabolic in time and elliptic in space, are solved by a TVD scheme with characteristic flux splitting. The results of the present work are discussed and compared with available measurements and other analyses. The comparison shows that among the predictions, the current 1-D direct simulation results agree best with the experimental data. Furthermore, the computer time requirements are much (an order of magnitude) smaller than those of previously reported multidimensional analyses.

Direct simulation for the instability and breakup of laminar liquid jets

NASA Astrophysics Data System (ADS)

Chuech, S. G.; Przekwas, A. J.; Yang, H. Q.; Gross, K. W.

1990-07-01

A direct numerical simulation method is described for predicting the deformation of laminar liquid jets. In the present nonlinear direct simulation, the convective term, which has been discarded in past linear analyses by Rayleigh and others, is included in the hydrodynamic equations. It is shown that only by maintaining full complexity of the nonlinear surface tension term accurate drop formation can be predicted. The continuity and momentum equations in the transient form are integrated on an adaptive grid, conforming the jet and surface wave shape. The equations, which are parabolic in time and elliptic in space, are solved by a TVD scheme with characteristic flux splitting. The results of the present work are discussed and compared with available measurements and other analyses. The comparison shows that among the predictions, the current 1-D direct simulation results agree best with the experimental data. Furthermore, the computer time requirements are much (an order of magnitude) smaller than those of previously reported multidimensional analyses.

CAN-DO, CFD-based Aerodynamic Nozzle Design and Optimization program for supersonic/hypersonic wind tunnels

NASA Technical Reports Server (NTRS)

Korte, John J.; Kumar, Ajay; Singh, D. J.; White, J. A.

1992-01-01

A design program is developed which incorporates a modern approach to the design of supersonic/hypersonic wind-tunnel nozzles. The approach is obtained by the coupling of computational fluid dynamics (CFD) with design optimization. The program can be used to design a 2D or axisymmetric, supersonic or hypersonic, wind-tunnel nozzles that can be modeled with a calorically perfect gas. The nozzle design is obtained by solving a nonlinear least-squares optimization problem (LSOP). The LSOP is solved using an iterative procedure which requires intermediate flowfield solutions. The nozzle flowfield is simulated by solving the Navier-Stokes equations for the subsonic and transonic flow regions and the parabolized Navier-Stokes equations for the supersonic flow regions. The advantages of this method are that the design is based on the solution of the viscous equations eliminating the need to make separate corrections to a design contour, and the flexibility of applying the procedure to different types of nozzle design problems.

A numerical method for computing unsteady 2-D boundary layer flows

NASA Technical Reports Server (NTRS)

Krainer, Andreas

1988-01-01

A numerical method for computing unsteady two-dimensional boundary layers in incompressible laminar and turbulent flows is described and applied to a single airfoil changing its incidence angle in time. The solution procedure adopts a first order panel method with a simple wake model to solve for the inviscid part of the flow, and an implicit finite difference method for the viscous part of the flow. Both procedures integrate in time in a step-by-step fashion, in the course of which each step involves the solution of the elliptic Laplace equation and the solution of the parabolic boundary layer equations. The Reynolds shear stress term of the boundary layer equations is modeled by an algebraic eddy viscosity closure. The location of transition is predicted by an empirical data correlation originating from Michel. Since transition and turbulence modeling are key factors in the prediction of viscous flows, their accuracy will be of dominant influence to the overall results.

A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials

NASA Astrophysics Data System (ADS)

Sun, Zheng; Carrillo, José A.; Shu, Chi-Wang

2018-01-01

We consider a class of time-dependent second order partial differential equations governed by a decaying entropy. The solution usually corresponds to a density distribution, hence positivity (non-negativity) is expected. This class of problems covers important cases such as Fokker-Planck type equations and aggregation models, which have been studied intensively in the past decades. In this paper, we design a high order discontinuous Galerkin method for such problems. If the interaction potential is not involved, or the interaction is defined by a smooth kernel, our semi-discrete scheme admits an entropy inequality on the discrete level. Furthermore, by applying the positivity-preserving limiter, our fully discretized scheme produces non-negative solutions for all cases under a time step constraint. Our method also applies to two dimensional problems on Cartesian meshes. Numerical examples are given to confirm the high order accuracy for smooth test cases and to demonstrate the effectiveness for preserving long time asymptotics.

A computer code for three-dimensional incompressible flows using nonorthogonal body-fitted coordinate systems

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1986-01-01

In this report, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BFC) systems has been developed. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme is used to approximate the convection terms in the governing equations. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm (SIMPLE-C). Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present computer code. The user's guide and computer program listing of the present code are also included.