Relevant bibliographies by topics / Backward differencing

Contents

  1. Journal articles
  2. Books
  3. Conference papers

Academic literature on the topic 'Backward differencing'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Backward differencing.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Backward differencing"

1

Durran, Dale R., and Peter N. Blossey. "Implicit–Explicit Multistep Methods for Fast-Wave–Slow-Wave Problems." Monthly Weather Review 140, no. 4 (April 2012): 1307–25. http://dx.doi.org/10.1175/mwr-d-11-00088.1.

Full text
Abstract:
Implicit–explicit (IMEX) linear multistep methods are examined with respect to their suitability for the integration of fast-wave–slow-wave problems in which the fast wave has relatively low amplitude and need not be accurately simulated. The widely used combination of trapezoidal implicit and leapfrog explicit differencing is compared to schemes based on Adams methods or on backward differencing. Two new families of methods are proposed that have good stability properties in fast-wave–slow-wave problems: one family is based on Adams methods and the other on backward schemes. Here the focus is primarily on four specific schemes drawn from these two families: a pair of Adams methods and a pair of backward methods that are either (i) optimized for third-order accuracy in the explicit component of the full IMEX scheme, or (ii) employ particularly good schemes for the implicit component. These new schemes are superior, in many respects, to the linear multistep IMEX schemes currently in use. The behavior of these schemes is compared theoretically in the context of the simple oscillation equation and also for the linearized equations governing stratified compressible flow. Several schemes are also tested in fully nonlinear simulations of gravity waves generated by a localized source in a shear flow.
APA, Harvard, Vancouver, ISO, and other styles
2

Celenligil, M. C., and G. L. Mellor. "Numerical Solution of Two-Dimensional Turbulent Separated Flows Using a Reynolds Stress Closure Model." Journal of Fluids Engineering 107, no. 4 (December 1, 1985): 467–76. http://dx.doi.org/10.1115/1.3242515.

Full text
Abstract:
Turbulent boundary layer separation is studied using the turbulence closure model suggested by Mellor and Yamada. An explicit central finite-differencing scheme is used to solve the governing transport equations. Three flow problems are considered: separation on a flat surface, separation and reattachment over a backward-facing step, and turbulent free shear layer with streamwise curvature. In the problem of separation behind a backward-facing step, nearly cyclic vortex shedding is obtained whereas the other two problems are stationary. The computed results for both mean and turbulence quantities are in fairly good agreement with experimental data.
APA, Harvard, Vancouver, ISO, and other styles
3

KUMAR, B. V. RATHISH, and MANI MEHRA. "A WAVELET-TAYLOR GALERKIN METHOD FOR PARABOLIC AND HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS." International Journal of Computational Methods 02, no. 01 (March 2005): 75–97. http://dx.doi.org/10.1142/s0219876205000375.

Full text
Abstract:
In this study a set of new space and time accurate numerical methods based on different time marching schemes such as Euler, leap-frog and Crank-Nicolson for partial differential equations of the form [Formula: see text], where ℒ is linear differential operator and [Formula: see text] is a nonlinear function, are proposed. To produce accurate temporal differencing, the method employs forward/backward time Taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation. This yields a generalized time discretized scheme which is approximated in space by Galerkin method. The compactly supported orthogonal wavelet bases developed by Daubechies are used in Galerkin scheme. This new wavelet-Taylor Galerkin approach is successively applied to heat equation, convection equation and inviscid Burgers' equation.
APA, Harvard, Vancouver, ISO, and other styles
4

Bokanowski, Olivier, Athena Picarelli, and Christoph Reisinger. "High-order filtered schemes for time-dependent second order HJB equations." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 1 (January 2018): 69–97. http://dx.doi.org/10.1051/m2an/2017039.

Full text
Abstract:
In this paper, we present and analyse a class of “filtered” numerical schemes for second order Hamilton–Jacobi–Bellman (HJB) equations. Our approach follows the ideas recently introduced in B.D. Froese and A.M. Oberman, Convergent filtered schemes for the Monge-Ampère partial differential equation, SIAM J. Numer. Anal. 51 (2013) 423–444, and more recently applied by other authors to stationary or time-dependent first order Hamilton–Jacobi equations. For high order approximation schemes (where “high” stands for greater than one), the inevitable loss of monotonicity prevents the use of the classical theoretical results for convergence to viscosity solutions. The work introduces a suitable local modification of these schemes by “filtering” them with a monotone scheme, such that they can be proven convergent and still show an overall high order behaviour for smooth enough solutions. We give theoretical proofs of these claims and illustrate the behaviour with numerical tests from mathematical finance, focussing also on the use of backward differencing formulae for constructing the high order schemes.
APA, Harvard, Vancouver, ISO, and other styles
5

Durst, F., and J. C. F. Pereira. "Time-Dependent Laminar Backward-Facing Step Flow in a Two-Dimensional Duct." Journal of Fluids Engineering 110, no. 3 (September 1, 1988): 289–96. http://dx.doi.org/10.1115/1.3243547.

Full text
Abstract:
This paper presents results of numerical studies of the impulsively starting backward-facing step flow with the step being mounted in a plane, two-dimensional duct. Results are presented for Reynolds numbers of Re = 10; 368 and 648 and for the last two Reynolds numbers comparisons are given between experimental and numerical results obtained for the final steady state flow conditions. In the computational scheme, the convective terms in the momentum equations are approximated by a 13-point quadratic upstream weighted finite-difference scheme and a fully implicit first order forward differencing scheme is used to discretize the temporal derivatives. The computations show that for the higher Reynolds numbers, the flow starts to separate on the lower and upper corners of the step yielding two disconnected recirculating flow regions for some time after the flow has been impulsively started. As time progresses, these two separated flow regions connect up and a single recirculating flow region emerges. This separated flow region stays attached to the step, grows in size and approaches, for the time t → ∞, the dimensions measured and predicted for the separation region for steady laminar backward-facing flow. For the Reynolds number Re = 10 the separation starts at the bottom of the backward-facing step and the separation region enlarges with time until the steady state flow pattern is reached. At the channel wall opposite to the step and for Reynolds number Re = 368, a separated flow region is observed and it is shown to occur for some finite time period of the developing, impulsively started backward-facing step flow. Its dimensions change with time and reduce to zero before the steady state flow pattern is reached. For the higher Reynolds number Re = 648, the secondary separated flow region opposite to the wall is also present and it is shown to remain present for t → ∞. Two kinds of the inlet conditions were considered; the inlet mean flow was assumed to be constant in a first study and was assumed to increase with time in a second one. The predicted flow field for t → ∞ turned out to be identical for both cases. They were also identical to the flow field predicted for steady, backward-facing step flow using the same numerical grid as for the time-dependent predictions.
APA, Harvard, Vancouver, ISO, and other styles
6

YAO, JIANYAO, G. R. LIU, DONG QIAN, CHUNG-LUNG CHEN, and GEORGE X. XU. "A MOVING-MESH GRADIENT SMOOTHING METHOD FOR COMPRESSIBLE CFD PROBLEMS." Mathematical Models and Methods in Applied Sciences 23, no. 02 (January 8, 2013): 273–305. http://dx.doi.org/10.1142/s0218202513400046.

Full text
Abstract:
A computational fluid dynamics (CFD) solver based on the gradient smoothing method (GSM) with moving mesh enabled is presented in this paper. The GSM uses unstructured meshes which could be generated and remeshed easily. The spatial derivatives of field variables at nodes and midpoints of cell edges are calculated using the gradient smoothing operations. The presented GSM codes use second-order Roes upwind flux difference splitting method and second-order 3-level backward differencing scheme for the compressible Navier–Stokes equations with moving mesh, and the second-order of accuracy for both the spatial and temporal discretization is ensured. The spatial discretization accuracy is verified using the method of manufactured solutions (MMS) on both structured and unstructured triangle meshes, and the results show that the observed order of accuracy achieves 2 even when highly distorted meshes are used. The temporal discretization accuracy is verified using the results with different time step lengths, and second-order accuracy is also obtained. Therefore, it is confirmed that the proposed GSM-CFD solver is a uniform second-order scheme.
APA, Harvard, Vancouver, ISO, and other styles
7

Juncu, Gh, V. Lavric, and R. Mihail. "A comparison between the insensitive Runge—Kutta, the semi—implicit extrapolation and the backward differencing methods in solving the ODE systems which describe the radical hydrocarbons pyrolysis." Computers & Chemical Engineering 13, no. 9 (September 1989): 1075–79. http://dx.doi.org/10.1016/0098-1354(89)87048-6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Chang, C. A., and J. P. St.-Maurice. "Two-dimensional high-latitude thermospheric modeling: A comparison between moderate and extremely disturbed conditions." Canadian Journal of Physics 69, no. 8-9 (August 1, 1991): 1007–31. http://dx.doi.org/10.1139/p91-159.

Full text
Abstract:
A set of two-dimensional nonlinear calculations has been done to simulate the auroral region electrojet and to examine the effect of the electric field on the dynamics and thermodynamics of the thermosphere. A large number of physical and dynamical processes in the ionosphere have been considered, including the ion-drag force, the Coriolis force, gravitation, Joule heating, viscous heating and viscous work, solar extreme ultraviolet heating, thermal conduction, and cooling to space owing to infrared radiation of different species. Navier–Stokes equations for a compressible, viscous and thermal conducting fluid flow with source terms have been solved by a MacCormack explicit, alternative forward-backward finite differencing scheme in spherical coordinates. Results have been recorded at various time intervals for three hours simulation time, for altitudes between 80 and 450 km, and from the north pole to the equator. In addition to a strong zonal drift motion and to the basic upward and meridional motion away from the heated region, we obtain a complex structure of waves involving meridional and vertical winds, as well as the density and temperature fields. This computation suggests that waves play a much more important role than ordinary diffusion of energy and momentum is spreading the effects of the disturbances away from the electrojet region. The net result is that there is, strictly speaking, no steady state reached by the neutrals except for the bulk of the zonal flow. A second major feature that we obtain is that nonlinear terms can often dominate the momentum equation, which can reduce the magnitude of the zonal flow by a considerable amount, and can displace the region of maximum neutral flow away from where the electrojet is. The nonlinear terms are also responsible for the formation of a neutral density 'hole' at nonelectrojet latitudes. This hole is found below the region where Joule heating reaches its peak value and is used to enhance the neutral densities at high altitudes on a global scale.
APA, Harvard, Vancouver, ISO, and other styles
9

Shin, Dongho, and John C. Strikwerda. "Inf-sup conditions for finite-difference approximations of the stokes equations." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 39, no. 1 (July 1997): 121–34. http://dx.doi.org/10.1017/s0334270000009255.

Full text
Abstract:
AbstractInf-sup conditions are proven for three finite-difference approximations of the Stokes equa-tions. The finite-difference approximations use a staggered-mesh scheme and the schemes resulting from the backward and the forward differencings.
APA, Harvard, Vancouver, ISO, and other styles
10

Hatta, Natsuo, Hitoshi Fujimoto, and Hirohiko Takuda. "Deformation Process of a Water Droplet Impinging on a Solid Surface." Journal of Fluids Engineering 117, no. 3 (September 1, 1995): 394–401. http://dx.doi.org/10.1115/1.2817275.

Full text
Abstract:
This paper is concerned with numerical simulations of the deformation behavior of a liquid droplet impinging on a flat solid surface, as well as the flow field inside the droplet. In the present situation, the case where a droplet impinges on the surface at room temperature with a speed in the order of a few [m/s], is treated. These simulations were performed using the MAC-type solution method to solve a finite-differencing approximation of the Navier-Stokes equations governing an axisymmetric and incompressible fluid flow. For the first case where the liquid is water, the liquid film formed by the droplet impinging on the solid surface flows radially along it and expands in a fairly thin discoid-like shape. Thereafter, the liquid flow shows a tendency to stagnate at the periphery of the circular film, with the result that water is concentrated there is a doughnut-like shape. Subsequently, the water begins to flow backwards toward the center where it accumulates in the central region. For the second case where a n-heptane droplet impinges the surface, the film continues to spread monotonically up to a maximum diameter and there is no recoiling process to cause a backwards flow towards the central region. In this study the whole deformation process was investigated from numerical as well as experimental points of view. We find that the results obtained by the present mathematical model give fairly good agreement with the experimental observations. The effects of the viscous stresses and the surface tension on the deformation process of the droplets are estimated and discussed from a practical standpoint.
APA, Harvard, Vancouver, ISO, and other styles

Books on the topic "Backward differencing"

1

Center, Langley Research, ed. A spectrally accurate boundary-layer code for infinite swept wings. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1994.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
2

Center, Langley Research, ed. A spectrally accurate boundary-layer code for infinite swept wings. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1994.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
3

Krishnan, Radhakrishnan, ed. Computational study of flow establishment in hypersonic pulse facilities. [Cleveland, Ohio]: National Aeronautics and Space Administration, Lewis Research Center, Institute for Computational Mechanics in Propulsion, 1995.

Find full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Backward differencing"

1

Zhang, Junjian, Guoyi Ke, and Z. Charlie Zheng. "Time-Domain Simulation of Ultrasound Propagation With Fractional Laplacian." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-65966.

Full text
Abstract:
The simulation is developed for the purpose of simulating ultrasound propagation through biological tissues. The simulation is based on the time-domain conservation laws with the governing equations for acoustic pressure and velocity, with frequency dependent absorption and dispersion effects. We use forward differencing for velocity and backward differencing for pressure on the non-fractional derivative operator terms in spatial discretization. The fractional Laplacian operators are treated as Riesz derivatives. The shifted standard Grunwald approximation method is used to solve fractional derivative operator terms. To accommodate complicated biological tissue geometries, an immersed boundary method is developed that enables a Cartesian computational grid mesh to be used. The results are compared with those for a non-absorption homogeneous medium to discuss absorption and dispersion effects of biological material.
APA, Harvard, Vancouver, ISO, and other styles
2

Ray, K. P., R. K. Kulkarni, and B. Kasyap Ramkrishnan. "DOA estimation in a multipath environment using covariance differencing and iterative Forward and Backward spatial smoothing." In 2008 International Conference on Recent Advances in Microwave Theory and Applications (MICROWAVE). IEEE, 2008. http://dx.doi.org/10.1109/amta.2008.4763086.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Kim, Sung-Eun, and L. Srinivasa Mohan. "Prediction of Unsteady Loading on a Circular Cylinder in High Reynolds Number Flows Using Large Eddy Simulation." In ASME 2005 24th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2005. http://dx.doi.org/10.1115/omae2005-67044.

Full text
Abstract:
Large eddy simulations were carried out for the flow around a hydrodynamically smooth, fixed circular cylinder at two Reynolds numbers, one at a subcritical Reynolds number (Re = 1.4 × 105) and the other at a supercritical Reynolds number (Re = 1.0 × 106). The computations were made using a parallelized finite-volume Navier-Stokes solver based on a multidimensional linear reconstruction scheme that allows use of unstructured meshes. Central differencing was used for discretization of both convection and diffusion terms. Time-advancement scheme, based on an implicit, non-iterative fractional-step method, was adopted in conjunction with a three-level, backward second-order temporal discretization. Subgrid-scale turbulent viscosity was modeled by a dynamic Smagorinsky model adapted to arbitrary unstructured meshes with the aid of a test-filter applicable to arbitrary unstructured meshes. The present LES results closely reproduced the flow features observed in experiments at both Reynolds numbers. The time-averaged mean drag coefficient, root-mean-square force coefficients and the frequency content of fluctuating forces (vortex-shedding frequency) are predicted with a commendable accuracy.
APA, Harvard, Vancouver, ISO, and other styles
4

Kang, Dong Jin, Sang Soo Bae, and Jae Won Kim. "Navier-Stokes Simulation of the MIT Flapping Foil Experiment Using an Unstructured Finite Volume Method." In ASME 1999 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/99-gt-214.

Full text
Abstract:
A Navier-Stokes simulation of the MIT flapping foil experiment is presented. The MIT experiment was designed to provide a good quality database for unsteady boundary layer flows. The unsteady boundary layer around a hydrofoil was generated by flapping two airfoils upstream of the hydrofoil. Present Navier-Stokes simulation is carried out on the entire experimental domain, including the flapping airfoils as well as the downstream fixed hydrofoil. Present Navier-Stokes code uses an unstructured finite volume method based on the SIMPLE algorithm. It uses QUICK scheme for the convective terms and the second order Euler backward differencing for time derivatives to keep second order accuracy spatially and temporally. All other spatial derivatives are approximated by using central difference scheme. All comparisons of present time averaged and unsteady solutions with the corresponding experimental data are satisfactory: all unsteady solutions are compared in terms of time mean and first harmonic. The first harmonic of the velocity shows a peak inside the boundary layer along the surfaces of the hydrofoil and has a local minimum near the edge of the boundary layer. The local minimum becomes manifest as the boundary layer grows. The unsteadiness in the free stream is transferred inside the boundary layer when an unsteady vortex impinges on the surface. The entrained unsteadiness travels with a local velocity slower than that in the free stream. This causes phase lag of the first harmonic between the free stream and the boundary layer and local minimum of the first harmonic near the edge of the boundary layer.
APA, Harvard, Vancouver, ISO, and other styles
5

Brusiani, Federico, Piero Pelloni, and Giulio Cazzoli. "Definition of a LES Numerical Methodology for the Simulation of Engine Flows on Fixed Grid." In ASME 2008 Internal Combustion Engine Division Spring Technical Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/ices2008-1658.

Full text
Abstract:
To improve the overall engine performance, it is necessary to clearly understand the main unsteady phenomena that occur inside an IC engine. Since experimental technique can provide only lump parameters, the CFD numerical approach has been identified as a valid alternative tool to perform detailed investigations on the fluid dynamics behaviours. The numerical analysis of engine flows is commonly performed by using RANS approach. Adopting a RANS methodology only the mean flow variable distributions could be obtained because the time average of the generic flow variable fluctuation is zero by definition. To perform an effective analysis about the unsteady characteristic of a generic flow and, in particular, of an engine flow it is necessary to improve the numerical solution level adopting the LES (Large Eddy Simulation) approach. LES solves directly the large scales of motion (responsible for the main energy transport inside the flow) while only the small scales are modelled using a Sub-Grid Scale model. Moreover, the LES approach could also be used as test bench case to properly define and understand how it is possible to improve the solution accuracy of RANS simulation. This paper regards the LES analysis of a steady non-reactive wall-bounded flow over a test bench engine geometry. In particular, two LES models, i.e., the Wall Adaptive Local Eddy-Viscosity (WALE) [25] model and the one-equation Dynamic Model by Kim and Menon [23, 24, 29] have been tested. The numerical set-up has been defined performing a preliminary parametric CFD simulations on a basic flow over a backward facing step case. In particular, a bounded second order central differencing scheme was adopted and a discussion of the kinetic energy conservation attitude of such a scheme is performed. LES results have been compared to available experimental LDA measurements of mean and rms fluctuations of both axial and tangential velocity components and with numerical predictions obtained by an optimized RANS simulation of the same case. This paper shows the advantages and the limits of the LES simulation approach applied to IC engine flows.
APA, Harvard, Vancouver, ISO, and other styles
6

Gan, Jiaye, Hong-sik Im, Daniel Espinal, Alexis Lefebvre, and Ge-Cheng Zha. "Investigation of a Compressor Rotor Non-Synchronous Vibration With and Without Fluid-Structure Interaction." In ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/gt2014-26478.

Full text
Abstract:
This paper study the non-synchronous vibration (NSV) of a high speed multistage axial compressor using rigid blade and vibrating blade with fluid-structural interaction (FSI). The unsteady Reynolds-averaged Navier-Stokes (URANS) equations and mode based structural dynamic equations are solved. A low diffusion E-CUSP Reimann solver with a 3rd order WENO scheme for the inviscid fluxes and a 2nd order central differencing for the viscous terms are employed. A 1/7th annulus sector of IGV-rotor-stator is used with a time shifted phase lag BC at circumferential boundaries. An interpolation sliding boundary condition is used for the rotor-stator interaction. The URANS simulation for rigid blades shows that the leading edge (LE) tornado vortices, roughly above 80% rotor span, travel backwards relative to the rotor rotation and cause an excitation with the frequency agreeing with the measured NSV frequency. The predicted excitation frequency of the traveling vortices in the rigid blade simulation is a non-engine order frequency of 2603 Hz, which agrees very well with the NSV rig testing. For the FSI simulation, the results show that there exist two dominant frequencies in the spectrum of the blade vibration. The lower dominant frequency is close to the first bending mode. The higher dominant frequency close to the first torsional mode agrees very well with the measured NSV frequency. The simulation conducted in this paper appears to indicate that the NSV is excited by the traveling vortex.
APA, Harvard, Vancouver, ISO, and other styles
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography