scholarly journals A Gas Dynamics Method Based on the Spectral Deferred Corrections (SDC) Time Integration Technique and the Piecewise Parabolic Method (PPM)

2011 ◽  
Vol 01 (04) ◽  
pp. 303-317 ◽  
Author(s):  
Samet Y. Kadioglu
Keyword(s):  
Gas Dynamics ◽  
Time Integration ◽  
Integration Technique ◽  
Piecewise Parabolic ◽  
Spectral Deferred Corrections ◽  
Dynamics Method

scholarly journals Application of a Novel Picard-Type Time-Integration Technique to the Linear and Non-Linear Dynamics of Mechanical Structures: An Exemplary Study

2021 ◽  
Vol 11 (9) ◽  
pp. 3742
Author(s):  
Evgenii Oborin ◽  
Hans Irschik
Keyword(s):  
Time Integration ◽  
Harmonic Excitation ◽  
Free Vibrations ◽  
Observation Time ◽  
Double Pendulum ◽  
Integration Technique ◽  
Linear Dynamics ◽  
Non Linear ◽  
Linear Vibrations ◽  
Numerical Time Integration

Applications of a novel time-integration technique to the non-linear and linear dynamics of mechanical structures are presented, using an extended Picard-type iteration. Explicit discrete-mechanics approximations are taken as starting guess for the iteration. Iteration and necessary symbolic operations need to be performed only before time-stepping procedure starts. In a previous investigation, we demonstrated computational advantages for free vibrations of a hanging pendulum. In the present paper, we first study forced non-linear vibrations of a tower-like mechanical structure, modeled by a standing pendulum with a non-linear restoring moment, due to harmonic excitation in primary parametric vertical resonance, and due to excitation recordings from a real earthquake. Our technique is realized in the symbolic computer languages Mathematica and Maple, and outcomes are successfully compared against the numerical time-integration tool NDSolve of Mathematica. For out method, substantially smaller computation times, smaller also than the real observation time, are found on a standard computer. We finally present the application to free vibrations of a hanging double pendulum. Excellent accuracy with respect to the exact solution is found for comparatively large observation periods.

Mixed Time Integration Parallel Algorithm for Nonlinear Dynamic Analysis

2014 ◽  
Vol 580-583 ◽  
pp. 3038-3041
Author(s):  
Chao Jiang Fu
Keyword(s):  
Dynamic Analysis ◽  
Parallel Algorithm ◽  
Nonlinear Dynamic ◽  
Time Integration ◽  
Nonlinear Dynamic Analysis ◽  
Integration Technique ◽  
Explicit Time Integration ◽  
Implicit Algorithm ◽  
Integration Techniques ◽  
Implicit And Explicit

The mixed time integration parallel algorithm for nonlinear dynamic analysis was presented by synthesising the implicit and explicit time integration techniques. The parallel algorithm employing mixed time integration technique was devised with domain decomposition. Concurrency was introduced into this algorithm by integrating interface nodes with explicit time integration technique and solving local subdomains with implicit algorithm. Numerical example was implemented to validate the performance of the parallel algorithm. Numerical studies indicate that the proposed algorithm is superior in performance to the implicit algorithm.

scholarly journals Computational Methods for Lifetime Prediction of Metallic Components under High-Temperature Fatigue

Metals ◽  
2019 ◽  
Vol 9 (4) ◽  
pp. 390 ◽  
Author(s):  
Vitaliy Kindrachuk ◽  
Bernard Fedelich ◽  
Birgit Rehmer ◽  
Frauke Peter
Keyword(s):  
Life Prediction ◽  
Time Integration ◽  
Fatigue Loading ◽  
Parametric Models ◽  
Computational Techniques ◽  
Loading History ◽  
Integration Technique ◽  
Element Simulation ◽  
Austenitic Cast Iron ◽  
Viscoplastic Solid

The issue of service life prediction of hot metallic components subjected to cyclic loadings is addressed. Two classes of lifetime models are considered, namely, the incremental lifetime rules and the parametric models governed by the fracture mechanics concept. Examples of application to an austenitic cast iron are presented. In addition, computational techniques to accelerate the time integration of the incremental models throughout the fatigue loading history are discussed. They efficiently solve problems where a stabilized response of a component is not observed, for example due to the plastic strain which is no longer completely reversed and accumulates throughout the fatigue history. The performance of such an accelerated integration technique is demonstrated for a finite element simulation of a viscoplastic solid under repeating loading–unloading cycles.

An Essentially Non-Oscillatory Spectral Deferred Correction Method for Conservation Laws

2016 ◽  
Vol 13 (05) ◽  
pp. 1650027 ◽  
Author(s):  
Samet Y. Kadioglu ◽  
Veli Colak
Keyword(s):  
Conservation Laws ◽  
Fourth Order ◽  
Time Integration ◽  
High Order ◽  
Test Problems ◽  
Order Of Accuracy ◽  
Volume Method ◽  
Spectral Deferred Correction ◽  
Spectral Deferred Corrections ◽  
Eno Scheme

We present a computational method based on the Spectral Deferred Corrections (SDC) time integration technique and the Essentially Non-Oscillatory (ENO) finite volume method for the conservation laws (one-dimensional Euler equations). The SDC technique is used to advance the solutions in time with high-order of accuracy. The ENO method is used to define high-order cell edge quantities that are then used to evaluate numerical fluxes. The coupling of the SDC method with a high-order finite volume method (Piece-wise Parabolic Method (PPM)) for solving the conservation laws is first carried out by Layton et al. in [Layton, A. T. and Minion, M. L. [2004] “Conservative multi-implicit spectral deferred correction methods for reacting gas dynamics,” J. Comput. Phys. 194(2), 697–714]. Issues about this approach have been addressed and some improvements have been added to it in [Kadioglu et al. [2012] “A gas dynamics method based on the spectral deferred corrections (SDC) time integration technique and the piecewise parabolic method (PPM),” Am. J. Comput. Math. 1–4, 303–317]. Here, we investigate the implications when the PPM method is replaced with the well-known ENO method. We note that the SDC-PPM method is fourth-order accurate in time and space. Therefore, we kept the order of accuracy of the ENO procedure as fourth-order in order to be able to make a consistent comparison between the two approaches (SDC-ENO versus SDC-PPM methods). We have tested the new SDC-ENO technique by solving several test problems involving moderate to strong shock waves and smooth/complex flow structures. Our numerical results show that we have numerically achieved the formally fourth-order convergence of the new method for smooth problems. Our numerical results also indicate that the newly proposed technique performs very well providing highly resolved shock discontinuities and fairly good contact solutions. More importantly, the discontinuities in the flow test problems are captured with essentially no-oscillations. We have numerically compared the fourth-order SDC-ENO scheme to the fourth-order SDC-PPM method for the same test problems. The results are similar for most of the test problems except in some cases the SDC-PPM method suffers from minor oscillations compared to SDC-ENO scheme being completely oscillation free.

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