The Critical Time Step for Finite-Element Solutions to Two-Dimensional Heat-Conduction Transients

1978 ◽  
Vol 100 (1) ◽  
pp. 120-127 ◽  
Author(s):  
G. E. Myers
Keyword(s):  
Boundary Conditions ◽  
Nodal Point ◽  
Critical Time ◽  
Time Step ◽  
Various Boundary Conditions ◽  
Quadrilateral Elements ◽  
Triangular Elements ◽  
The Finite Difference Method ◽  
Critical Time Step ◽  
Element Shape

Computationally-useful methods of estimating the critical time step for linear triangular elements and for linear quadrilateral elements are given. Irregular nodal-point arrangements, position-dependent properties, and a variety of boundary conditions can be accommodated. The effects of boundary conditions and element shape on the critical time step are discussed. Numerical examples are presented to illustrate the effect of various boundary conditions and for comparison to the finite-difference method.

Implicit-Explicit Finite Elements in Transient Analysis: Stability Theory

1978 ◽  
Vol 45 (2) ◽  
pp. 371-374 ◽  
Author(s):  
T. J. R. Hughes ◽  
W. K. Liu
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Transient Analysis ◽  
Critical Time ◽  
Unconditional Stability ◽  
Time Step ◽  
Explicit Finite Element ◽  
New Family ◽  
Critical Time Step ◽  
Analysis Stability

A stability analysis is carried out for a new family of implicit-explicit finite-element algorithms. The analysis shows that unconditional stability may be achieved for the implicit finite elements and that the critical time step of the explicit elements governs for the system.

scholarly journals A Weighted Residual Parabolic Acceleration Time Integration Method for Problems in Structural Dynamics

2007 ◽  
Vol 7 (3) ◽  
pp. 227-238 ◽  
Author(s):  
S.H. Razavi ◽  
A. Abolmaali ◽  
M. Ghassemieh
Keyword(s):  
Fourth Order ◽  
Initial Conditions ◽  
Time Integration ◽  
Critical Time ◽  
Linear Acceleration ◽  
Time Step ◽  
Time Integration Method ◽  
Acceleration Method ◽  
The Stability ◽  
Critical Time Step

AbstractIn the proposed method, the variation of displacement in each time step is assumed to be a fourth order polynomial in time and its five unknown coefficients are calculated based on: two initial conditions from the previous time step; satisfying the equation of motion at both ends of the time step; and the zero weighted residual within the time step. This method is non-dissipative and its dispersion is considerably less than in other popular methods. The stability of the method shows that the critical time step is more than twice of that for the linear acceleration method and its convergence is of fourth order.

Increasing the critical time step: micro-inertia, inertia penalties and mass scaling

2011 ◽  
Vol 47 (6) ◽  
pp. 657-667 ◽  
Author(s):  
Harm Askes ◽  
Duc C. D. Nguyen ◽  
Andy Tyas
Keyword(s):  
Critical Time ◽  
Time Step ◽  
Mass Scaling ◽  
Critical Time Step

NPSS Volume Dynamic Capability for Real-Time Physics Based Engine Modeling

2011 ◽  
Author(s):  
Christopher Argote ◽  
Brian K. Kestner ◽  
Dimitri N. Mavris
Keyword(s):  
Boundary Conditions ◽  
Real Time ◽  
Fluid Dynamic ◽  
Critical Time ◽  
Momentum Conservation ◽  
Drop Out ◽  
Dynamic Equations ◽  
High Fidelity ◽  
Time Step ◽  
Engine Cycle

This paper introduces a new capability and method for solving transient engine cycles for the potential application of real-time simulation in the cycle analysis code Numerical Propulsion System Simulation (NPSS). This method utilizes a new element which models volume dynamics, a set of equations that characterize the unsteady behavior of fluid dynamic and thermodynamic properties with respect to a volume and boundary conditions. These equations are derived from the Euler equations for conservation of mass, momentum, and energy. Physics based real-time engine models often consider the effects of volume dynamics; however it is normal to see the momentum conservation drop out. This is largely due to the high frequency response of momentum which yields smaller time steps thus increasing the cost associated with computation time. The new high fidelity volume dynamics element is introduced with all three conservations laws working together. NPSS’s interpreted language provides the flexibility to allow the volume dynamics to be solved explicitly, however by rearranging the momentum equation, it can be solved implicitly therefore increasing the critical time step. In addition to improving transient modeling fidelity, the new volume dynamics element can be used to drive the cycle. Rather than balancing error terms in a Newton-Raphson solver, the volume dynamic equations provide the necessary communication between the engine cycle and boundary conditions. These equations alone can drive the engine model towards a steady state solution. Using a basic forward Euler numerical integration technique to solve the volume dynamic equations the engine cycle only requires a single pass per time step. This document illustrates the development of both the new element and the methodology in cycle modeling using the volume dynamics. Two example models are created and analyzed in this paper, first, a simple inlet, duct, nozzle system is analyzed. Second, a separate flow long duct turbojet is examined. These two models are used to demonstrate the real time capabilities of the high fidelity transient analysis, as well as highlight some of the challenges in the implementation of volume dynamics on a given cycle.

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