Relevant bibliographies by topics / Type-depedent finite difference scheme

Academic literature on the topic 'Type-depedent finite difference scheme'

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Published: 4 June 2021
Last updated: 19 February 2022

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Journal articles on the topic "Type-depedent finite difference scheme"

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Cheng, Xiaohan, Jianhu Feng, Supei Zheng, and Xueli Song. "A new type of finite difference WENO schemes for Hamilton–Jacobi equations." International Journal of Modern Physics C 30, no. 02n03 (February 2019): 1950020. http://dx.doi.org/10.1142/s0129183119500207.

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In this paper, we propose a new type of finite difference weighted essentially nonoscillatory (WENO) schemes to approximate the viscosity solutions of the Hamilton–Jacobi equations. The new scheme has three properties: (1) the scheme is fifth-order accurate in smooth regions while keep sharp discontinuous transitions with no spurious oscillations near discontinuities; (2) the linear weights can be any positive numbers with the symmetry requirement and that their sum equals one; (3) the scheme can avoid the clipping of extrema. Extensive numerical examples are provided to demonstrate the accuracy and the robustness of the proposed scheme.
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Vulanović, Relja. "An Almost Sixth-Order Finite-Difference Method for Semilinear Singular Perturbation Problems." Computational Methods in Applied Mathematics 4, no. 3 (2004): 368–83. http://dx.doi.org/10.2478/cmam-2004-0020.

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AbstractThe discretization meshes of the Shishkin type are more suitable for high- order finite-difference schemes than Bakhvalov-type meshes. This point is illustrated by the construction of a hybrid scheme for a class of semilinear singularly perturbed reaction-diffusion problems. A sixth-order five-point equidistant scheme is used at most of the mesh points inside the boundary layers, whereas lower-order three-point schemes are used elsewhere. It is proved under certain conditions that this combined scheme is almost sixth-order accurate and that its error does not increase when the perturbation parameter tends to zero.
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Hureuski, A. N. "Using IIR filters to build high-order finite difference schemes for the unsteady Schrödinger equation." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 55, no. 4 (January 7, 2020): 413–24. http://dx.doi.org/10.29235/1561-2430-2019-55-4-413-424.

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High-order finite difference schemes for the time-dependent Schrödinger equation are investigated. Digital signal processing methods allowed proving the conservativeness of high-order finite difference schemes for the unsteady Schrödinger equation. The eighth-order scheme coefficients were found with the help of the proved theoretical results. The conditions for equivalence between the eighth-order finite difference scheme and the scheme in the form of a cascade of allpass first-order filters were found. The numerical analysis of the proposed scheme was made. It was shown that the high-order finite difference schemes gave better results on solving the linear Schrödinger equations comparing to the well-known fourthorder scheme on the six-point stencil, however, the high-order schemes in couple with the second-order splitting algorithm to the nonlinear Schrödinger equation do not lead to a radical improvement in the quality of numerical results. Practical issues implementing the proposed numerical technique are considered. The obtained results can be used to construct efficient solvers for linear and nonlinear Schrödinger-type equations by applying the splitting schemes of adequate accuracy order.
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Kettunen, Lauri, Jonni Lohi, Jukka Räbinä, Sanna Mönkölä, and Tuomo Rossi. "Generalized finite difference schemes with higher order Whitney forms." ESAIM: Mathematical Modelling and Numerical Analysis 55, no. 4 (July 2021): 1439–60. http://dx.doi.org/10.1051/m2an/2021026.

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Finite difference kind of schemes are popular in approximating wave propagation problems in finite dimensional spaces. While Yee’s original paper on the finite difference method is already from the sixties, mathematically there still remains questions which are not yet satisfactorily covered. In this paper, we address two issues of this kind. Firstly, in the literature Yee’s scheme is constructed separately for each particular type of wave problem. Here, we explicitly generalize the Yee scheme to a class of wave problems that covers at large physics field theories. For this we introduce Yee’s scheme for all problems of a class characterised on a Minkowski manifold by (i) a pair of first order partial differential equations and by (ii) a constitutive relation that couple the differential equations with a Hodge relation. In addition, we introduce a strategy to systematically exploit higher order Whitney elements in Yee-like approaches. This makes higher order interpolation possible both in time and space. For this, we show that Yee-like schemes preserve the local character of the Hodge relation, which is to say, the constitutive laws become imposed on a finite set of points instead of on all ordinary points of space. As a result, the usage of higher order Whitney forms does not compel to change the actual solution process at all. This is demonstrated with a simple example.
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Kim, Sung-Hoon, and Youn-sik Park. "An Improved Finite Difference Type Numerical Method for Structural Dynamic Analysis." Shock and Vibration 1, no. 6 (1994): 569–83. http://dx.doi.org/10.1155/1994/139352.

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An improved finite difference type numerical method to solve partial differential equations for one-dimensional (1-D) structure is proposed. This numerical scheme is a kind of a single-step, second-order accurate and implicit method. The stability, consistency, and convergence are examined analytically with a second-order hyperbolic partial differential equation. Since the proposed numerical scheme automatically satisfies the natural boundary conditions and at the same time, all the partial differential terms at boundary points are directly interpretable to their physical meanings, the proposed numerical scheme has merits in computing 1-D structural dynamic motion over the existing finite difference numeric methods. Using a numerical example, the suggested method was proven to be more accurate and effective than the well-known central difference method. The only limitation of this method is that it is applicable to only 1-D structure.
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Mohsen, A., H. El-Zoheiry, and L. Iskandar. "A highly accurate finite-difference scheme for a boussinesq-type equation." Applied Mathematics and Computation 55, no. 2-3 (May 1993): 201–12. http://dx.doi.org/10.1016/0096-3003(93)90021-6.

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Lee, Chun-Te, Jeng-Eng Lin, Chun-Che Lee, and Mei-Li Liu. "Some Remarks on the Stability Condition of Numerical Scheme of the KdV-type Equation." Journal of Mathematics Research 9, no. 4 (June 29, 2017): 11. http://dx.doi.org/10.5539/jmr.v9n4p11.

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This paper has employed a comparative study between the numerical scheme and stability condition. Numerical calculations are carried out based on three different numerical schemes, namely the central finite difference, fourier leap-frog, and fourier spectral RK4 schemes. Stability criteria for different numerical schemes are developed for the KdV equation, and numerical examples are put to test to illustrate the accuracy and stability between the solution profile and numerical scheme.
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Molavi-Arabshahi, Mahboubeh, and Zahra Saeidi. "Application of Compact Finite Difference Method for Solving Some Type of Fractional Derivative Equations." International Journal of Circuits, Systems and Signal Processing 15 (September 6, 2021): 1324–35. http://dx.doi.org/10.46300/9106.2021.15.143.

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In this paper, the compact finite difference scheme as unconditionally stable method is applied to some type of fractional derivative equation. We intend to solve with this scheme two kinds of a fractional derivative, first a fractional order system of Granwald-Letnikov type 1 for influenza and second fractional reaction sub diffusion equation. Also, we analyzed the stability of equilibrium points of this system. The convergence of the compact finite difference scheme in norm 2 are proved. Finally, various cases are used to test the numerical method. In comparison to other existing numerical methods, our results show that the scheme yields an accurate solution that is quick to compute.
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Koroglu, Canan, and Ayhan Aydin. "An Unconventional Finite Difference Scheme for Modified Korteweg-de Vries Equation." Advances in Mathematical Physics 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/4796070.

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A numerical solution of the modified Korteweg-de Vries (MKdV) equation is presented by using a nonstandard finite difference (NSFD) scheme with theta method which includes the implicit Euler and a Crank-Nicolson type discretization. Local truncation error of the NSFD scheme and linear stability analysis are discussed. To test the accuracy and efficiency of the method, some numerical examples are given. The numerical results of NSFD scheme are compared with the exact solution and a standard finite difference scheme. The numerical results illustrate that the NSFD scheme is a robust numerical tool for the numerical integration of the MKdV equation.
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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 (October 18, 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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Dissertations / Theses on the topic "Type-depedent finite difference scheme"

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Ly, Eddie, and Eddie Ly@rmit edu au. "Numerical schemes for unsteady transonic flow calculation." RMIT University. Mathematics and Geospacial Sciences, 1999. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20081212.163408.

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An obvious reason for studying unsteady flows is the prediction of the effect of unsteady aerodynamic forces on a flight vehicle, since these effects tend to increase the likelihood of aeroelastic instabilities. This is a major concern in aerodynamic design of aircraft that operate in transonic regime, where the flows are characterised by the presence of adjacent regions of subsonic and supersonic flow, usually accompanied by weak shocks. It has been a common expectation that the numerical approach as an alternative to wind tunnel experiments would become more economical as computers became less expensive and more powerful. However even with all the expected future advances in computer technology, the cost of a numerical flutter analysis (computational aeroelasticity) for a transonic flight remains prohibitively high. Hence it is vitally important to develop an efficient, cheaper (in the sense of computational cost) and physically accurate flutter simulation tech nique which is capable of reproducing the data, which would otherwise be obtained from wind tunnel tests, at least to some acceptable engineering accuracy, and that it is essentially appropriate for industrial applications. This need motivated the present research work on exploring and developing efficient and physically accurate computational techniques for steady, unsteady and time-linearised calculations of transonic flows over an aircraft wing with moving shocks. This dissertation is subdivided into eight chapters, seven appendices and a bibliography listing all the reference materials used in the research work. The research work initially starts with a literature survey in unsteady transonic flow theory and calculations, in which emphasis is placed upon the developments in these areas in the last three decades. Chapter 3 presents the small disturbance theory for potential flows in the subsonic, transonic and supersonic regimes, including the required boundary conditions and shock jump conditions. The flow is assumed irrotational and inviscid, so that the equation of state, continuity equation and Bernoulli's equation formulated in Appendices A and B can be employed to formulate the governing fluid equation in terms of total velocity potential. Furthermore for transonic flow with free-stream Mach number close to unity, we show in Appendix C that the shocks that appear are weak enough to allow us to neglect the flow rotationality. The formulations are based on the main assumption that aerofoil slopes are everywhere small, and the flow quantities are small perturbations about their free-stream values. In Chapter 4, we developed an improved approximate factorisation algorithm that solves the two-dimensional steady subsonic small disturbance equation with nonreflecting far-field boundary conditions. The finite difference formulation for the improved algorithm is presented in Appendix D, with the description of the solver used for solving the system of difference equations described in Appendix E. The calculation of steady and unsteady nonlinear transonic flows over a realistic aerofoil are considered in Chapter 5. Numerical solution methods, based on the finite difference approach, for solving the two-dimensional steady and unsteady, general-frequency transonic small disturbance equations are presented, with the corresponding finite difference formulation described in Appendix F. The theories and solution methods for the time-linearised calculations, in the frequency and time domains, for the problem of unsteady transonic flow over a thin planar wing undergoing harmonic oscillation are presented in Chapters 6 and 7, respectively. The time-linearised calculations include the periodic shock motion via the shock jump correction procedure. This procedure corrects the solution values behind the shock, to accommodate the effect of shock motion, and consequently, the solution method will produce a more accurate time-linearised solution for supercritical flow. Appendix G presents the finite difference formulation of these time-linearised solution methods. The aim is to develop an efficient computational method for calculating oscillatory transonic aerodynamic quantities efficiently for use in flutter analyses of both two- and three-dimensional wings with lifting surfaces. Chapter 8 closes the dissertation with concluding remarks and future prospects on the current research work.
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Terefe, Yibeltal Adane. "Bifurcation analysis and nonstandard finite difference schemes for Kermack and McKendrick type epidemiological models." Diss., University of Pretoria, 2012. http://hdl.handle.net/2263/24917.

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The classical SIR and SIS epidemiological models are extended by considering the number of adequate contacts per infective in unit time as a function of the total population in such a way that this number grows less rapidly as the total population increases. A diffusion term is added to the SIS model and this leads to a reaction–diffusion equation, which governs the spatial spread of the disease. With the parameter R0 representing the basic reproduction number, it is shown that R0 = 1 is a forward bifurcation for the SIR and SIS models, with the disease–free equilibrium being globally asymptotic stable when R0 is less than 1. In the case when R0 is greater than 1, for both models, the endemic equilibrium is locally asymptotically stable and traveling wave solutions are found for the SIS diffusion model. Nonstandard finite difference (NSFD) schemes that replicate the dynamics of the continuous SIR and SIS models are presented. In particular, for the SIS model, a nonstandard version of the Runge-Kutta method having high order of convergence is investigated. Numerical experiments that support the theory are provided. On the other hand the SIS model is extended to a Volterra integral equation, for which the existence of multiple endemic equilibria is proved. This fact is confirmed by numerical simulations.
Dissertation (MSc)--University of Pretoria, 2012.
Mathematics and Applied Mathematics
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Hall, Eric Joseph. "Accelerated numerical schemes for deterministic and stochastic partial differential equations of parabolic type." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/8038.

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First we consider implicit finite difference schemes on uniform grids in time and space for second order linear stochastic partial differential equations of parabolic type. Under sufficient regularity conditions, we prove the existence of an appropriate asymptotic expansion in powers of the the spatial mesh and hence we apply Richardson's method to accelerate the convergence with respect to the spatial approximation to an arbitrarily high order. Then we extend these results to equations where the parabolicity condition is allowed to degenerate. Finally, we consider implicit finite difference approximations for deterministic linear second order partial differential equations of parabolic type and give sufficient conditions under which the approximations in space and time can be simultaneously accelerated to an arbitrarily high order.
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Book chapters on the topic "Type-depedent finite difference scheme"

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Zhu, Q. Y. "An Improved Finite Difference Scheme for Solving the Equation of Filtration Type in Porous Textiles with Phase Change Materials." In Computational Mechanics, 389. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-75999-7_189.

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Penenko, Alexey, Vladimir Penenko, Elena Tsvetova, and Zhadyra Mukatova. "Consistent Discrete-Analytical Schemes for the Solution of the Inverse Source Problems for Atmospheric Chemistry Models with Image-Type Measurement Data." In Finite Difference Methods. Theory and Applications, 378–86. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11539-5_43.

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Rucker, Rudy. "Continuous-Valued Cellular Automata in Two Dimensions." In New Constructions in Cellular Automata. Oxford University Press, 2003. http://dx.doi.org/10.1093/oso/9780195137170.003.0016.

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We explore a variety of two-dimensional continuous-valued cellular automata (CAs). We discuss how to derive CA schemes from differential equations and look at CAs based on several kinds of nonlinear wave equations. In addition we cast some of Hans Meinhardt’s activator-inhibitor reaction-diffusion rules into two dimensions. Some illustrative runs of CAPOW, a. CA simulator, are presented. A cellular automaton, or CA, is a computation made up of finite elements called cells. Each cell contains the same type of state. The cells are updated in parallel, using a rule which is homogeneous, and local. In slightly different words, a CA is a computation based upon a grid of cells, with each cell containing an object called a state. The states are updated in discrete steps, with all the cells being effectively updated at the same time. Each cell uses the same algorithm for its update rule. The update algorithm computes a cell’s new state by using information about the states of the cell’s nearby space-time neighbors, that is, using the state of the cell itself, using the states of the cell’s nearby neighbors, and using the recent prior states of the cell and its neighbors. The states do not necessarily need to be single numbers, they can also be data structures built up from numbers. A CA is said to be discrete valued if its states are built from integers, and a CA is continuous valued if its states are built from real numbers. As Norman Margolus and Tommaso Toffoli have pointed out, CAs are well suited for modeling nature [7]. The parallelism of the CA update process mirrors the uniform flow of time. The homogeneity of the CA update rule across all the cells corresponds to the universality of natural law. And the locality of CAs reflect the fact that nature seems to forbid action at a distance. The use of finite space-time elements for CAs are a necessary evil so that we can compute at all. But one might argue that the use of discrete states is an unnecessary evil.
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Meish, Vladimyr, and Yuliia Meish. "THE WAVE PROCESSES IN THREE-LAYER SHELLS OF ROTATIONWITH TAKING INTO ACCOUNT THE DISCRETE FILLER AT NON-STATIONARY LOADS." In Integration of traditional and innovation processes of development of modern science. Publishing House “Baltija Publishing”, 2020. http://dx.doi.org/10.30525/978-9934-26-021-6-36.

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Thin-walled shell structures in the form of plates and shells of various shapes have a high bearing capacity, lightness, and relative ease of manufacture. Three-layer shell elements, which consist of two bearing layers and a filler, which ensures their joint work, are widely used in mechanical engineering, industrial and civil construction, aviation and space technology, shipbuilding. When calculating the strength of three-layer shell structures with a discrete filler under dynamic loads, it becomes necessary to determine the stress-strain state both in the area of a sharp change in the geometry of the structure and at a considerable distance from the heterogeneity. The complexity of the processes that arise in this case necessitates the use of modern numerical methods for solving dynamic problems of the behavior of three-layer shell elements with a discrete filler. In this regard, the determination of the stress-strain state of three-layer shells with a discrete filler under non-stationary loads and the development of an effective numerical method for solving problems of this class is an urgent problem in the mechanics of a deformable solid. On the basis of the theory of threelayered shells with applying the hypotheses for each layer the nonstationary vibrations threelayered shells of revolution with allowance of discrete fillers are investigated. Hamilton-Ostrogradskyy variational principle for dynamical processes is used for deduction of the motion equations. An efficient numerical method for solution of problems on nonstationary behaviour of threelayers shells of revolution with allowance of discrete fillers are used. The wide diapason of geometrical, and physico-mechanical parameters of nonhomohenes threelayered structure are considerated. On the basis of the offered model nonstationary problems of the forced nonlinear vibrations of threelayered shells of revolution of various structure are solved and analysed. The basis of the developed numerical method for the study of nonstationary oscillations is the application of explicit finite-difference schemes to solve the initial differential equations in partial derivatives. The theory is based on the relations of the theory of three-layer shells of revolution taking into account the discreteness of the filler, which are based on the hypotheses of the geometrically nonlinear theory of shells and rods of the Timoshenko type.
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Conference papers on the topic "Type-depedent finite difference scheme"

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Direk, Zilal, and Maksat Ashyraliyev. "A second order of accuracy finite difference scheme for the integral-differential equation of the hyperbolic type." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2014). AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4893866.

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Raif, Markus, Jürgen F. Mayer, and Heinz Stetter. "Comparison of a TVD-Upwind Scheme and a Central Difference Scheme for Navier-Stokes Turbine Stage Flow Calculation." In ASME 1996 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-gt-031.

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The differences of two distinct numerical schemes implemented in one code called ITSM3D are presented for a turbine stage test case. Thus both schemes are used with exactly the same computational infrastructure, e. g, same grids, boundary conditions, acceleration strategies, time-stepping, turbulence model etc. The two methods are based on an explicit Runge-Kutta-type finite volume scheme expressed in cylindrical coordinates and have been developed at the Institut für Thermische Strömungsmaschinen und Maschinenlaboratorium of the University of Stuttgart. One scheme is a node centered 3rd order TVD scheme according to Osher and the other belongs to the cell vertex central difference type with the concept of artificial viscosity. The model of Baldwin-Lomax is used in order to simulate turbulent effects. Non-reflective boundary conditions are taken at stator inlet and rotor outlet to avoid non-physical reflections. A multigrid technique in combination with implicit residual smoothing and local time-stepping is employed to accelerate the computation. The test case for this comparison is the last stage of a low-pressure turbine. The computational results obtained are discussed and compared to each other as well as to experimental data. They are presented as pressure and Mach number isoline contours and diagrams of circumferential averaged quantities at inlet and outlet planes of stator and rotor versus radial position.
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Shokrieh, M. M., and A. Karamnejad. "Transient Response of Strain Rate Dependent Composite Plates Using Finite Difference Method." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-40063.

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In the present work, the response of laminated composite plate under dynamic loading is investigated using a macro-mechanical approach by use of a finite difference model which accounts for geometric nonlinearity and strain rate effects. Coupled nonlinear equations of motion of a laminated plate based on classical laminated plate theory (CLPT) and first-order shear deformation laminated plate theory (FSDT) are derived and reduced to nonlinear ordinary differential equations in time domain by finite difference approximations for displacements. Newmark time integration scheme in association with Newton-Raphson iteration method is applied to solve the system of nonlinear equations. Sudden material property degradation rules are modified to account for strain rate effects. A progressive damage model is developed based on the modified material property degradation rules and Hashin-type failure criteria and added to a finite difference model. The model is implemented into a computer code in Mathematica 6. The model is validated by comparison of the present results with those are available in the literature. The effects of transverse shear strain are studied by comparison of the results obtained using CLPT and FSDT. In order to investigate the strain rate effects, a clamped Glass/Epoxy composite plate subjected to a triangular load is considered. Results for static model, in which the mechanical properties are constant and dynamic model which has strain rate dependent mechanical properties are compared for various stacking sequences and load magnitudes. The results show that the deflections are overestimated by static model and the difference between static and dynamic models results increases with the magnitude of load. Furthermore, the variation trend of maximum displacement with stacking sequence is the same for both material models.
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To, C. W. S., and M. L. Liu. "Large Geometrically Nonlinear Responses of Discretized Plate Structures Under Nonstationary Random Excitations." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/cie-9061.

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Abstract In the investigation reported here novel techniques for the computation of highly nonlinear response statistics, such as mean square and covariance of generalized displacements of large scale discretized plate and shell structures have been developed. The techniques combine the versatile finite element method and the stochastic central difference method as well as derivatives of the latter such that complex aerospace and naval structures under intensive transient disturbances represented as nonstationary random processes can be considered. The flat triangular plate finite element is of the Mindlin type and is based on the hybrid strain formulation. The updated Lagrangiah hybrid strain based formulation is capable of dealing with deformations of finite rotations and finite strains. Explicit expressions for the consistent element mass and stiff matrices were previously obtained, and therefore no numerical matrix inversion and integration is necessary in the element matrix derivation. Several additional features are novel. First, the so-called averaged deterministic central difference scheme is employed in the co-ordinate updating process for large deformations. Second, application of the time co-ordinate transformation in conjunction with the stochastic central difference method enables one to deal with highly stiff discretized structures. Third, application of the adaptive time schemes makes it convenient to solve a wide variety of highly nonlinear systems. Finally, the recursive nature of the stochastic central difference method makes it possible to deal with a wide class of nonstationary random process.
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Hao-Xin, Jiang, Chen Mao-Zhang, and Tsui Chih-Ya. "Some Problems in Calculating Flow Around Two-Dimensional Cascade Profiles." In ASME 1985 Beijing International Gas Turbine Symposium and Exposition. American Society of Mechanical Engineers, 1985. http://dx.doi.org/10.1115/85-igt-123.

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A new method which can be used to construct a H-type grid for cascade flow calculation is presented in this paper. To test the feasibility of the grid, the subsonic and transonic full potential equations are solved by using finite difference approximations on a transformed coordinate system. It is found that in order to improve computing accuracy and reduce cost, four conditions should be fulfilled in constructing cascade grids. Also, the artificial viscosity scheme should be improved for cascade calculations.
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Troyani, Nando, Orlando M. Ayala, and Luis Montano. "Approximate Optimal Initial Temperature Distribution From a Three Dimensional Model for Processes Requiring Coiling." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-43917.

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A numerical strategy to determine an estimate to the optimal initial distribution of temperature for industrial processes requiring coiling of bars in hot metal rolling operations based on a three-dimensional mathematical model for the evolution of temperature in a shape changing domain is presented. The corresponding numerical solution is presented as well. The solution integrates a two dimensional geometrically adaptive finite element solution in the coiling plane for a shape changing domain with a finite difference one-dimensional solution in the widthwise direction of the bar using a novel numerical separation of variables strategy. Time is discretized according to a Crank-Nicolson type scheme. The results of a specific numerical study for the coiling of hot steel between the roughing stands and the finishing stands are presented.
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Costura, David M., Patrick B. Lawless, and Steven H. Frankel. "A Computational Model for the Study of Gas Turbine Combustor Dynamics." In ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/98-gt-342.

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A dynamic combustor model is developed for inclusion into a one-dimensional full gas turbine engine simulation code. A flux-difference splitting algorithm is used to numerically integrate the quasi-one-dimensional Euler equations, supplemented with species mass conservation equations. The combustion model involves a single-step, global finite-rate chemistry scheme with a temperature-dependent activation energy. Source terms are used to account for mass bleed and mass injection, with additional capabilities to handle momentum and energy sources and sinks. Numerical results for cold and reacting flow for a can-type gas turbine combustor are presented. Comparisons with experimental data from this combustor are also made.
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Chaudhri, Usman, and Kendrick Aung. "Effects of Multi-Grade Oils in Modeling Non-Newtonian Rheology Between Piston and Cylinder Surfaces in Engine Initial Start Up Conditions." In ASME 2014 Internal Combustion Engine Division Fall Technical Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/icef2014-5408.

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This paper presents the results of a transient analysis of hydrodynamic lubrication between piston and cylinder surfaces in engine Initial startup conditions with a Non Newtonian lubricant under oscillatory motion. Effects of different multi-grade oil viscosities are also investigated in the simulation. The time dependent Reynolds equations use a Maxwell type model to analyze fluid rheology. A perturbation scheme is used to derive coupled non linear partial differential equations to obtain the fluid velocity. The oil film profile is predicted by solving the two-dimensional Reynolds equations using the finite difference computational method. The piston velocities in engine secondary motion are adjusted by using fourth order Runge-Kutta technique. Using different oil viscosities, the effect of viscoelasticity on lubricant velocity and pressure fields is examined and the influence of film thickness on lubricant characteristics is investigated. Numerical simulations show that piston eccentricities and film thickness profiles vary under different multi grade oils at engine start up conditions.
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Höhn, Wolfgang. "Numerical Investigation of Blade Flutter at or Near Stall in Axial Flow Turbomachines." 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-0265.

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During the design of the compressor and turbine stages of today’s aeroengines, aerodynamically induced vibrations become increasingly important since higher blade load and better efficiency are desired. In this paper the development of a method based on the unsteady, compressible Navier-Stokes equations in two dimensions is described in order to study the physics of flutter for unsteady viscous flow around cascaded vibrating blades at stall. The governing equations are solved by a finite difference technique in boundary fitted coordinates. The numerical scheme uses the Advection Upstream Splitting Method to discretize the convective terms and central differences discretizing the viscous terms of the fully non-linear Navier-Stokes equations on a moving H-type mesh. The unsteady governing equations are explicitly and implicitly marched in time in a time-accurate way using a four stage Runge-Kutta scheme on a parallel computer or an implicit scheme of the Beam-Warming type on a single processor. Turbulence is modelled using the Baldwin-Lomax turbulence model. The blade flutter phenomenon is simulated by imposing a harmonic motion on the blade, which consists of harmonic body translation in two directions and a rotation, allowing an interblade phase angle between neighboring blades. Non-reflecting boundary conditions are used for the unsteady analysis at inlet and outlet of the computational domain. The computations are performed on multiple blade passages in order to account for nonlinear effects. A subsonic massively stalled unsteady flow case in a compressor cascade is studied. The results, compared with experiments and the predictions of other researchers, show reasonable agreement for inviscid and viscous flow cases for the investigated flow situations with respect to the Steady and unsteady pressure distribution on the blade in separated flow areas as well as the aeroelastic damping. The results show the applicability of the scheme for stalled flow around cascaded blades. As expected the viscous and inviscid computations show different results in regions where viscous effects are important, i.e. in separated flow areas. In particular, different predictions for inviscid and viscous flow for the aerodynamic damping for the investigated flow cases are found.
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Kiani, Yasser, and Mohammad Reza Eslami. "Large Amplitude Thremally Induced Vibration of Circular FGM Plate." In ASME 2014 12th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/esda2014-20406.

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Vibration of a solid circular plate subjected to rapid surface heating is analyzed in this research. Properties of the plate are all temperature and position dependent. Plate is modeled using the first order shear deformation theory. To account for the large deformations, the von Kármán type of geometrical non-linearity is taken into account. Plate is subjected to surface heating at both top and bottom surfaces. Time dependent one-dimensional heat conduction equation is solved via an iterative finite difference scheme and thermal force and thermal moment resultants are evaluated at each time step. Non-linear motion equations of the plate are established with the aid of Hamilton’s principle and the generalized Ritz method. Solution of such equations is obtained employing a hybrid Newton-Raphson-Newmark method. It is shown that thermally induced vibrations exist for the sufficiently thin FGM plate.
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