Relevant bibliographies by topics / Second-order backward time scheme

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
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Academic literature on the topic 'Second-order backward time scheme'

Author: Grafiati
Published: 19 January 2023

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Journal articles on the topic "Second-order backward time scheme"

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Vabishchevich, Petr N. "Factorized Schemes of Second-Order Accuracy for Numerically Solving Unsteady Problems." Computational Methods in Applied Mathematics 17, no. 2 (April 1, 2017): 323–35. http://dx.doi.org/10.1515/cmam-2016-0038.

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AbstractSchemes with the second-order approximation in time are considered for numerically solving the Cauchy problem for an evolutionary equation of first order with a self-adjoint operator. The implicit two-level scheme based on the Padé polynomial approximation is unconditionally stable. It demonstrates good asymptotic properties in time and provides an adequate evolution in time for individual harmonics of the solution (has spectral mimetic (SM) stability). In fact, the only drawback of this scheme is the necessity to solve an equation with an operator polynomial of second degree at each time level. We consider modifications of these schemes, which are based on solving equations with operator polynomials of first degree. Such computational implementations occur, for example, if we apply the fully implicit two-level scheme (the backward Euler scheme). A three-level modification of the SM-stable scheme is proposed. Its unconditional stability is established in the corresponding norms. The emphasis is on the scheme, where the numerical algorithm involves two stages, namely, the backward Euler scheme of first order at the first (prediction) stage and the following correction of the approximate solution using a factorized operator. The SM-stability is established for the proposed scheme. To illustrate the theoretical results of the work, a model problem is solved numerically.
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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.

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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.
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BERNARDI, CHRISTINE, and ENDRE SÜLI. "TIME AND SPACE ADAPTIVITY FOR THE SECOND-ORDER WAVE EQUATION." Mathematical Models and Methods in Applied Sciences 15, no. 02 (February 2005): 199–225. http://dx.doi.org/10.1142/s0218202505000339.

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The aim of this paper is to show that, for a linear second-order hyperbolic equation discretized by the backward Euler scheme in time and continuous piecewise affine finite elements in space, the adaptation of the time steps can be combined with spatial mesh adaptivity in an optimal way. We derive a priori and a posteriori error estimates which admit, as much as it is possible, the decoupling of the errors committed in the temporal and spatial discretizations.
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Sahu, Subal Ranjan, and Jugal Mohapatra. "Numerical investigation of time delay parabolic differential equation involving two small parameters." Engineering Computations 38, no. 6 (January 20, 2021): 2882–99. http://dx.doi.org/10.1108/ec-07-2020-0369.

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Purpose The purpose of this study is to provide a robust numerical method for a two parameter singularly perturbed delay parabolic initial boundary value problem (IBVP). Design/methodology/approach To solve the problem, the authors have used a hybrid scheme combining the midpoint scheme, the upwind scheme and the second-order central difference scheme for the spatial derivatives. The backward Euler scheme on a uniform mesh is used to approximate the time derivative. Here, the authors have used Shishkin type meshes for spatial discretization. Findings It is observed that the proposed method converges uniformly with almost second-order spatial accuracy with respect to the discrete maximum norm. Originality/value This paper deals with the numerical study of a two parameter singularly perturbed delay parabolic IBVP. To solve the problem, the authors have used a hybrid scheme combining the midpoint scheme, the upwind scheme and the second-order central difference scheme for the spatial derivatives. The backward Euler scheme on a uniform mesh is used to approximate the time derivative. The convergence analysis is carried out. It is observed that the proposed method converges uniformly with almost second-order spatial accuracy with respect to the discrete maximum norm. Numerical experiments illustrate the efficiency of the proposed scheme.
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Ravindran, S. S. "An Extrapolated Second Order Backward Difference Time-Stepping Scheme for the Magnetohydrodynamics System." Numerical Functional Analysis and Optimization 37, no. 8 (May 4, 2016): 990–1020. http://dx.doi.org/10.1080/01630563.2016.1181651.

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Wang, Danxia, Ni Miao, and Jing Liu. "A second-order numerical scheme for the Ericksen-Leslie equation." AIMS Mathematics 7, no. 9 (2022): 15834–53. http://dx.doi.org/10.3934/math.2022867.

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<abstract><p>In this paper, we consider a finite element approximation for the Ericksen-Leslie model of nematic liquid crystal. Based on a saddle-point formulation of the director vector, a second-order backward differentiation formula (BDF) numerical scheme is proposed, where a pressure-correction strategy is used to decouple the computation of the pressure from that of the velocity. Designing this scheme leads to solving a linear system at each time step. Furthermore, via implementing rigorous theoretical analysis, we prove that the proposed scheme enjoys the energy dissipation law. Some numerical simulations are also performed to demonstrate the accuracy of the proposed scheme.</p></abstract>
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Park, Sang-Hun, and Tae-Young Lee. "High-Order Time-Integration Schemes with Explicit Time-Splitting Methods." Monthly Weather Review 137, no. 11 (November 1, 2009): 4047–60. http://dx.doi.org/10.1175/2009mwr2885.1.

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Abstract New high-order time-integration schemes for fully elastic models are presented. The new schemes, formulated using the Richardson extrapolation that employs leapfrog-type schemes, can give a good performance for linear model problems and ensure overall stability when they are combined with a forward–backward scheme for fast waves. The new and existing schemes show differences in the order of accuracy. Thus, they can be useful for investigating the impacts of time-integration scheme accuracy on the performance of numerical models. The high-order schemes are found to play an important role in the improvement of high-resolution simulations, according to idealized tests. The new schemes are less efficient than other well-known schemes at moderate spatial resolutions. However, the new schemes can be more efficient than the existing schemes when the resolution becomes very high.
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Chibuisi, C., B. O. Osu, U. W. Sirisena, K. Uchendu, and C. Granados. "The Computational Solution of First Order Delay Differential Equations Using Second Derivative Block Backward Differentiation Formulae." International Journal of Mathematical Analysis and Optimization: Theory and Applications 7, no. 2 (March 2022): 88–106. http://dx.doi.org/10.52968/28304669.

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In this paper, we implemented second derivative block backward differentiation formulae methods in solving first order delay differential equations without the application of interpolation methods in investigating the delay argument. The delay argument was evaluated using a suitable idea of sequence which we incorporated into some first order delay differential equations before its numerical evaluations. The construction of the continuous expressions of these of block methods was executed through the use of second derivative backward differentiation formulae method on the bases of linear multistep collocation approach using matrix inversion method to derive the discrete schemes. After the numerical experiments, the new proposed method was observed to be convergent, stable and less time consuming. From the numerical solutions obtained, the scheme for step number k = 4 performed better in terms of accuracy than that of the schemes for step numbers k = 3 and 2 when compared with other existing methods.
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He, Haiyan, Kaijie Liang, and Baoli Yin. "A numerical method for two-dimensional nonlinear modified time-fractional fourth-order diffusion equation." International Journal of Modeling, Simulation, and Scientific Computing 10, no. 01 (February 2019): 1941005. http://dx.doi.org/10.1142/s1793962319410058.

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In this paper, we consider the finite element method for two-dimensional nonlinear modified time-fractional fourth-order diffusion equation. In order to avoid using higher order elements, we introduce an intermediate variable [Formula: see text] and translate the fourth-order derivative of the original problem into a second-order coupled system. We discretize the fractional time derivative terms by using the [Formula: see text]-approximation and discretize the first-order time derivative term by using the second-order backward differentiation formula. In the fully discrete scheme, we implement the finite element method for the spatial approximation. Unconditional stability of the fully discrete scheme is proven and its optimal convergence order is obtained. Numerical experiments are carried out to demonstrate our theoretical analysis.
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Hou, Yaxin, Ruihan Feng, Yang Liu, Hong Li, and Wei Gao. "A MFE method combined with L1-approximation for a nonlinear time-fractional coupled diffusion system." International Journal of Modeling, Simulation, and Scientific Computing 08, no. 01 (January 10, 2017): 1750012. http://dx.doi.org/10.1142/s179396231750012x.

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In this paper, a nonlinear time-fractional coupled diffusion system is solved by using a mixed finite element (MFE) method in space combined with L1-approximation and implicit second-order backward difference scheme in time. The stability for nonlinear fully discrete finite element scheme is analyzed and a priori error estimates are derived. Finally, some numerical tests are shown to verify our theoretical analysis.
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Dissertations / Theses on the topic "Second-order backward time scheme"

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Descamps, Théo. "Numerical analysis and development of accurate models in a CFD solver dedicated to naval applications with waves." Thesis, Ecole centrale de Nantes, 2022. http://www.theses.fr/2022ECDN0049.

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L’objectif de cette thèse est de développer des solveurs numériques et des méthodologies afin d’améliorer le temps de calcul et la précision des simulations de tenue à la mer et de résistance ajoutée sur houle. Tout d’abord, une synthèse de l’algorithme du solver foamStar développé en interne est effectuée. A partir de cette analyse, une modification est proposée afin de pouvoir utiliser le "Multidimensional Universal Limiterfor Explicit Solution" (MULES) avec un schéma temporel backward d’ordre deux. Ensuite, plusieurs études successives sont réalisées afin de : vérifier l’implémentation du schéma backward ; définir une configuration numérique et des maillages efficaces pour la simulation de houle. Les cas d’étude sont : les tourbillons de Taylor-Green, la houle régulière non linéaire se propageant dans un domaine periodique, et enfin, la houle régulière générée avec des zones de relaxation et des configurations numériques proches de celles utilisées pour des applications navales. Dans la dernière partie de cette thèse, une étude préliminaire est réalisée en simulant un porte-conteneur avec une vitesse d’avance dans des houles régulières de face. Les recommandations définies tout au long de cette thèse sont également évaluées
The objective of the present thesis is to develop solvers and methodologies in order to improve the computational cost andthe accuracy with regard to the thematics of seakeeping and added resistance. First, a synthetic workflow of the algorithmof the in-house solver foamStar is proposed. From this analysis a modification is proposed in order to use the Multidimensional Universal Limiter for Explicit Solution (MULES) with a second-order backward time scheme. Then, successive studies are done in order to: verify the implementation of the backward scheme; define an efficient numerical set-up and adequate mesh structures for numerical wave simulations. The case studies are, Taylor-Green vortices, nonlinear regular wave propagating in a periodic domain, and finally, regular waves generated with relaxation zones considering numerical configurations close to what is used for naval applications. In the last part of this Thesis, a preliminary study is done simulating a containership with forward speed in head regular waves. The recommendations derived all along this thesis are also evaluated
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Books on the topic "Second-order backward time scheme"

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Ayyar, R. V. Vaidyanatha. From Equity to Preferential Equity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199474943.003.0014.

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This chapter describes at great length the extension of reservations (quotas) to Other Backward Classes (OBCs), by far the most important and most controversial initiative during Arjun Singh’s second stint as Minister, MHRD. It also describes the policy initiatives to advance the education of Muslims including a special focus on Muslims in programmes like SSA, constitution of a National Commission for Minority Educational Institutions with far reaching powers, of the Rajendra Sachar committee on the social economic and educational status of the Muslim, and the Ranganath Mishra Commission for Religious and Linguistic Minorities. In order to place these developments in a historical perspective the chapter offers an analysis of different dimensions of equity in education, the policies adopted from time to time advance equity in education, the distinction between equalization of opportunities and preferential equity, the seminal contribution of Ram Maonhar Lohia to the concretisation of the concept of preferential equity in the Indian context, and the sociological and political connotations of inclusion in education.
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Sobczyk, Eugeniusz Jacek. Uciążliwość eksploatacji złóż węgla kamiennego wynikająca z warunków geologicznych i górniczych. Instytut Gospodarki Surowcami Mineralnymi i Energią PAN, 2022. http://dx.doi.org/10.33223/onermin/0222.

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Hard coal mining is characterised by features that pose numerous challenges to its current operations and cause strategic and operational problems in planning its development. The most important of these include the high capital intensity of mining investment projects and the dynamically changing environment in which the sector operates, while the long-term role of the sector is dependent on factors originating at both national and international level. At the same time, the conditions for coal mining are deteriorating, the resources more readily available in active mines are being exhausted, mining depths are increasing, temperature levels in pits are rising, transport routes for staff and materials are getting longer, effective working time is decreasing, natural hazards are increasing, and seams with an increasing content of waste rock are being mined. The mining industry is currently in a very difficult situation, both in technical (mining) and economic terms. It cannot be ignored, however, that the difficult financial situation of Polish mining companies is largely exacerbated by their high operating costs. The cost of obtaining coal and its price are two key elements that determine the level of efficiency of Polish mines. This situation could be improved by streamlining the planning processes. This would involve striving for production planning that is as predictable as possible and, on the other hand, economically efficient. In this respect, it is helpful to plan the production from operating longwalls with full awareness of the complexity of geological and mining conditions and the resulting economic consequences. The constraints on increasing the efficiency of the mining process are due to the technical potential of the mining process, organisational factors and, above all, geological and mining conditions. The main objective of the monograph is to identify relations between geological and mining parameters and the level of longwall mining costs, and their daily output. In view of the above, it was assumed that it was possible to present the relationship between the costs of longwall mining and the daily coal output from a longwall as a function of onerous geological and mining factors. The monograph presents two models of onerous geological and mining conditions, including natural hazards, deposit (seam) parameters, mining (technical) parameters and environmental factors. The models were used to calculate two onerousness indicators, Wue and WUt, which synthetically define the level of impact of onerous geological and mining conditions on the mining process in relation to: —— operating costs at longwall faces – indicator WUe, —— daily longwall mining output – indicator WUt. In the next research step, the analysis of direct relationships of selected geological and mining factors with longwall costs and the mining output level was conducted. For this purpose, two statistical models were built for the following dependent variables: unit operating cost (Model 1) and daily longwall mining output (Model 2). The models served two additional sub-objectives: interpretation of the influence of independent variables on dependent variables and point forecasting. The models were also used for forecasting purposes. Statistical models were built on the basis of historical production results of selected seven Polish mines. On the basis of variability of geological and mining conditions at 120 longwalls, the influence of individual parameters on longwall mining between 2010 and 2019 was determined. The identified relationships made it possible to formulate numerical forecast of unit production cost and daily longwall mining output in relation to the level of expected onerousness. The projection period was assumed to be 2020–2030. On this basis, an opinion was formulated on the forecast of the expected unit production costs and the output of the 259 longwalls planned to be mined at these mines. A procedure scheme was developed using the following methods: 1) Analytic Hierarchy Process (AHP) – mathematical multi-criteria decision-making method, 2) comparative multivariate analysis, 3) regression analysis, 4) Monte Carlo simulation. The utilitarian purpose of the monograph is to provide the research community with the concept of building models that can be used to solve real decision-making problems during longwall planning in hard coal mines. The layout of the monograph, consisting of an introduction, eight main sections and a conclusion, follows the objectives set out above. Section One presents the methodology used to assess the impact of onerous geological and mining conditions on the mining process. Multi-Criteria Decision Analysis (MCDA) is reviewed and basic definitions used in the following part of the paper are introduced. The section includes a description of AHP which was used in the presented analysis. Individual factors resulting from natural hazards, from the geological structure of the deposit (seam), from limitations caused by technical requirements, from the impact of mining on the environment, which affect the mining process, are described exhaustively in Section Two. Sections Three and Four present the construction of two hierarchical models of geological and mining conditions onerousness: the first in the context of extraction costs and the second in relation to daily longwall mining. The procedure for valuing the importance of their components by a group of experts (pairwise comparison of criteria and sub-criteria on the basis of Saaty’s 9-point comparison scale) is presented. The AHP method is very sensitive to even small changes in the value of the comparison matrix. In order to determine the stability of the valuation of both onerousness models, a sensitivity analysis was carried out, which is described in detail in Section Five. Section Six is devoted to the issue of constructing aggregate indices, WUe and WUt, which synthetically measure the impact of onerous geological and mining conditions on the mining process in individual longwalls and allow for a linear ordering of longwalls according to increasing levels of onerousness. Section Seven opens the research part of the work, which analyses the results of the developed models and indicators in individual mines. A detailed analysis is presented of the assessment of the impact of onerous mining conditions on mining costs in selected seams of the analysed mines, and in the case of the impact of onerous mining on daily longwall mining output, the variability of this process in individual fields (lots) of the mines is characterised. Section Eight presents the regression equations for the dependence of the costs and level of extraction on the aggregated onerousness indicators, WUe and WUt. The regression models f(KJC_N) and f(W) developed in this way are used to forecast the unit mining costs and daily output of the designed longwalls in the context of diversified geological and mining conditions. The use of regression models is of great practical importance. It makes it possible to approximate unit costs and daily output for newly designed longwall workings. The use of this knowledge may significantly improve the quality of planning processes and the effectiveness of the mining process.
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Book chapters on the topic "Second-order backward time scheme"

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Wuilbaut, T., and H. Deconinck. "Improving Monotonicity of the 2 nd Order Backward Difference Time Integration Scheme by Temporal Limiting." In Computational Fluid Dynamics 2008, 733–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01273-0_97.

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Forth, S. A. "A Second Order Accurate, Space-Time Limited, BDF Scheme for the Linear Advection Equation." In Godunov Methods, 335–42. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4615-0663-8_35.

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Benkhaldoun, Fayssal, and Abdallah Bradji. "A Second Order Time Accurate Finite Volume Scheme for the Time-Fractional Diffusion Wave Equation on General Nonconforming Meshes." In Large-Scale Scientific Computing, 95–104. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-41032-2_10.

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Du, Rui-lian, and Zhi-zhong Sun. "A Temporal Second-Order Scheme for Time Fractional Mixed Diffusion and Wave Equation with an Initial Singularity." In Proceedings of the International Conference on Fractional Differentiation and its Applications (ICFDA’21), 132–40. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-04383-3_15.

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Du, Rui-lian, and Zhi-zhong Sun. "A Temporal Second-Order Scheme for Time Fractional Mixed Diffusion and Wave Equation with an Initial Singularity." In Proceedings of the International Conference on Fractional Differentiation and its Applications (ICFDA’21), 132–40. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-04383-3_15.

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Notsu, Hirofumi, and Masahisa Tabata. "Error Estimates of a Stabilized Lagrange–Galerkin Scheme of Second-Order in Time for the Navier–Stokes Equations." In Mathematical Fluid Dynamics, Present and Future, 497–530. Tokyo: Springer Japan, 2016. http://dx.doi.org/10.1007/978-4-431-56457-7_18.

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Cui, Yan, and Xiaoshan Wang. "Finite-Time Consensus for Second-Order Leader-Following Multi-agent Systems with Disturbances Based on the Event-Triggered Scheme." In Lecture Notes in Electrical Engineering, 471–86. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-32-9682-4_50.

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Alikhanov, Anatoly A., and Inna Z. Kodzokova. "A Higher Order Difference Scheme for the Time Fractional Diffusion Equation with the Steklov Nonlocal Boundary Value Problem of the Second Kind." In Lecture Notes in Computer Science, 164–71. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57099-0_15.

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Benkhaldoun, Fayssal, and Abdallah Bradji. "Note on the Convergence of a Finite Volume Scheme for a Second Order Hyperbolic Equation with a Time Delay in Any Space Dimension." In Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, 315–24. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43651-3_28.

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Li, Huaqing, Dawen Xia, Qingguo Lü, Zheng Wang, Xiangzhao Wu, Huiwei Wang, and Lianghao Ji. "Consensus analysis of multi-agent systems with second-order nonlinear dynamics and general directed topology: an event-triggered scheme." In Second-Order Consensus of Continuous-Time Multi-Agent Systems, 139–76. Elsevier, 2021. http://dx.doi.org/10.1016/b978-0-32-390131-4.00015-7.

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Conference papers on the topic "Second-order backward time scheme"

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Chuang, Han-Sheng, and Steven T. Wereley. "In-Vitro Wall Shear Stress Measurements for Microfluid Flows by Using Second-Order SPE Micro-PIV." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-41171.

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Conventional single pixel evaluation (SPE) significantly improves the spatial resolution of PIV measurements to the physical limit of a CCD camera based on the forward difference interrogation (FDI). This paper further enhances the computational algorithm to second-order accuracy by simply modifying the numerical scheme with the central difference interrogation (CDI). The proposed central difference scheme basically superposes the forward-time and the backward-time correlation domains, thus resulting in reduced bias error as well as rapid background noise elimination. An assessment of the CDI SPE algorithm regarding the measurement errors was achieved via numerous synthetic images subject to a four-roll mill flow. In addition, preliminary wall shear stress (WSS) measurements regarding different algorithms are also evaluated with an analytical turbulent boundary flow. CDI scheme showed a 0.32% error deviated from the analytical solution and improved the same error in FFT-based correlation correlation (FFT-CC) by 32.35%. To demonstrate the performance in practice, in-vitro measurements were implemented in a serpentine microchannel made of polydimethyl siloxane (PDMS) for both CDI SPE and spatial cross-correlation. A series of steady-state flow images at five specified regions of interest were acquired using micro-PIV system. Final comparisons of the WSS regarding the Pearson correlation coefficient, R2, between the numerical schemes and the simulations showed that an overall result was improved by CDI SPE due to the fine resolution and the enhanced accuracy.
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Kim, Young Jun, Benjamin Bouscasse, Sopheak Seng, and David Le Touze. "Numerical Study on the Temporal Discretization Schemes in Two-Phase Wave Simulation." In ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/omae2019-96278.

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Abstract The generation and propagation of waves in a viscous flow solver are indispensable part of naval computational fluid dynamic (CFD) applications. This paper presents numerical simulations of two-dimensional wave propagation in the framework of two-phase finite volume method (FVM) with different temporal discretization schemes. Implicit Euler, Crank-Nicolson (CN) and second-order backward temporal discretization schemes are compared by using viscous flow solver based on the open source library OpenFOAM. The combinations of each temporal discretization scheme and explicit limiter are used for the formulation of the Volume Of Fluid (VOF) field convection equation. A new formulation using the second-order backward temporal discretization scheme with explicit limiter are investigated. Two-dimensional periodic domains are considered to compare different time-stepping methods. Also, five different refinement levels of meshes are used to study the convergence properties of each method. The non-linear wave is generated with stream function wave theory using ‘foamStar’, which is a specialized OpenFOAM library package developed by Bureau Veritas in collaboration with École Centrale de Nantes.
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Spakovsky, Z. S. "Backward Traveling Rotating Stall Waves in Centrifugal Compressors." In ASME Turbo Expo 2002: Power for Land, Sea, and Air. ASMEDC, 2002. http://dx.doi.org/10.1115/gt2002-30379.

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Rotating stall waves that travel against the direction of rotor rotation are reported for the first time and a new, low-order analytical approach to model centrifugal compressor stability is introduced. The model is capable of dealing with unsteady radially swirling flows and the dynamic effects of impeller-diffuser component interaction as it occurs in centrifugal compression systems. A simple coupling criterion is developed from first principles to explain the interaction mechanism important for system stability. The model findings together with experimental data explain the mechanism for first-ever observed backward traveling rotating stall in centrifugal compressors with vaned diffusers. Based on the low-order model predictions, an air injection scheme between the impeller and the vaned diffuser is designed for the NASA Glenn CC3 high-speed centrifugal compressor. The steady air injection experiments show an increase of 25% in surge-margin with an injection mass flow of 0.5% of the compressor mass flow. In addition, it is experimentally demonstrated that this injection scheme is robust to impeller tip-clearance effects and that a reduced number of injectors can be applied for similar gains in surge-margin. The results presented in this paper firmly establish the connection between the experimentally observed dynamic phenomena in the NASA CC3 centrifugal compressor and a first principles based coupling criterion. In addition, guidelines are given for the design of centrifugal compressors with enhanced stability.
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Bakolas, Vasilios, and Wolfgang Borchers. "Variable Timestepping in EHD Problems." In World Tribology Congress III. ASMEDC, 2005. http://dx.doi.org/10.1115/wtc2005-63116.

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Transient EHD calculations have moved to the center of the attention in the past years as more machine elements that operate under variable operating conditions, such as automotive engine components, are examined. Almost all of the transient calculations today are carried out with a constant time step using first or second order discretisation for the determination of the time derivatives. Recently, a method was proposed that could control the time stepping of a transient calculation using first order time derivatives. In this paper, a method is presented for the control of the time step in transient calculations. The method employs a second order backward differentiation scheme with variable time stepping for the determination of the time derivatives. The time interval between successive calculations is determined depending on an estimate of the local truncation error without solving additional large linear systems, thus allowing for larger time steps when the time derivative is almost constant. This time stepping control method was implemented in an EHD simulation code that employed multi-grid and multi-level multi-summation techniques. Results presented in this paper prove that the proposed method can significantly reduce the number of necessary time steps of a transient calculation without any loss of accuracy of the results.
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Cinnella, P., P. De Palma, G. Pascazio, and M. Napolitano. "A Numerical Method for Turbomachinery Aeroelasticity." In ASME Turbo Expo 2002: Power for Land, Sea, and Air. ASMEDC, 2002. http://dx.doi.org/10.1115/gt2002-30321.

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This work provides an accurate and efficient numerical method for turbomachinery flutter. The unsteady Euler or Reynolds-averaged Navier–Stokes (RANS) equations are solved in integral form, the blade passages being discretised using a background fixed C-grid and a body-fitted C-grid moving with the blade. In the overlapping region data are exchanged between the two grids at every time step, using bilinear interpolation. The method employs Roe’s second-order-accurate flux difference splitting scheme for the inviscid fluxes, a standard second-order discretisation of the viscous terms, and a three-level backward difference formula for the time derivatives. The state-of-the-art second-order accuracy of numerical methods for unsteady compressible flows with shocks is thus carried over, for the first time to the authors knowledge, to flutter computations. The dual time stepping technique is used to evaluate the nonlinear residual at each time step, thus extending to turbomachinery aeroelasticity the state-of-the-art efficiency of unsteady RANS solvers. The code is proven to be accurate and efficient by computing the 4th Aeroelastic Standard Configuration, namely, the subsonic flow through a turbine cascade with flutter instability in the first bending mode, where viscous effect are found practically negligible. Then, the very severe 11th Aeroelastic Standard Configuration is computed, namely, the transonic flow through a turbine cascade at off-design conditions, where the turbulence model is found to be the critical feature of the method.
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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.

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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.
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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.

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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.
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Kasac, J., J. Deur, B. Novakovic, and I. Kolmanovsky. "A BPTT-Like Optimal Control Algorithm With Vehicle Dynamics Control Application." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-67319.

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The paper presents a gradient-based numerical algorithm for optimal control of nonlinear multivariable systems with control and state vectors constraints. The algorithm has a backward-in-time recurrent structure similar to the backpropagation-through-time (BPTT) algorithm, which is mostly used as a learning algorithm for dynamic neural networks. This paper presents an enhancement of the basic optimization algorithm. Our enhanced algorithm uses high-order Adams time-discretization schemes instead of the basic Euler discretization method, and a numerical calculation of Jacobians as an alternative to analytical Jacobians. Two examples are considered to illustrate the algorithm and its performance. The first example is that of a tubular reactor, for which an analytical solution is available, which can be readily used for validation of our approach. The second example is related to controlling vehicle dynamics based on a realistic high order model.
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Ceschini, Giuseppe Fabio, Nicolò Gatta, Mauro Venturini, Thomas Hubauer, and Alin Murarasu. "Resistant Statistical Methodologies for Anomaly Detection in Gas Turbine Dynamic Time Series: Development and Field Validation." In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gt2017-63410.

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The reliability of gas turbine health state monitoring and forecasting depends on the quality of sensor measurements directly taken from the unit. Outlier detection techniques have acquired a major importance, as they are capable of removing anomalous measurements and improve data quality. To this purpose, statistical parametric methodologies are widely employed thanks to the limited knowledge of the specific unit required to perform the analysis. The backward and forward moving window (BFMW) k-σ methodology proved its effectiveness in a previous study performed by the authors, to also manage dynamic time series, i.e. during a transient. However, the estimators used by the k-σ methodology are usually characterized by low statistical robustness and resistance. This paper aims at evaluating the benefits of implementing robust statistical estimators for the BFMW framework. Three different approaches are considered in this paper. The first methodology, k-MAD, replaces mean and standard deviation of the k-σ methodology with median and mean absolute deviation (MAD), respectively. The second methodology, σ-MAD, is a novel hybrid scheme combining the k-σ and the k-MAD methodologies for the backward and the forward windows, respectively. Finally, the bi-weight methodology implements bi-weight mean and bi-weight standard deviation as location and dispersion estimators. First, the parameters of these methodologies are tuned and the respective performance is compared by means of simulated data. Different scenarios are considered to evaluate statistical efficiency, robustness and resistance. Subsequently, the performance of these methodologies is further investigated by injecting outliers in field data sets taken on selected Siemens gas turbines. Results prove that all the investigated methodologies are suitable for outlier identification. Advantages and drawbacks of each methodology allow the identification of different scenarios in which their application can be most effective.
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Marques, Nelson P. C., and José C. F. Pereira. "Compressible Fluid Flow and Heat Transfer Navier-Stokes Predictions on Unstructured Grids." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-0861.

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Abstract A second-order accurate finite volume method for solving compressible 2D flows on hybrid structured-unstructured grids is presented. Separate reconstruction and evolution steps are taken to discretize the convective terms. For the reconstruction step, a data-dependent Least-Squares procedure is used, while for the evolution step two recent flux functions are included: the HLLC approximate Riemann solver and the AUSM+ flux vector splitting. Steady-state solutions are obtained with an implicit backward Euler scheme. The assembled system is solved by iterative means (BiCGSTAB, GMRES) with ILU pre-conditioning. Two internal, steady, 2D flow test cases are presented to validate the code: a supersonic 10° ramp inside a channel and a laminar flow through a double-throated nozzle. The code proved accurate with the use of both flux functions when comparing the computed results with both an analytical (ramp) and a reference solution (nozzle). The GMRES solver generally required less CPU time until convergence for the inviscid test-case while the BiCGSTAB solver got the edge for the viscous calculations.
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Reports on the topic "Second-order backward time scheme"

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Integrated Design Optimization for Long Span Steel Transfer Truss at Redevelopment of Hong Kong Kwong Wah Hospital. The Hong Kong Institute of Steel Construction, August 2022. http://dx.doi.org/10.18057/icass2020.p.365.

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Long-span steel trusses are increasingly used in high-rise buildings to replace reinforced concrete thick transfer plate due to light weight and high load-bearing capacity. To support multi-stories above the steel transfer truss, a comprehensive method based on second-order direct analysis method has been applied for optimization design of long-span steel transfer truss in the Redevelopment of Hong Kong Kwong Wah Hospital (KWH) – Phase 1. In the project, a 35m long-span steel transfer truss is adopted at the 3rd to 5th floors to support the above 15-story reinforced concrete structure. Innovative technologies such as the integrated global and local optimization, the integrated design and construction have been explored and made to achieve better uniformity and harmony in structure. In particular, twin trusses with better structural performance, less fabrication cost and ease of constructability are studied and finally adopted in main trusses to replace original single trusses. The optimal scheme has brought both cost and time saving in fabrication, construction, operation and maintenance stages.
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