Adaptive Time Stepping with the Modified Local Error Method for Coupled Flow-Geomechanics Modeling

2017 ◽  
Author(s):  
Cheng An ◽  
Peng Zhou ◽  
Bicheng Yan ◽  
Yuhe Wang ◽  
John Killough
Keyword(s):  
Local Error ◽  
Coupled Flow ◽  
Time Stepping ◽  
Adaptive Time ◽  
Error Method ◽  
Adaptive Time Stepping

AN ADAPTIVE TIME-STEPPING PROCEDURE BASED ON THE SCALED BOUNDARY FINITE ELEMENT METHOD FOR ELASTODYNAMICS

2012 ◽  
Vol 09 (01) ◽  
pp. 1240007 ◽  
Author(s):  
Z. H. ZHANG ◽  
Z. J. YANG ◽  
GUOHUA LIU
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Local Error ◽  
Error Estimator ◽  
Time Step ◽  
Time Stepping ◽  
Time Increment ◽  
Adaptive Time ◽  
Adaptive Time Stepping ◽  
Scaled Boundary Finite Element

This study develops an adaptive time-stepping procedure of Newmark integration scheme for transient elastodynamic problems, based on the semi-analytical scaled boundary finite element method (SBFEM). In each time step, a posteriori local error estimator based on the linear distributed acceleration is employed to estimate the error caused by the time discretization. The total energy of the domain, consisting of the kinetic energy and the strain energy, is calculated semi-analytically. The time increment is automatically adjusted according to a simple criterion. Three examples with stress wave propagation were modeled. The numerical results show that the developed method is capable of limiting the local error estimator within specified targets by using an optimal time increment in each time step.

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.

Fast Conjugate Heat Transfer Simulation of Long Transient Flexible Operations Using Adaptive Time Stepping

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
R. Maffulli ◽  
L. He ◽  
P. Stein ◽  
G. Marinescu
Keyword(s):  
Heat Transfer ◽  
Conjugate Heat Transfer ◽  
Time Derivative ◽  
Computational Cost ◽  
Strong Impact ◽  
Time Step ◽  
Time Stepping ◽  
Adaptive Time ◽  
Fully Coupled ◽  
Adaptive Time Stepping

The emerging renewable energy market calls for more advanced prediction tools for turbine transient operations in fast startup/shutdown cycles. Reliable numerical analysis of such transient cycles is complicated by the disparity in time scales of the thermal responses in fluid and solid domains. Obtaining fully coupled time-accurate unsteady conjugate heat transfer (CHT) results under these conditions would require to march in both domains using the time-step dictated by the fluid domain: typically, several orders of magnitude smaller than the one required by the solid. This requirement has strong impact on the computational cost of the simulation as well as being potentially detrimental to the accuracy of the solution due to accumulation of round-off errors in the solid. A novel loosely coupled CHT methodology has been recently proposed, and successfully applied to both natural and forced convection cases that remove these requirements through a source-term based modeling (STM) approach of the physical time derivative terms in the relevant equations. The method has been shown to be numerically stable for very large time steps with adequate accuracy. The present effort is aimed at further exploiting the potential of the methodology through a new adaptive time stepping approach. The proposed method allows for automatic time-step adjustment based on estimating the magnitude of the truncation error of the time discretization. The developed automatic time stepping strategy is applied to natural convection cases under long (2000 s) transients: relevant to the prediction of turbine thermal loads during fast startups/shutdowns. The results of the method are compared with fully coupled unsteady simulations showing comparable accuracy with a significant reduction of the computational costs.

scholarly journals An error-controlled adaptive time-stepping method for particle advancement in coupled CFD-DEM simulations

2021 ◽  
Vol 379 ◽  
pp. 203-216
Author(s):  
Hariswaran Sitaraman ◽  
Deepthi Vaidhynathan ◽  
Ray Grout ◽  
Thomas Hauser ◽  
Christine M. Hrenya ◽  
...  
Keyword(s):  
Time Stepping ◽  
Dem Simulations ◽  
Adaptive Time ◽  
Adaptive Time Stepping
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