Local error control inSDIRK-methods

1986 ◽  
Vol 26 (1) ◽  
pp. 100-113 ◽  
Author(s):  
Syvert P. Nørsett ◽  
Per G. Thomsen
Keyword(s):  
Error Control ◽  
Local Error

An Efficient Algorithm for Damage-Coupled Visco-Plastic Fatigue Model

2004 ◽  
Author(s):  
A. H. Zhao ◽  
C. L. Chow
Keyword(s):  
Error Control ◽  
Three Dimensional ◽  
Numerical Algorithms ◽  
Fatigue Loading ◽  
Material Model ◽  
Tensile Creep ◽  
Local Error ◽  
Single Element ◽  
Numerical Examples ◽  
Uniaxial Test

The paper describes the development of an efficient and robust numerical algorithm for a damage-coupled visco-plastic-fatigue material model. The material chosen for the investigation is a eutectic material, Sn-Pb solder, exhibiting strain-softening behavior. The numerical algorithms employs a modified explicit method with adaptive sub-stepping based on the local error control for which the stress (constitutive) Jacobian explicit solution is derived. The algorithm is implemented in a commercial finite element (FE) code ABAQUS (Version 6.2) via its user-defined material subroutine. The validity of the algorithm is examined with several numerical examples, including (i) single-element simulations for uniaxial test, tensile creep, and fatigue simulations to attain an optimized algorithm, and (ii) two three-dimensional analyses of a miniature specimen under monotonic tensile loading and fatigue loading. The numerical examples illustrate the effectiveness of the modified explicit algorithm in predicting cyclic thermoviscoplastic behavior of a solder material. The algorithm is considered a generalized methodology that can be readily applied characterize thermoviscoplastic behavior and fatigue life of similar materials.

Towards developing an adaptive time stepping for compressible unsteady flows

2019 ◽  
Vol 29 (2) ◽  
pp. 487-503 ◽  
Author(s):  
Nikhil Kalkote ◽  
Ashwani Assam ◽  
Vinayak Eswaran
Keyword(s):  
Error Control ◽  
Transient Flow ◽  
Stokes Equations ◽  
Local Error ◽  
Time Step ◽  
Content Type ◽  
Time Stepping ◽  
Adaptive Time ◽  
Time Accuracy ◽  
Adaptive Time Stepping

Purpose The purpose of this paper is to solve unsteady compressible Navier–Stokes equations without the commonly used dual-time loop. The authors would like to use an adaptive time-stepping (ATS)-based local error control instead of CFL-based time-stepping technique. Also, an all-speed flow algorithm is implemented with simple low dissipation AUSM convective scheme, which can be computed without preconditioning which in general destroys the time accuracy. Design/methodology/approach In transient flow computations, the time-step is generally determined from the CFL condition. In this paper, the authors demonstrate the usefulness of ATS based on local time-stepping previously used extensively in ordinary differential equations (ODE) integration. This method is implemented in an implicit framework to ensure the numerical domain of dependence always contains the physical domain of dependence. Findings In this paper, the authors limit their focus to capture the unsteady physics for three cases: Sod’s shock-tube problem, Stokes’ second problem and a circular cylinder. The use of ATS with local truncation error control enables the solver to use the maximum allowable time-step, for the prescribed tolerance of error. The algorithm is also capable of converging very rapidly to the steady state (if there is any) after the initial transient phase. The authors present here only the first-order time-stepping scheme. An algorithmic comparison is made between the proposed adaptive time-stepping method and the commonly used dual time-stepping approach that indicates the former will be more efficient. Originality/value The original method of ATS based on local error control is used extensively in ODE integration, whereas, this method is not so popular in the computational fluid dynamics (CFD) community. In this paper, the authors investigate its use in the unsteady CFD computations. The authors hope that it would provide CFD researchers with an algorithm based on an adaptive time-stepping approach for unsteady calculations.

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