Incompressibility in Dynamic Relaxation

1987 ◽  
Vol 54 (3) ◽  
pp. 539-544 ◽  
Author(s):  
S. A. Silling
Keyword(s):  
Solid Mechanics ◽  
Linear Equations ◽  
Time Integration ◽  
Natural State ◽  
System Of Linear Equations ◽  
Dynamic Relaxation ◽  
Explicit Time Integration ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
Incompressibility Constraint

A method is described for enforcing the incompressibility constraint in large-deformation solid mechanics computations using dynamic relaxation. The method is well-suited to explicit time-integration schemes because it does not require the solution of a system of linear equations. It is based on an analogy with thermoelasticity involving manipulation of the natural state of a solid.

3D nonlinear MHD calculations using implicit and explicit time integration schemes

1986 ◽  
Vol 65 (2) ◽  
pp. 253-272 ◽  
Author(s):  
L. Garcia ◽  
H.R. Hicks ◽  
B.A. Carreras ◽  
L.A. Charlton ◽  
J.A. Holmes
Keyword(s):  
Time Integration ◽  
Explicit Time Integration ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
Implicit And Explicit

scholarly journals Implicit or explicit time integration schemes in the PFEM modeling of metal cutting processes

2021 ◽  
Author(s):  
J. M. Rodriguez ◽  
S. Larsson ◽  
J. M. Carbonell ◽  
P. Jonsén
Keyword(s):  
Metal Cutting ◽  
Computing Time ◽  
Time Integration ◽  
Correct Selection ◽  
Explicit Time Integration ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
Time Marching ◽  
Cutting Processes ◽  
Implicit And Explicit

AbstractThis work presents the development of an explicit/implicit particle finite element method (PFEM) for the 2D modeling of metal cutting processes. The purpose is to study the efficiency of implicit and explicit time integration schemes in terms of precision, accuracy and computing time. The formulation for implicit and explicit time marching schemes is developed, and a detailed study on the explicit solution steps is presented. The PFEM remeshing procedures for insertion and removal of particles have been improved to model the multiple scales of time and/or space of the solution. The detection and treatment of the rigid tool contact are presented for both, implicit and explicit schemes. The performance of explicit/implicit integration is studied with a set of different two-dimensional orthogonal cutting tests of AISI 4340 steel at cutting speeds ranging from 1 m/s up to 30 m/s. It was shown that if the correct selection of the time integration scheme is made, the computing time can decrease up to 40 times. It allows us to affirm that the computing time of the PFEM simulations can be excessive due to the used time marching scheme independently of the meshing process. As a practical result, a set of recommendations to select the time integration schemes for a given cutting speed are given. This is intended to minimize one of the negative constraints pointed out by the industry when using metal cutting simulators.

Multirate Implicit-Explicit Time Integration Schemes in Atmospheric Modelling

2010 ◽  
Author(s):  
Martin Schlegel ◽  
Oswald Knoth ◽  
Martin Arnold ◽  
Ralf Wolke ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Time Integration ◽  
Explicit Time Integration ◽  
Atmospheric Modelling ◽  
Integration Schemes ◽  
Time Integration Schemes

scholarly journals Damping Acoustic Modes in Compressible Horizontally Explicit Vertically Implicit (HEVI) and Split-Explicit Time Integration Schemes

2018 ◽  
Vol 146 (6) ◽  
pp. 1911-1923 ◽  
Author(s):  
Joseph B. Klemp ◽  
William C. Skamarock ◽  
Soyoung Ha
Keyword(s):  
Acoustic Waves ◽  
Acoustic Noise ◽  
Equations Of Motion ◽  
Time Integration ◽  
Time Step ◽  
Explicit Time Integration ◽  
Physical Interest ◽  
Acoustic Modes ◽  
Integration Schemes ◽  
Time Integration Schemes

Although the equations of motion for a compressible atmosphere accommodate acoustic waves, these modes typically play an insignificant role in atmospheric processes of physical interest. In numerically integrating the compressible equations, it is often beneficial to filter these acoustic modes to control acoustic noise and prevent its artificial growth. Here, a new technique is proposed for filtering the 3D divergence that may damp acoustic modes more effectively than filters previously implemented in numerical modes using horizontally explicit vertically implicit (HEVI) and split-explicit time integration schemes. With this approach, a divergence damping term is added as a final adjustment to the horizontal velocity at the new time level after completing the vertically implicit portion of the time step. In this manner, the divergence used in the filter term has exactly the same numerical form as that used in the discrete pressure equation. Analysis of the dispersion equation for this form of the filter documents its stability characteristics and confirms that it effectively damps acoustic modes with little artificial influence on the amplitude or propagation of the gravity wave modes that are of physical interest. Some specific aspects of the implementation of the filter in the Model for Prediction Across Scales (MPAS) are discussed, and results are presented to illustrate some of the beneficial aspects of suppressing acoustic noise.

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