Parallel Computation of the Point Neutron Kinetic Equations Using Parallel Revisionist Integral Deferred Correction

2018 ◽  
Author(s):  
Yun Cai ◽  
Xingjie Peng ◽  
Qing Li ◽  
Zhizhu Zhang ◽  
Zhumin Jiang ◽  
...  
Keyword(s):  
Time Integration ◽  
Kinetic Equations ◽  
Accurate Method ◽  
Small Time ◽  
Time Step ◽  
Deferred Correction ◽  
Time Integration Method ◽  
Speed Up ◽  
Point Kinetics ◽  
Reactivity Insertion

The point kinetics is very important to the safety of the reactor operation. However, these equations are stiff and usually solved with very small time step. These equations are solved by Revisionist integral deferred correction (RIDC), which is a parallel time integration method. RIDC is a highly accurate method, and it reduces the error by iteration. Based on C++ and MPI, a four-core fourth-order RIDC is implemented and tested by several cases, such as step, ramp, and sinusoidal reactivity insertion. Compared with other methods, the time step of RIDC in the step reactivity insertion case is smaller, but it’s larger in the case of the sinusoidal reactivity insertion. RIDC can keep high accuracy while the time step is appropriately large. The numerical results also show that the speed-up ratio can achieve 2 when 4 processors are used.

A Precise and Stiffly Stable Time Integration Method for Vibration Equations

2001 ◽  
Author(s):  
Takeshi Fujikawa ◽  
Etsujiro Imanishi
Keyword(s):  
Integration Method ◽  
Time Integration ◽  
Low Frequency ◽  
Quadratic Function ◽  
Time Step ◽  
Integration Algorithm ◽  
Time Integration Method ◽  
Time Integration Algorithm ◽  
Time Integration Methods ◽  
Motion Problems

Abstract A method of time integration algorithm is presented for solving stiff vibration and motion problems. It is absolutely stable, numerically dissipative, and much accurate than other dissipative time integration methods. It achieves high-frequency dissipation, while minimizing unwanted low-frequency dissipation. In this method change of acceleration during time step is expressed as quadratic function including some parameters, whose appropriate values are determined through numerical investigation. Two calculation examples are demonstrated to show the usefulness of this method.

scholarly journals A Weighted Residual Parabolic Acceleration Time Integration Method for Problems in Structural Dynamics

2007 ◽  
Vol 7 (3) ◽  
pp. 227-238 ◽  
Author(s):  
S.H. Razavi ◽  
A. Abolmaali ◽  
M. Ghassemieh
Keyword(s):  
Fourth Order ◽  
Initial Conditions ◽  
Time Integration ◽  
Critical Time ◽  
Linear Acceleration ◽  
Time Step ◽  
Time Integration Method ◽  
Acceleration Method ◽  
The Stability ◽  
Critical Time Step

AbstractIn the proposed method, the variation of displacement in each time step is assumed to be a fourth order polynomial in time and its five unknown coefficients are calculated based on: two initial conditions from the previous time step; satisfying the equation of motion at both ends of the time step; and the zero weighted residual within the time step. This method is non-dissipative and its dispersion is considerably less than in other popular methods. The stability of the method shows that the critical time step is more than twice of that for the linear acceleration method and its convergence is of fourth order.

Modified precise direct time integration method for the transient response analysis of viscoelastic systems using an internal variable model

2019 ◽  
Vol 26 (3-4) ◽  
pp. 161-174
Author(s):  
Taufeeq Ur Rehman Abbasi ◽  
Hui Zheng
Keyword(s):  
State Space ◽  
Integration Method ◽  
Time Integration ◽  
Internal Variable ◽  
New Method ◽  
Computational Time ◽  
Direct Integration ◽  
Computational Accuracy ◽  
Time Step ◽  
Time Integration Method

Engineering systems for different levels of energy dissipation use internal variable models, which may lead to tremendous problems in accurate analysis. This article aims to provide an alternative direct integration method for the analysis of systems involving an anelastic displacement field model. A new state-space formulation built on an augmented set of anelastic variables for asymmetric systems is developed. Then, a precise time integration method based on state-space matrix formulation is proposed by introducing a Legendre–Gauss quadrature. The new integration method in terms of numerical stability and its implementation is discussed. The effect of sensitivity of the selection of the time-step and computational time on the performance of the new method is investigated by using a multi-degree-of-freedom system. The performance of the new method is also evaluated in terms of both computational accuracy and efficiency at higher degrees of freedom by using a continuum system. It is demonstrated that the computational accuracy and efficiency of the new method on large-scale problems are higher than that of the direct integration linear displacement–velocity method.

Research in Numerical Simulation of Lager Multi-Scale Water Conveyance Tunnel Based on Mixed Time Integration Method

2012 ◽  
Vol 203 ◽  
pp. 432-437
Author(s):  
Jun Jie Zhao ◽  
Yan Zhi Yang
Keyword(s):  
Numerical Simulation ◽  
Computational Efficiency ◽  
Integration Method ◽  
Time Integration ◽  
Scale Model ◽  
Integration Time ◽  
Time Step ◽  
Detailed Model ◽  
Multi Scale ◽  
Time Integration Method

The global integration time step of multi-scale model is subject to local detailed model, resulting in lower computational efficiency. Mixed time integration method uses different integration time-step in different scale model, it can effectively avoid the above problem. Rest on a large-scale water tunnel under construction, in order to achieve the synchronization of the global and the local simulation, the paper establishes multi-scale finite element model of the tunnel, and calculate it by mixed time integration method. The final calculation and analysis show that the algorithm can guarantee the computational accuracy of multi-scale numerical simulation, and can effectively improve the computational efficiency, it can also provide references for related tunnel project.

Unconditional Stability in Numerical Time Integration Methods

1973 ◽  
Vol 40 (2) ◽  
pp. 417-421 ◽  
Author(s):  
R. D. Krieg
Keyword(s):  
Time Integration ◽  
Step Size ◽  
Time Step ◽  
Central Difference ◽  
Integration Methods ◽  
Time Step Size ◽  
Time Integration Method ◽  
Time Integration Methods ◽  
Numerical Time Integration ◽  
Difference Time

Methods of numerical time integration of the equation M¯q¨ + K¯q = f are examined in this paper. A particular class of explicit time integration methods is defined and this class is searched for an unconditionally stable method. The class is found to contain no such method and, furthermore, is found to contain no method with a larger stable time step size than that characterized by the simple central difference time integration method.

A Numerical Solution to the Point Kinetic Equations Using Diagonally Implicit Runge Kutta Method

2016 ◽  
Author(s):  
Zhizhu Zhang ◽  
Yun Cai
Keyword(s):  
Kinetic Equations ◽  
Fixed Time ◽  
Time Step ◽  
Perfect Agreement ◽  
Computation Efficiency ◽  
Runge Kutta Method ◽  
Adaptive Time Step ◽  
Long Time ◽  
Runge Kutta ◽  
Point Kinetics

It would take a long time to solve the point kinetics equations by using full implicit Runge-Kutta (FIRK) for the strong stiffness. Diagonally implicit Runge-Kutta (DIRK) is a useful tool like FIRK to solve the stiff differential equations, while it could greatly reduce the computation compared to FIRK. By embedded low-order Runge-Kutta, DIRK is implemented with the time step adaptation technique, which improves the computation efficiency of DIRK. Through four typical cases with step, ramp sinusoidal and zig-zag reactivity insertions, it shows that the results obtained by DIRK are in perfect agreement with other available results and DIRK with adaptive time step technique has more efficiency than DIRK with the fixed time step.

scholarly journals A comparative study of kinetics of nuclear reactors

2009 ◽  
Vol 24 (3) ◽  
pp. 167-176 ◽  
Author(s):  
Khalilurrahman Obaidurrahman ◽  
Om Singh
Keyword(s):  
Heavy Water ◽  
Computer Code ◽  
Accurate Method ◽  
Operating Conditions ◽  
Pressurized Water ◽  
Safe Limits ◽  
Water Reactors ◽  
Breeder Reactors ◽  
Point Kinetics ◽  
Reactivity Insertion

The paper deals with the study of reactivity initiated transients to investigate major differences in the kinetics behavior of various reactor systems under different operating conditions. The article also states guidelines to determine the safety limits on reactivity insertion rates. Three systems, light water reactors (pressurized water reactors), heavy water reactors (pressurized heavy water reactors), and fast breeder reactors are considered for the sake of analysis. The upper safe limits for reactivity insertion rate in these reactor systems are determined. The analyses of transients are performed by a point kinetics computer code, PKOK. A simple but accurate method for accounting total reactivity feedback in kinetics calculations is suggested and used. Parameters governing the kinetics behavior of the core are studied under different core states. A few guidelines are discussed to project the possible kinetics trends in the next generation reactors.

Adaptive Time Integration Method for DAEs of Multibody Systems

2012 ◽  
Author(s):  
Jieyu Ding ◽  
Zhenkuan Pan
Keyword(s):  
Multibody Systems ◽  
Integration Method ◽  
Time Integration ◽  
Differential Algebraic Equations ◽  
Richardson Extrapolation ◽  
Time Interval ◽  
Time Step ◽  
Time Integration Method ◽  
Adaptive Time Integration ◽  
Adaptive Time

An adaptive time integration method is developed for the index-3 differential-algebraic equations (DAEs) of multibody systems to improve the computational efficiency as well as the accuracy of the results. Based on the modified general-α method, the adaptive time integration is presented. At each discrete time interval, the time step size is changed through Richardson extrapolation with definable computation accuracy. A rotary rod slider system is used to validate the presented adaptive time integration. The accuracy and efficiency are determined by the expected order of the accuracy in Richardson extrapolation.

Time Integration Method With Structure-Dependent Difference Equations

2013 ◽  
Author(s):  
Shuenn-Yih Chang ◽  
Chiu-Li Huang
Keyword(s):  
High Frequency ◽  
Integration Method ◽  
Time Integration ◽  
Low Frequency ◽  
Unconditional Stability ◽  
Total Response ◽  
Time Step ◽  
Order Accuracy ◽  
Time Integration Method ◽  
Frequency Responses

A novel family of structure-dependent integration method is proposed for time integration. This family method can have the possibility of unconditional stability, second-order accuracy and the explicitness of each time step. Since it can integrate the most important advantage of an implicit method, unconditional stability, and that of an explicit method, the explicitness of each time step, a lot of computational efforts can be saved in solving an inertial type problem, where the total response is dominated by low frequency modes and high frequency responses are of no interest.

Sign in / Sign up

Export Citation Format

Share Document