scholarly journals Finite element/finite volume approaches with adaptive time stepping strategies for transient thermal problems

Sadhana ◽  
1994 ◽  
Vol 19 (5) ◽  
pp. 765-783 ◽  
Author(s):  
Ram V Mohan ◽  
Kumar K Tamma
Keyword(s):  
Finite Element ◽  
Finite Volume ◽  
Time Stepping ◽  
Adaptive Time ◽  
Transient Thermal ◽  
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.

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.

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