An adaptive time‐stepping scheme for the numerical simulation of Cahn‐Hilliard equation with variable mobility

2019 ◽  
Vol 99 (7) ◽  
Author(s):  
Abdullah Shah ◽  
Muhammad Sabir ◽  
Sana Ayub
Keyword(s):  
Numerical Simulation ◽  
Time Stepping ◽  
Hilliard Equation ◽  
Adaptive Time ◽  
Cahn Hilliard Equation ◽  
Adaptive Time Stepping

An Adaptive Time-Stepping Strategy for the Cahn-Hilliard Equation

2012 ◽  
Vol 11 (4) ◽  
pp. 1261-1278 ◽  
Author(s):  
Zhengru Zhang ◽  
Zhonghua Qiao
Keyword(s):  
Difference Scheme ◽  
Numerical Simulations ◽  
Large Time ◽  
Second Order ◽  
Time Stepping ◽  
Hilliard Equation ◽  
Adaptive Time ◽  
Energy Stable ◽  
Cahn Hilliard Equation ◽  
Adaptive Time Stepping

AbstractThis paper studies the numerical simulations for the Cahn-Hilliard equation which describes a phase separation phenomenon. The numerical simulation of the Cahn-Hilliard model needs very long time to reach the steady state, and therefore large time-stepping methods become useful. The main objective of this work is to construct the unconditionally energy stable finite difference scheme so that the large time steps can be used in the numerical simulations. The equation is discretized by the central difference scheme in space and fully implicit second-order scheme in time. The proposed scheme is proved to be unconditionally energy stable and mass-conservative. An error estimate for the numerical solution is also obtained with second order in both space and time. By using this energy stable scheme, an adaptive time-stepping strategy is proposed, which selects time steps adaptively based on the variation of the free energy against time. The numerical experiments are presented to demonstrate the effectiveness of the adaptive time-stepping approach.

Parameter-Free Time Adaptivity Based on Energy Evolution for the Cahn-Hilliard Equation

2016 ◽  
Vol 19 (5) ◽  
pp. 1542-1563 ◽  
Author(s):  
Fuesheng Luo ◽  
Tao Tang ◽  
Hehu Xie
Keyword(s):  
Large Time ◽  
Main Idea ◽  
Energy Evolution ◽  
Time Step ◽  
Time Stepping ◽  
Hilliard Equation ◽  
Phase Field Models ◽  
Adaptive Time ◽  
Cahn Hilliard Equation ◽  
Adaptive Time Stepping

AbstractIt is known that large time-stepping method are useful for simulating phase field models. In this work, an adaptive time-stepping strategy is proposed based on numerical energy stability and equi-distribution principle. The main idea is to use the energy variation as an indicator to update the time step, so that the resulting algorithm is free of user-defined parameters, which is different from several existing approaches. Some numerical experiments are presented to illustrate the effectiveness of the algorithms.

scholarly journals Numerical simulation of diffusion MRI signals using an adaptive time-stepping method

2013 ◽  
Vol 59 (2) ◽  
pp. 441-454 ◽  
Author(s):  
Jing-Rebecca Li ◽  
Donna Calhoun ◽  
Cyril Poupon ◽  
Denis Le Bihan
Keyword(s):  
Numerical Simulation ◽  
Diffusion Mri ◽  
Time Stepping ◽  
Adaptive Time ◽  
Adaptive Time Stepping

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

An Adaptive Time Stepping Method for Transient Dynamic Response Analysis

2016 ◽  
Vol 6 (2) ◽  
pp. 152-170
Author(s):  
Jianguo Huang ◽  
Huashan Sheng
Keyword(s):  
Dynamic Response ◽  
Response Analysis ◽  
Dynamic Response Analysis ◽  
Transient Dynamic ◽  
Time Stepping ◽  
Adaptive Time ◽  
Spatial Discretisation ◽  
Transient Dynamic Response ◽  
Adaptive Time Stepping ◽  
Reduced Problem

AbstractAn efficient adaptive time stepping method is proposed for transient dynamic response analysis, which is frequently encountered in civil engineering and elsewhere. The reduced problem following the spatial discretisation can be discretised in the time by a C0-continuous discontinuous Galerkin method, and the adaptive time stepping strategy is based on optimal a posteriori error estimates developed using the energy method. Some numerical experiments demonstrate the effectiveness of our approach.

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