Relevant bibliographies by topics / Lax-Wendroff scheme

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Academic literature on the topic 'Lax-Wendroff scheme'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 June 2025

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Journal articles on the topic "Lax-Wendroff scheme"

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Nigar, Sultana Laek Sazzad Andallah. "Stability Analysis Of First And Second Order Explicit Finite Difference Scheme of Advection-Diffusion Equation." Multicultural Education 8, no. 2 (2022): 52. https://doi.org/10.5281/zenodo.5973240.

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<em>This article studies two first order schemes, FTBSCS and FTCSCS and propose a second order Lax-Wendroff type scheme for the numerical solutions of advection-diffusion equation (ADE) as an initial and boundary value problem. In previous Lax-Wendroff scheme was introduced only for hyperbolic partial differential equation (PDE) but here a new second order Lax-Wendroff type explicit finite difference scheme is proposed for parabolic ADE. For proposed second order Lax-Wendorff type scheme of ADE, we discretise the first order terms of ADE in second order like Lax-Wendorff scheme for hyperbolic partial differential equation. We perform stability analysis of these numerical schemes and determine the condition of stability in terms of temporal and spatial step sizes, advection co-efficient and diffusion co-efficient. The stability conditions of these schemes lead to determine the efficiency of these schemes in terms of the time step restrictions. Finally, we compare these schemes in terms of stability condition and efficiency as well.</em>
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Laek Sazzad Andallah, Nigar Sultana,. "Investigation of Water Pollution in the River with Second-Order Explicit Finite Difference Scheme of Advection-Diffusion Equation and First-Order Explicit Finite Difference Scheme of Advection-Diffusion Equation." Mathematical Statistician and Engineering Applications 71, no. 2 (2022): 12–27. http://dx.doi.org/10.17762/msea.v71i2.62.

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The perseverance of this research article is to investigate water pollution in rivers with a second-order explicit finite difference scheme of advection-diffusion equation (ADE) and a first-order explicit finite difference scheme of ADE. For investigation, two numerical schemes exploit here FTCSCS and second-order Lax-Wendroff type of ADE which is our new proposed one. In earlier Lax-Wendroff, type scheme existed only for hyperbolic partial differential equation (PDE), here a new second-order Lax-Wendroff type scheme is proposed for parabolic PDE and in addition assist to investigate water pollution with an expectation of better yield compared to the existing one. We implement numerical schemes to estimate the pollutant in water at different times and different points of water bodies. We investigate the numerical behaviour of water pollution by implementing the explicit centred difference scheme (FTCSCS) for advection-diffusion and for our proposed second-order Lax-Wendroff type scheme. Our computational result verifies the qualitative behavior of the solution of ADE for various considerations of the parameters.
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Dong, Haoyu, Changna Lu, and Hongwei Yang. "The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations." Mathematics 6, no. 10 (2018): 211. http://dx.doi.org/10.3390/math6100211.

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We develop a Lax–Wendroff scheme on time discretization procedure for finite volume weighted essentially non-oscillatory schemes, which is used to simulate hyperbolic conservation law. We put more focus on the implementation of one-dimensional and two-dimensional nonlinear systems of Euler functions. The scheme can keep avoiding the local characteristic decompositions for higher derivative terms in Taylor expansion, even omit partly procedure of the nonlinear weights. Extensive simulations are performed, which show that the fifth order finite volume WENO (Weighted Essentially Non-oscillatory) schemes based on Lax–Wendroff-type time discretization provide a higher accuracy order, non-oscillatory properties and more cost efficiency than WENO scheme based on Runge–Kutta time discretization for certain problems. Those conclusions almost agree with that of finite difference WENO schemes based on Lax–Wendroff time discretization for Euler system, while finite volume scheme has more flexible mesh structure, especially for unstructured meshes.
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Lu, Changna, Luoyan Xie, and Hongwei Yang. "The Simple Finite Volume Lax-Wendroff Weighted Essentially Nonoscillatory Schemes for Shallow Water Equations with Bottom Topography." Mathematical Problems in Engineering 2018 (2018): 1–15. http://dx.doi.org/10.1155/2018/2652367.

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A Lax-Wendroff-type procedure with the high order finite volume simple weighted essentially nonoscillatory (SWENO) scheme is proposed to simulate the one-dimensional (1D) and two-dimensional (2D) shallow water equations with topography influence in source terms. The system of shallow water equations is discretized using the simple WENO scheme in space and Lax-Wendroff scheme in time. The idea of Lax-Wendroff time discretization can avoid part of characteristic decomposition and calculation of nonlinear weights. The type of simple WENO was first developed by Zhu and Qiu in 2016, which is more simple than classical WENO fashion. In order to maintain good, high resolution and nonoscillation for both continuous and discontinuous flow and suit problems with discontinuous bottom topography, we use the same idea of SWENO reconstruction for flux to treat the source term in prebalanced shallow water equations. A range of numerical examples are performed; as a result, comparing with classical WENO reconstruction and Runge-Kutta time discretization, the simple Lax-Wendroff WENO schemes can obtain the same accuracy order and escape nonphysical oscillation adjacent strong shock, while bringing less absolute truncation error and costing less CPU time for most problems. These conclusions agree with that of finite difference Lax-Wendroff WENO scheme for shallow water equations, while finite volume method has more flexible mesh structure compared to finite difference method.
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Fadhli Ahmad, Mohammad, Mohd Sofiyan Suliman, and . "Deficiency of finite difference methods for capturing shock waves and wave propagation over uneven bottom seabed." International Journal of Engineering & Technology 7, no. 3.28 (2018): 97. http://dx.doi.org/10.14419/ijet.v7i3.28.20977.

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The implementation of finite difference method is used to solve shallow water equations under the extreme conditions. The cases such as dam break and wave propagation over uneven bottom seabed are selected to test the ordinary schemes of Lax-Friederichs and Lax-Wendroff numerical schemes. The test cases include the source term for wave propagation and exclude the source term for dam break. The main aim of this paper is to revisit the application of Lax-Friederichs and Lax-Wendroff numerical schemes at simulating dam break and wave propagation over uneven bottom seabed. For the case of the dam break, the two steps of Lax-Friederichs scheme produce non-oscillation numerical results, however, suffering from some of dissipation. Moreover, the two steps of Lax-Wendroff scheme suffers a very bad oscillation. It seems that these numerical schemes cannot solve the problem at discontinuities which leads to oscillation and dissipation. For wave propagation case, those numerical schemes produce inaccurate information of free surface and velocity due to the uneven seabed profile. Therefore, finite difference is unable to model shallow water equations under uneven bottom seabed with high accuracy compared to the analytical solution.
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Chen, Jing-Bo. "High-order time discretizations in seismic modeling." GEOPHYSICS 72, no. 5 (2007): SM115—SM122. http://dx.doi.org/10.1190/1.2750424.

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Seismic modeling plays an important role in explor-ation geophysics. High-order modeling schemes are in demand for practical reasons. In this context, I present three kinds of high-order time discretizations: Lax-Wendroff methods, Nyström methods, and splitting methods. Lax-Wendroff methods are based on the Taylor expansion and the replacement of high-order temporal derivatives by spatial derivatives, Nyström methods are simplified Runge-Kutta algorithms, and splitting methods comprise substeps for one-step computation. Based on these methods, three schemes with third-order and fourth-order accuracy in time and pseudospectral discretizations in space are presented. I also compare their accuracy, stability, and computational complexity, and discuss advantages and shortcomings of these algorithms. Numerical experiments show that the fourth-order Lax-Wendroff scheme is more efficient for short-time simulations while the fourth-order Nyström scheme and the third-order splitting scheme are more efficient for long-term computations.
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Appadu, A. R. "Numerical Solution of the 1D Advection-Diffusion Equation Using Standard and Nonstandard Finite Difference Schemes." Journal of Applied Mathematics 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/734374.

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Three numerical methods have been used to solve the one-dimensional advection-diffusion equation with constant coefficients. This partial differential equation is dissipative but not dispersive. We consider the Lax-Wendroff scheme which is explicit, the Crank-Nicolson scheme which is implicit, and a nonstandard finite difference scheme (Mickens 1991). We solve a 1D numerical experiment with specified initial and boundary conditions, for which the exact solution is known using all these three schemes using some different values for the space and time step sizes denoted byhandk, respectively, for which the Reynolds number is 2 or 4. Some errors are computed, namely, the error rate with respect to theL1norm, dispersion, and dissipation errors. We have both dissipative and dispersive errors, and this indicates that the methods generate artificial dispersion, though the partial differential considered is not dispersive. It is seen that the Lax-Wendroff and NSFD are quite good methods to approximate the 1D advection-diffusion equation at some values ofkandh. Two optimisation techniques are then implemented to find the optimal values ofkwhenh=0.02for the Lax-Wendroff and NSFD schemes, and this is validated by numerical experiments.
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Ren, Zhiming, Qianzong Bao, and Bingluo Gu. "Time-dispersion correction for arbitrary even-order Lax-Wendroff methods and the application on full-waveform inversion." GEOPHYSICS 86, no. 5 (2021): T361—T375. http://dx.doi.org/10.1190/geo2020-0934.1.

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A second-order accurate finite-difference (FD) approximation is commonly used to approximate the second-order time derivative of a wave equation. The second-order accurate FD scheme may introduce time dispersion in wavefield extrapolation. Lax-Wendroff methods can suppress such dispersion by replacing the high-order time FD error terms with space FD error-correcting terms. However, the time dispersion cannot be completely eliminated and the computation cost dramatically increases with increasing order of (temporal) accuracy. To mitigate the problem, we have extended the existing time-dispersion correction scheme for the second- or fourth-order Lax-Wendroff method to a scheme for arbitrary even-order methods, which uses the forward and inverse time-dispersion transform (FTDT and ITDT) to add and remove the time dispersion from synthetic data. We test the correction scheme using a homogeneous model and the Sigsbee2A model. The modeling examples suggest that the use of derived FTDT and ITDT pairs on high-order Lax-Wendroff methods can effectively remove time-dispersion errors from high-frequency waves while using longer time steps than allowed in low-order Lax-Wendroff methods. We investigate the influence of the time dispersion on full-waveform inversion (FWI) and show an antidispersion workflow. We apply the FTDT to source terms and recorded traces before inversion, resulting in the source and adjoint wavefields containing equal time dispersion from source-side wave propagation and the modeled and observed traces accumulating equal time dispersion from source- and receiver-side wave propagation. The inversion results reveal that the antidispersion workflow is capable of increasing the accuracy of FWI for arbitrary even-order Lax-Wendroff methods. In addition, the high-order method can obtain better inversion results compared to the second-order method with the same antidispersion workflow.
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Rahman, Md Mizanur, K. Hasan, Zhiqian Sang, and Zing Ni. "Lax-Wendroff method for incompressible flow." Journal of Physics: Conference Series 2313, no. 1 (2022): 012002. http://dx.doi.org/10.1088/1742-6596/2313/1/012002.

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Abstract The Lax-Wendroff scheme is extended to incompressible fluid flow problems within the framework of artificial compressibility method (ACM) utilizing a “cell-centered finite-volume” Δ-approximation on a non-orthogonal non-staggered grid. An ACM induces a transformation between conservative and primitive variables; the physical relevance of ACM is to bring about “matrix preconditionings”, provoking density perturbations. The coupled algorithm is pressure-based; it benefits from enhanced accuracy and greater flexibility using the “monotone upstream-centered schemes for conservation laws (MUSCL)” approach. Numerical experiments in reference to “buoyancy-driven” flows with strong sources illustrate that the entire strategy augments overall damping capability and robustness adhering to the factored pseudo-time integration method. Conclusively, the associated limiter function has little influence on the high resolution for selected test cases.
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Bergmann, Tim, Joakim O. Blanch, Johan O. A. Robertsson, and Klaus Holliger. "A simplified Lax‐Wendroff correction for staggered‐grid FDTD modeling of electromagnetic wave propagation in frequency‐dependent media." GEOPHYSICS 64, no. 5 (1999): 1369–77. http://dx.doi.org/10.1190/1.1444642.

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The Lax‐Wendroff correction is an elegant method for increasing the accuracy and computational efficiency of finite‐difference time‐domain (FDTD) solutions of hyperbolic problems. However, the conventional approach leads to implicit solutions for staggered‐grid FDTD approximations of Maxwell’s equations with frequency‐dependent constitutive parameters. To overcome this problem, we propose an approximation that only retains the purely acoustic, i.e., lossless, terms of the Lax‐Wendroff correction. This modified Lax‐Wendroff correction is applied to an O(2, 4) accurate staggered‐grid FDTD approximation of Maxwell’s equations in the radar frequency range (≈10 MHz–10 GHz). The resulting pseudo-O(4, 4) scheme is explicit and computationally efficient and exhibits all the major numerical characteristics of an O(4, 4) accurate FDTD scheme, even for strongly attenuating and dispersive media. The numerical properties of our approach are constrained by classical numerical dispersion and von Neumann‐Routh stability analyses, verified by comparisons with pertinent 1-D analytical solutions and illustrated through 2-D simulations in a variety of surficial materials. Compared to the O(2, 4) scheme, the pseudo-O(4, 4) scheme requires 64% fewer grid points in two dimensions and 78% in three dimensions to achieve the same level of numerical accuracy, which results in large savings in core memory.
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Dissertations / Theses on the topic "Lax-Wendroff scheme"

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Bedjaoui, Nabil, Joaquim Correia, Sackmone Sirisack, and Bouasy Doungsavanh. "Traffic Modelling and Some Inequalities in Banach Spaces." Master's thesis, Edited by Thepsavanh Kitignavong, Faculty of Natural Sciences, National University of Laos, 2017. http://hdl.handle.net/10174/26575.

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Modelling traffic flow has been around since the appearance of traffic jams. Ideally, if we can correctly predict the behavior of vehicle flow given an initial set of data, then adjusting the flow in crucial areas can maximize the overall throughput of traffic along a stretch of road. We consider a mathematical model for traffic flow on single land and without exits or entries. So, we are just observing what happens as time evolves if we fix at initial time (t = 0) some special distribution of cars (initial datum u_0). Because we do approximations, we need the notion of convergence and its corresponding topology. The numerical approximation of scalar conservation laws is carried out by using conservative methods such as the Lax-Friedrichs and the Lax-Wendroff schemes. The Lax-Friedrichs scheme gives regular numerical solutions even when the exact solution is discontinuous (shock waves). We say the scheme is diffusive meaning that the scheme is solving in fact an evolution equation of the form u_t+f(u)_x = epsilon u_xx, where epsilon is a small parameter depending on ∆x and ∆t. The Lax-Wendroff scheme is more precise than the Lax-Friedrichs scheme, and give the right position of the discontinuities for the shock waves. But it develop oscillations. We say the scheme is dispersive what means the scheme is solving approximatively an evolution equation of the form u_t + f(u)_x = delta u_xxx, where delta is a small parameter depending on ∆x and ∆t. An elaboration and an implementation of Lax-Friedrichs schemes and of Lax-Wendroff schemes even extended to second order provided numerical solutions to the problem of traffic flows on the road. Since along the roads the schemes present the same features as for conservation laws, the new and original aspect is given by the treatment of the solution at junctions. Our tests show the effectiveness of the approximations, revealing that Lax-Wendroff schemes is more accurate than Lax-Friedrichs schemes.
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Mohammd, W. A. "A two-step Lax-Wendroff finite difference scheme applied to internal combustion engine gas flow calculations." Thesis, University of Manchester, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.336416.

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DIAZZI, LORENZO. "Simulazioni Numeriche di Opportune Equazioni dell'Elettromagnetismo Applicate al Caso di un'Antenna Biconica." Doctoral thesis, Università degli studi di Modena e Reggio Emilia, 2020. http://hdl.handle.net/11380/1200564.

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Partendo da un'estensione delle classiche equazioni dell'elettromagnetismo sono state implementati opportuni schemi numerici al fine studiare il "near-field" di un'antenna biconica. L'estensione delle equazioni di Maxwell è stata necessaria per modellizzare una nuova situazione: è stata infatti considerata la possibilità di avere regioni spaziali in cui la divergenza del campo elettrico non fosse nulla, in particolare nelle zone in prossimità delle guide, trattate come conduttori non-perfetti. Le simulazioni sono state ambientate in uno spazio tridimensionale descritto in coordinate cilindriche e le equazioni sono state discretizzate usando schemi alle differenze finite. Dapprima sono stati condotti esperimenti numerici relativamente alla propagazione di onde solitoniche nel vuoto, quindi si è passati a considerare casi in cui queste attraversassero mezzi con diversa conduttività. Successivamente sono state individuate condizioni al bordo adatte a simulare l'interazione di un solitone con delle guide conduttrici ed infine, i risultati sono stati applicati al caso, più complesso, del campo elettromagnetico generato da un'antenna biconica. Solo in parte sono stati raggiunti gli obbiettivi preposti, ovvero comprendere a fondo il modo in cui un'onda elettromagnetica si comporta nel passaggio da uno stato in cui la sua evoluzione è guidata, ad uno in cui si propaga come onda libera.<br>By working with an extensions of the classical set of electromagnetic equations, we implemented some numerical techniques to study the near-field of a biconic antenna. Though the usual Maxwell's equations are included in the model, the generalization is necessary to handle the possible creation of regions displaying non-vanishing divergence in proximity of the boundaries, where perfect conductivity is not given for granted. Finite-difference schemes have been primarily used in a three-dimensional domain described by cylindrical coordinates. The numerical experiments include the simulation of solitary waves in vacuum and their behaviour when passing through media of different conductivity. In a successive development these waves are studied in conjunction with boundary constraints, due to the their interaction with the conductive guides. The goal of this analysis, only in part achieved, is a full understanding of the passage of the electromagnetic wave from the state of guided evolution to the one when the signal travels in free space.
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MACCA, Emanuele. "Shock-Capturing methods: Well-Balanced Approximate Taylor and Semi-Implicit schemes." Doctoral thesis, Università degli Studi di Palermo, 2022. https://hdl.handle.net/10447/556029.

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Žáček, Petr. "Počítačové modelování transportu mozkomíšní tekutiny." Master's thesis, 2012. http://www.nusl.cz/ntk/nusl-305159.

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Modelling of cerebrospinal fluid flow is important for understanding its influence on central nervous system, especially spinal cord. One of the reasons for its study is a disease called syringomyelia that probably develops as a result of severance of neural pathways by bubbles emerging during the propagation of pressure (expan- sion) disturbances through spinal cord and its surroundings. It is characterized by fluid-filled cavities in spinal cord. In this thesis, a model of fluid-filled co-axial elastic tubes is proposed that can help us simulate pressure disturbances propa- gation through spinal cord including its interactions and possible increase as the result of interferences or reflection. We derive quasi-one-dimensional governing equations in the form of nonlinear hyperbolic system of conservational laws and with its numerical solution by two-step Lax-Wendroff method with added artifi- cial viscosity we can quantitatively estimate almost twofold increase of pressure difference. 1
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Book chapters on the topic "Lax-Wendroff scheme"

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Corre, C., Y. Huang, and A. Lerat. "A dramatic improvement of an implicit Lax-Wendroff scheme for steady compressible viscous flow calculations." In Fifteenth International Conference on Numerical Methods in Fluid Dynamics. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0107105.

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Fridrich, David, Richard Liska, and Burton Wendroff. "Cell-Centred Lagrangian Lax–Wendroff HLL Hybrid Schemes in Cylindrical Geometry." In Theory, Numerics and Applications of Hyperbolic Problems I. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91545-6_43.

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Baeza, A., P. Mulet, and D. Zorío. "High Order in Space and Time Schemes Through an Approximate Lax-Wendroff Procedure." In Lecture Notes in Computational Science and Engineering. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-65870-4_31.

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Corre, B., K. Khalfallah, and A. Lerat. "An Efficient Relaxation Method for a Centred Navier-Stokes Solver." In Numerical Methods for Fluid Dynamics V. Oxford University PressOxford, 1996. http://dx.doi.org/10.1093/oso/9780198514800.003.0030.

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Abstract An implicit unsteady scheme of Lax-Wendroff type was developed in ([5]-[10]) to solve the Euler and Navier-Stokes equations; its internal dissipation is very low but just sufficient to compute accurate solutions of steady aerodynamic problems without using any artificial viscosity or upwinding. Practical calculations yielded very satisfactory results in terms of accuracy (see [6),(10)). These results were obtained by using an approximate spatial factorization of the implicit stage. Recently, the efficiency of the 2D and 3D Euler solver was greatly improved by applying some line relaxation method ([2), (7)). The aim of this paper is to study a similar method for viscous problems. The structure of the original Navier-Stokes solver does not allow a direct extension of the relaxation method to the viscous case. Therefore a new hybrid scheme has been developed : it offers features well suited for an efficient relaxation - basically diagonal dominance - and meanwhile preserves the solution accuracy thanks to a low numerical dissipation in the viscous zone.
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Abgrall, Rémi, Katherine Mer, and B. Nkonga. "A Lax–Wendroff type theorem for residual schemes." In Innovative Methods for Numerical Solution of Partial Differential Equations. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810816_0012.

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LERAT, Alain, Christophe CORRE, and Ying HUANG. "Somewhere between the Lax-Wendroff and Roe schemes for calculating multidimensional compressible flows." In Innovative Methods for Numerical Solution of Partial Differential Equations. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810816_0010.

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Conference papers on the topic "Lax-Wendroff scheme"

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Szema, K., S. Ramakrishnan, V. Shankar, and K. Rajagopal. "Application of a generalized Lax-Wendroff scheme for unstructured Euler computations." In 14th Applied Aerodynamics Conference. American Institute of Aeronautics and Astronautics, 1996. http://dx.doi.org/10.2514/6.1996-2401.

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Sakami, M., K. Mitra, and P. F. Hsu. "Transient Radiative Transfer in Anisotropically Scattering Media Using Monotonicity-Preserving Schemes." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-1376.

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Abstract This research work deals with the analysis of transient radiative transfer in one-dimensional scattering medium. The time-dependant discrete ordinates method was used with an upwind monotonic scheme: the piecewise parabolic scheme. This scheme was chosen over a total variation diminishing version of the Lax-Wendroff scheme. These schemes were originally developed to solve Eulerian advection problem in hydrodynamics. The capability of these schemes to handle sharp discontinuity in a propagating electromagnetic wave front was compared. The accuracy and the efficiency of the discrete ordinates method associated with the piecewise parabolic advection scheme were studied. Comparisons with Monte Carlo and integral formulation methods show the accuracy and the efficiency of this proposed method. Parametric study for optically thin and thick medium, different albedos and phase functions is then made in the unsteady state zone.
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Clark, William S., and Kenneth C. Hall. "A Numerical Model of the Onset of Stall Flutter in Cascades." In ASME 1995 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/95-gt-377.

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In this paper, we present a computational fluid dynamic model of the unsteady flow associated with the onset of stall flutter in turbomachinery cascades. The unsteady flow is modeled using the laminar Navier-Stokes equations. We assume that the unsteadiness in the flow is a small harmonic disturbance about the mean or steady flow. Therefore, the unsteady flow is governed by a small-disturbance form of the Navier-Stokes equations. These linear variable coefficient equations are discretized on a deforming computational grid and solved efficiently using a multiple-grid Lax-Wendroff scheme. A number of numerical examples are presented which demonstrate the destabilizing influence of viscosity on the aeroelastic stability of airfoils in cascade, especially for torsional modes of blade vibration.
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Liu, Jianjun. "Numerical Simulation of Asymmetric Exhaust Flows Using an Actuator Disc Blade Row Model." In ASME 2002 Pressure Vessels and Piping Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/pvp2002-1591.

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This paper describes the numerical simulation of the asymmetric exhaust flows by using a 3D viscous flow solver incorporating an actuator disc blade row model. The three dimensional Reynolds-Averaged Navier-Stokes equations are solved by using the TVD Lax-Wendroff scheme. The convergence to a steady state is speeded up by using the V-cycle multigrid algorithm. Turbulence eddy viscosity is estimated by the Baldwin-Lomax model. Multiblock method is applied to cope with the complicated physical domains. Actuator disc model is used to represent a turbine blade row and to achieve the required flow turning and entropy rise across the blade row. The solution procedure and the actuator disc boundary conditions are described. The stream traces in various sections of the exhaust hood are presented to demonstrate the complicity of the flow patterns existing in the exhaust hood.
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Liu, Jianjun, Yongqiang Cui, and Hongde Jiang. "Investigation of Flow in a Steam Turbine Exhaust Hood With/Without Turbine Exit Conditions Simulated." In ASME Turbo Expo 2001: Power for Land, Sea, and Air. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/2001-gt-0488.

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Experimental and numerical investigations for the flow in an exhaust hood model of large steam turbines have been carried out in order to understand the complex 3D flow pattern existing in the hood and also to validate the CFD solver. The model is a typical design for 300/600 MW steam turbines currently in operation. Static pressure at the diffuser tip and hub endwalls and at hood outer casing is measured and nonuniform circumferential distributions of static pressure are noticed. Velocity field at the model exit is measured and compared with the numerical prediction. The multigrid multiblock 3D Navier-Stokes solver used for the simulations is based upon the TVD Lax-Wendroff scheme and the Baldwin-Lomax turbulence model. Good agreement between numerical results and experimental data is demonstrated. It is found that the flow pattern and hood performance are very different with or without the turbine exit flow conditions simulated.
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Hall, Kenneth C., William S. Clark, and Christopher B. Lorence. "A Linearized Euler Analysis of Unsteady Transonic Flows in Turbomachinery." In ASME 1993 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/93-gt-094.

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A computational method for efficiently predicting unsteady transonic flows in two- and three-dimensional cascades is presented. The unsteady flow is modelled using a linearized Euler analysis whereby the unsteady flow field is decomposed into a nonlinear mean flow plus a linear harmonically varying unsteady flow. The equations that govern the perturbation flow, the linearized Euler equations, are linear variable coefficient equations. For transonic flows containing shocks, shock capturing is used to model the shock impulse (the unsteady load due to the harmonic motion of the shock). A conservative Lax-Wendroff scheme is used to obtain a set of linearized finite volume equations that describe the harmonic small disturbance behavior of the flow. Conditions under which such a discretization will correctly predict the shock impulse are investigated. Computational results are presented that demonstrate the accuracy and efficiency of the present method as well as the essential role of unsteady shock impulse loads on the flutter stability of fans.
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Zhu, Yi, and J. J. Chattot. "Computation of the scattering of TM plane waves from a perfectly conducting square-comparison of Yee's algorithm Lax-Wendroff method and Ni's scheme." In IEEE Antennas and Propagation Society International Symposium 1992 Digest. IEEE, 1992. http://dx.doi.org/10.1109/aps.1992.221930.

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8

Hall, Kenneth C., and Christopher B. Lorence. "Calculation of Three-Dimensional Unsteady Flows in Turbomachinery Using the Linearized Harmonic Euler Equations." In ASME 1992 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/92-gt-136.

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Abstract:
An efficient three-dimensional Euler analysis of unsteady flows in turbomachinery is presented. The unsteady flow is modelled as the sum of a steady or mean flow field plus a harmonically varying small perturbation flow. The linearized Euler equations, which describe the small perturbation unsteady flow, are found to be linear, variable coefficient differential equations whose coefficients depend on the mean flow. A pseudo-time time-marching finite-volume Lax-Wendroff scheme is used to discretize and solve the linearized equations for the unknown perturbation flow quantities. Local time stepping and multiple-grid acceleration techniques are used to speed convergence. For unsteady flow problems involving blade motion, a harmonically deforming computational grid which conforms to the motion of the vibrating blades is used to eliminate large error-producing extrapolation terms that would otherwise appear in the airfoil surface boundary conditions and in the evaluation of the unsteady surface pressure. Results are presented for both linear and annular cascade geometries, and for the latter, both rotating and nonrotating blade rows.
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9

Heider, R., J. M. Duboue, B. Petot, G. Billonnet, V. Couaillier, and N. Liamis. "Three-Dimensional Analysis of Turbine Rotor Flow Including Tip Clearance." In ASME 1993 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/93-gt-111.

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A 3D Navier-Stokes investigation of a high pressure turbine rotor blade including tip clearance effects is presented. The 3D Navier-Stokes code developed at ONERA solves the three-dimensional unsteady set of mass-averaged Navier-Stokes equations by the finite volume technique. A one step Lax-Wendroff type scheme is used in a rotating frame of reference. An implicit residual smoothing technique has been implemented, which accelerates the convergence towards the steady state. A mixing length model adapted to 3D configurations is used. The turbine rotor flow is calculated at transonic operating conditions. The tip clearance effect is taken into account. The gap region is discretized using more than 55,000 points within a multi-domain approach. The solution accounts for the relative motion of the blade and casing surfaces. The total mesh is composed of five sub-domains and counts 710,000 discretization points. The effect of the tip clearance on the main flow is demonstrated. The calculation results are compared to a 3D inviscid calculation, without tip clearance.
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10

Clark, William S., and Kenneth C. Hall. "A Time-Linearized Navier-Stokes Analysis of Stall Flutter." 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-383.

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A computational method for accurately and efficiently predicting unsteady viscous flow through two-dimensional cascades is presented. The method is intended to predict the onset of the aeroelastic phenomenon of stall flutter. In stall flutter, viscous effects significantly impact the aeroelastic stability of a cascade. In the present effort, the unsteady flow is modeled using a time-linearized Navier-Stokes analysis. Thus, the unsteady flow field is decomposed into a nonlinear spatially varying mean flow plus a small-perturbation harmonically varying unsteady flow. The resulting equations that govern the perturbation flow are linear, variable coefficient partial differential equations. These equations are discretized on a deforming, multi-block, computational mesh and solved using a finite-volume Lax-Wendroff integration scheme. Numerical modelling issues relevant to the development of the unsteady aerodynamic analysis, including turbulence modelling, are discussed. Results from the present method are compared to experimental stall flutter data, and to a nonlinear time-domain Navier-Stoke analysis. The results presented demonstrate the ability of the present time-linearized analysis to model accurately the unsteady aerodynamics associated with turbomachinery stall flutter.
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Reports on the topic "Lax-Wendroff scheme"

1

Jiang, Yan, Chi-Wang Shu, and Mengping Zhang. An alternative formulation of finite difference WENO schemes with Lax-Wendroff time discretization for conservation laws. Defense Technical Information Center, 2012. http://dx.doi.org/10.21236/ada568106.

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