scholarly journals A computationally-efficient, semi-implicit, iterative method for the time-integration of reacting flows with stiff chemistry

2015 ◽  
Vol 295 ◽  
pp. 740-769 ◽  
Author(s):  
B. Savard ◽  
Y. Xuan ◽  
B. Bobbitt ◽  
G. Blanquart
Keyword(s):  
Iterative Method ◽  
Time Integration ◽  
Reacting Flows ◽  
Computationally Efficient ◽  
Implicit Iterative Method

Direct Sensitivity Analysis of Multibody Systems: A Vehicle Dynamics Benchmark

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Alfonso Callejo ◽  
Daniel Dopico
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Automatic Differentiation ◽  
Time Integration ◽  
General Purpose ◽  
Contact Forces ◽  
Design Parameters ◽  
Computational Techniques ◽  
Computationally Efficient ◽  
Integration Algorithm

Algorithms for the sensitivity analysis of multibody systems are quickly maturing as computational and software resources grow. Indeed, the area has made substantial progress since the first academic methods and examples were developed. Today, sensitivity analysis tools aimed at gradient-based design optimization are required to be as computationally efficient and scalable as possible. This paper presents extensive verification of one of the most popular sensitivity analysis techniques, namely the direct differentiation method (DDM). Usage of such method is recommended when the number of design parameters relative to the number of outputs is small and when the time integration algorithm is sensitive to accumulation errors. Verification is hereby accomplished through two radically different computational techniques, namely manual differentiation and automatic differentiation, which are used to compute the necessary partial derivatives. Experiments are conducted on an 18-degree-of-freedom, 366-dependent-coordinate bus model with realistic geometry and tire contact forces, which constitutes an unusually large system within general-purpose sensitivity analysis of multibody systems. The results are in good agreement; the manual technique provides shorter runtimes, whereas the automatic differentiation technique is easier to implement. The presented results highlight the potential of manual and automatic differentiation approaches within general-purpose simulation packages, and the importance of formulation benchmarking.

Effects of circumferential and axial grooves on the nonlinear oscillations of the full floating ring bearing supported turbocharger rotor

2018 ◽  
Vol 233 (5) ◽  
pp. 741-757 ◽  
Author(s):  
Congcong Zhang ◽  
Rixiu Men ◽  
Hong He ◽  
Wei Chen
Keyword(s):  
Finite Difference ◽  
Reynolds Equation ◽  
Nonlinear Oscillations ◽  
Time Integration ◽  
Response Analysis ◽  
Integration Step ◽  
Computationally Efficient ◽  
Fluid Forces ◽  
Transient Simulations ◽  
The Impact

It is seen that with the reduction in land areas owing to the floating-rings featured grooves, there is reduction in the load capacities and bearing torques of the oil-films, which have an influence on the nonlinear oscillations of turbocharger rotors. In the present paper, the impact of the reduced load capacities and bearing torques caused by circumferential or/and axial grooves in full-floating-ring bearings on the nonlinear oscillations of turbocharger rotors is investigated. The numerical solution of the Reynolds equation for full-floating-ring bearings with grooves by means of a finite difference or finite element approach imposes a prohibitive simulation times, sine in every time-integration step a direct discretization of the Reynolds equation has to be solved simultaneously with the rotor model. To be able to perform transient simulations, a computationally efficient full-floating-ring bearing model is mandatory. To surmount this problem, a very time-efficient but rather precise method is proposed. The major point of the proposed method is the manipulation of the Reynolds equation to allow a speed parameter varying within (−1, +1) to reflect the relative weights of the journal and floating ring’s rotation and squeezing effects. Given the diameter-to-length ratio of each fluid film, groove widths, and boundary conditions, the fluid force databases can be easily established by the finite difference method. During the transient response analysis, the required fluid forces and bearing torques from each film can be evaluated by interpolation using the existent forces and torques of the closest points in the databases. Using transient simulations with the proposed method, the effect of circumferential or/and axial grooves in full-floating-ring bearings on the amplitudes and frequencies of the nonlinear oscillations of turbocharger rotors is qualitatively investigated. It is shown that the reduction of the load capacities and bearing torques due to grooves exert a large influence on the nonlinear rotor oscillations.

scholarly journals Time Domain Room Acoustic Solver with Fourth-Order Explicit FEM Using Modified Time Integration

2020 ◽  
Vol 10 (11) ◽  
pp. 3750 ◽  
Author(s):  
Takumi Yoshida ◽  
Takeshi Okuzono ◽  
Kimihiro Sakagami
Keyword(s):  
Conventional Method ◽  
Fourth Order ◽  
Time Domain ◽  
Time Integration ◽  
Sound Field ◽  
Time Discretization ◽  
Computationally Efficient ◽  
Order Accuracy ◽  
Practical Applications ◽  
Acoustic Methods

This paper presents a proposal of a time domain room acoustic solver using novel fourth-order accurate explicit time domain finite element method (TD-FEM), with demonstration of its applicability for practical room acoustic problems. Although time domain wave acoustic methods have been extremely attractive in recent years as room acoustic design tools, a computationally efficient solver is demanded to reduce their overly large computational costs for practical applications. Earlier, the authors proposed an efficient room acoustic solver using explicit TD-FEM having fourth-order accuracy in both space and time using low-order discretization techniques. Nevertheless, this conventional method only achieves fourth-order accuracy in time when using only square or cubic elements. That achievement markedly impairs the benefits of FEM with geometrical flexibility. As described herein, that difficulty is solved by construction of a specially designed time-integration method for time discretization. The proposed method can use irregularly shaped elements while maintaining fourth-order accuracy in time without additional computational complexity compared to the conventional method. The dispersion and dissipation characteristics of the proposed method are examined respectively both theoretically and numerically. Moreover, the practicality of the method for solving room acoustic problems at kilohertz frequencies is presented via two numerical examples of acoustic simulations in a rectangular sound field including complex sound diffusers and in a complexly shaped concert hall.

Newmark-Beta Method in Discrete Elastic Rods Algorithm to Avoid Energy Dissipation

2019 ◽  
Vol 86 (8) ◽  
Author(s):  
Weicheng Huang ◽  
Mohammad Khalid Jawed
Keyword(s):  
Energy Dissipation ◽  
Time Integration ◽  
Integration Scheme ◽  
Integration Step ◽  
Elastic Rods ◽  
Computationally Efficient ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Time Integration Scheme

Discrete elastic rods (DER) algorithm presents a computationally efficient means of simulating the geometrically nonlinear dynamics of elastic rods. However, it can suffer from artificial energy loss during the time integration step. Our approach extends the existing DER technique by using a different time integration scheme—we consider a second-order, implicit Newmark-beta method to avoid energy dissipation. This treatment shows better convergence with time step size, specially when the damping forces are negligible and the structure undergoes vibratory motion. Two demonstrations—a cantilever beam and a helical rod hanging under gravity—are used to show the effectiveness of the modified discrete elastic rods simulator.

Studies on the Accuracy Stability and Efficiency of a New Time Integration Scheme for Ballast Modeling Using the Discrete Element Method

2014 ◽  
Author(s):  
G. F. Mathews ◽  
R. L. Mullen ◽  
D. C. Rizos
Keyword(s):  
Particle Interaction ◽  
Time Integration ◽  
Discrete Element ◽  
Critical Discussion ◽  
Implicit Time ◽  
Integration Scheme ◽  
Computationally Efficient ◽  
Time Step ◽  
Central Difference ◽  
Time Integration Scheme

This paper presents the development of a semi-implicit time integration scheme, originally developed for structural dynamics in the 1970’s, and its implementation for use in Discrete Element Methods (DEM) for rigid particle interaction, and interaction of elastic bodies that are modeled as a cluster of rigid interconnected particles. The method is developed in view of ballast modeling that accounts for the flexibility of aggregates and the arbitrary shape and size of granules. The proposed scheme does not require any matrix inversions and is expressed in an incremental form making it appropriate for non-linear problems. The proposed method focuses on improving the efficiency, stability and accuracy of the solutions, as compared to current practice. A critical discussion of the findings of the studies is presented. Extended verification and assessment studies demonstrate that the proposed algorithm is unconditionally stable and accurate even for large time step sizes. It is demonstrated that the proposed method is at least as computationally efficient as the Central Difference Method. Guidelines for the implementation of the method to ballast modeling are discussed.

Study Method for Low Speed Flow Basic on Precondition

2014 ◽  
Vol 1070-1072 ◽  
pp. 1972-1977
Author(s):  
Lang Li ◽  
Guo Ping Cheng ◽  
Guo Quan Zhu ◽  
Wei Zhang
Keyword(s):  
Iterative Method ◽  
Stokes Equations ◽  
Time Derivative ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Speed ◽  
Speed Flow ◽  
Preconditioning Method ◽  
Derivative Term ◽  
Implicit Iterative Method

Based on Navier-stokes equations, Weiss-Smith matrix preconditioning method is implemented within pseudo time derivative term. AUSM+-up family schemes and LU-SGS implicit iterative method were used to solve low speed flows and were compared with literature data and theoretical value. Through comparing calculation with the literature data and theoretical value, The Results showed the preconditioning algorithm can be applied efficiently to the low speeds flow field ,All these works built foundations for further application of chemical flows.

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