Analysis of Semi-Implicit Time Integration Schemes For Direct Numerical Simulation of Turbulent Convection in Liquid Metals

1992 ◽  
pp. 542-551 ◽  
Author(s):  
M. Wörner ◽  
G. Grötzbach
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Liquid Metals ◽  
Time Integration ◽  
Turbulent Convection ◽  
Implicit Time ◽  
Integration Schemes ◽  
Implicit Time Integration ◽  
Time Integration Schemes

Comparison of Implicit Time Integration Schemes for Nonlinear Dynamic Problems

2010 ◽  
Author(s):  
Murat Demiral
Keyword(s):  
Dynamic Equilibrium ◽  
Time Integration ◽  
Nonlinear Problems ◽  
Implicit Time ◽  
Implicit Methods ◽  
Equilibrium Equations ◽  
Integration Schemes ◽  
Implicit Time Integration ◽  
Time Integration Schemes ◽  
The Stability

Implicit time integration schemes are used to obtain stable and accurate transient solutions of nonlinear problems. Methods that are unconditionally stable in linear analysis are sometimes observed to have convergence problems as in the case of solutions obtained with a trapezoidal method. On the other hand, a composite time integration method employing a trapezoidal rule and a three-point backward rule sequentially in two half steps can be used to obtain accurate results and enhance the stability of the system by means of a numerical damping introduced in the formulation. To have a better understanding of the differences in the numerical implementation of the algorithms of these two methods, a mathematical analysis of dynamic equilibrium equations is performed. Several practical problems are studied to compare the implicit methods.

Finite Element Simulation of Diffusion and Precipitation with Application to Internal Oxidation of Ni-Xwt%Cr Alloys at 950°C

2014 ◽  
Vol 783-786 ◽  
pp. 126-135
Author(s):  
Eric Feulvarch
Keyword(s):  
Finite Element ◽  
Internal Oxidation ◽  
Finite Differences ◽  
Time Integration ◽  
Small Time ◽  
Implicit Time ◽  
Integration Algorithm ◽  
Integration Schemes ◽  
Implicit Time Integration ◽  
Time Integration Schemes

For the simulation of internal oxidation phenomena, different numerical approaches are proposed in the literature based on 1D finite differences or on explicit time integration schemes which need small time-steps leading to very long computation times. The aim of this paper is to detail a multi-dimentional finite element approach which is coupled with an efficient implicit time integration algorithm. The thermodynamic activities and the total mass fractions are both used as principal nodal variables. The use of finite elements rather than finite differences greatly facilitates the meshing of 2D and 3D bodies. Its implicit time-integration allows using much larger time-steps without any degradation of the results. An application is proposed for the modeling of internal oxidation of chromia for Ni-Xwt%Cr alloys at 950°C by considering the barrier effect of precipitates.

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