A multi-index variable time step method for the dynamic simulation of multibody systems

1999 ◽  
Vol 44 (11) ◽  
pp. 1579-1598 ◽  
Author(s):  
J. Cardenal ◽  
J. Cuadrado ◽  
P. Morer ◽  
E. Bayo
Keyword(s):  
Dynamic Simulation ◽  
Multibody Systems ◽  
Step Method ◽  
Time Step ◽  
Multi Index ◽  
Variable Time ◽  
Variable Time Step ◽  
Time Step Method

A Multi-Index Variable Time Step Method for the Dynamic Simulation of Multibody Systems

1996 ◽  
Author(s):  
Jesús Cardenal ◽  
Javier Cuadrado ◽  
Eduardo Bayo
Keyword(s):  
Multibody Systems ◽  
New Method ◽  
Step Method ◽  
Time Step ◽  
Multi Index ◽  
Time Step Size ◽  
Variable Time ◽  
Simulation Process ◽  
Variable Time Step ◽  
Time Step Method

Abstract This paper presents a new multi-index variable time step method for the integration of the equations of motion of constrained multibody systems in descriptor form. The basis of the method is the augmented Lagrangian formulation with projections in index-3 and index-1. The new method takes advantage of the better performance of the index-3 formulation for large time steps and of the stability of the index-1 for low time steps, and automatically switches from one method to the other depending on the required accuracy and values of the time step. The modification of time steps is accomplished through the use of a global system invariant such as the kinetic energy stored in the penalty system. This energy provides a good measure of the global error introduced by the numerical integration during the simulation process, and permits a simple and reliable strategy for varying the time step. Overall, the new method is quite efficient and robust: it is suitable for stiff and non-stiff systems, it is robust for all time step sizes, it works for singular configurations, redundant constraints and topology changes. Also, the constraints in positions, velocities and accelerations are satisfied to machine precision during the simulation process. The method is always more accurate as the time step size decreases.

scholarly journals One Phase Moving Boundary Problem

2019 ◽  
Vol 9 (2) ◽  
pp. 3427-3431
Keyword(s):  
Boundary Problem ◽  
Moving Boundary ◽  
Moving Boundary Problem ◽  
Initial Time ◽  
Step Method ◽  
Time Step ◽  
Spherical Droplet ◽  
Variable Time ◽  
Variable Time Step ◽  
Time Step Method

In this paper we introduced a variable time step method to obtain interface to moving boundary problem for Slab and Sphere. We present the basic difficulty, apart from the need to find the moving boundary, that there is no domain for the space variable. This difficulty is handled by the age old principles of basic mathematics. Naturally, giving symbolic names to the unknowns develop equations involving them and solve it using the conditions of the problem. High order accurate initial time step sizes for given space step size are obtained with the help of Green’s theorem. The Subsequent time steps are obtained by an iterative scheme. This variable time step method handles Dirichlet’s problem of freezing or melting of a Slab and spherical droplet.

scholarly journals An improved moving-boundary heat exchanger model using the variable time step method

2012 ◽  
Vol 31 ◽  
pp. 97-102 ◽  
Author(s):  
Xing Xue ◽  
Junmin Wang ◽  
Xianming Feng ◽  
Weikang Chen ◽  
Baoqiang Li
Keyword(s):  
Heat Exchanger ◽  
Moving Boundary ◽  
Step Method ◽  
Time Step ◽  
Variable Time ◽  
Variable Time Step ◽  
Time Step Method
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