Conservative Split-Explicit Time Integration Methods for the Compressible Nonhydrostatic Equations

2007 ◽  
Vol 135 (8) ◽  
pp. 2897-2913 ◽  
Author(s):  
J. B. Klemp ◽  
W. C. Skamarock ◽  
J. Dudhia
Keyword(s):  
Equations Of Motion ◽  
Time Integration ◽  
Test Cases ◽  
Explicit Integration ◽  
Linear Dispersion ◽  
Acoustic Gravity Waves ◽  
Wide Range ◽  
Terrain Following ◽  
Integration Techniques ◽  
Time Integration Methods

Abstract Historically, time-split schemes for numerically integrating the nonhydrostatic compressible equations of motion have not formally conserved mass and other first-order flux quantities. In this paper, split-explicit integration techniques are developed that numerically conserve these properties by integrating prognostic equations for conserved quantities represented in flux form. These procedures are presented for both terrain-following height and hydrostatic pressure (mass) vertical coordinates, two potentially attractive frameworks for which the equation sets and integration techniques differ significantly. For each set of equations, the linear dispersion equation for acoustic/gravity waves is derived and analyzed to determine which terms must be solved in the small (acoustic) time steps and how these terms are represented in the time integration to achieve stability. Efficient techniques for including numerical filters for acoustic and external modes are also presented. Simulations for several idealized test cases in both the height and mass coordinates are presented to demonstrate that these integration techniques appear robust over a wide range of scales, from subcloud to synoptic.

Direct Time Integration Methods for Structural Acoustics and Far Field Scattering Computations

1995 ◽  
Vol 117 (4) ◽  
pp. 488-492 ◽  
Author(s):  
J. P. Wright
Keyword(s):  
Numerical Solutions ◽  
Time Integration ◽  
Three Dimensional ◽  
Spherical Geometry ◽  
Far Field ◽  
Structural Acoustics ◽  
Explicit Integration ◽  
Orthogonal Function ◽  
Preliminary Validation ◽  
Time Integration Methods

Procedures are described for doing: (a) transient three dimensional structural acoustics computations, using a combination of modal and finite element techniques in space and explicit integration in time; (b) far field scattering computations, using orthogonal function expansions and the method of characteristics. These methods are discussed and preliminary validation of the approach is accomplished by comparing numerical solutions with available analytic results for some problems in spherical geometry.

Implicit-Explicit Time Integration in Multibody Dynamics

2005 ◽  
Author(s):  
Martin Arnold ◽  
Gerhard Hippmann
Keyword(s):  
Multibody Dynamics ◽  
Large Scale ◽  
Multibody System ◽  
Equations Of Motion ◽  
Time Integration ◽  
Specific Structure ◽  
Implicit Methods ◽  
Explicit Time Integration ◽  
Dynamical Simulation ◽  
Time Integration Methods

Robust and efficient time integration methods in multibody dynamics are tailored to the specific structure of the equations of motion. In the present paper we discuss the combination of explicit methods for non-stiff solution components with implicit methods for stiff solution components and constraints. The methods are successfully used in the dynamical simulation of large-scale multibody system models that display a clear partitioning into stiff and non-stiff subsystems.

A Stable Fluid-Structure-Interaction Algorithm: Application to Industrial Problems

2005 ◽  
Vol 128 (4) ◽  
pp. 516-524 ◽  
Author(s):  
D. Abouri ◽  
A. Parry ◽  
A. Hamdouni ◽  
E. Longatte
Keyword(s):  
Tube Bundle ◽  
Equations Of Motion ◽  
Mechanical Analysis ◽  
Industrial Applications ◽  
Explicit Integration ◽  
Flow Meter ◽  
Navier Stokes Equation ◽  
Fluid Structure ◽  
Positive Displacement ◽  
Wide Range

Fluid-structure interactions occur in a wide range of industrial applications, including vibration of pipe-work, flow meters, and positive displacement systems as well as many flow control devices. This paper outlines computational methods for calculating the dynamic interaction between moving parts and the flow in a flow-meter system. Coupling of phenomena is allowed without need for access to the source codes and is thus suitable for use with commercially available codes. Two methods are presented: one with an explicit integration of the equations of motion of the mechanism and the other, with implicit integration. Both methods rely on a Navier-Stokes equation solver for the fluid flow. The more computationally expensive, implicit method is recommended for mathematically stiff mechanisms such as piston movement. Industrial-application examples shown are for positive displacement machines, axial turbines, and steam-generator tube-bundle vibrations. The advances in mesh technology, including deforming meshes with nonconformal sliding interfaces, open up this new field of application of computational fluid dynamics and mechanical analysis in flow meter design.

scholarly journals A Stable Fluid Rigid Body Interaction Algorithm: Application to Industrial Problems

2004 ◽  
Author(s):  
D. Abouri ◽  
A. Parry ◽  
A. Hamdouni
Keyword(s):  
Equations Of Motion ◽  
Mechanical Analysis ◽  
Industrial Applications ◽  
Navier Stokes ◽  
Explicit Integration ◽  
Flow Meter ◽  
Navier Stokes Equation ◽  
Positive Displacement ◽  
Flow Control Devices ◽  
Wide Range

Fluid-mechanism interactions occur in a wide range of flow meter categories including turbine and positive displacement systems as well as many flow control devices. This paper outlines computational methods for calculating the dynamic interaction between moving parts and the flow in a flow meter system. Coupling of phenomena is allowed without need for access to the source codes and is thus suitable for use with commercially available codes. Two methods are presented one with an explicit integration of the equations of motion of the mechanism and the other with implicit integration. Both methods rely on a Navier-Stokes equation solver for the fluid flow. The more computationally expensive implicit method is recommended for mathematically stiff mechanisms such as piston movement. Example industrial applications shown are for positive displacement machines and axial turbines. The advances in mesh technology including deforming meshes with non-conformal sliding interfaces opens up this new field of application for Computational Fluid Dynamics and mechanical analysis in flow meter design.

scholarly journals Effects of Precast Cladding Systems on Dynamic Characteristics of Steel Frame Buildings by Ambient and Free Vibration Tests

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Jun Ma ◽  
Shinji Nakata ◽  
Akihito Yoshida ◽  
Yukio Tamura
Keyword(s):  
Free Vibration ◽  
Dynamic Characteristics ◽  
Steel Frame ◽  
Ambient Vibration ◽  
Test Cases ◽  
Vibration Method ◽  
External Wall ◽  
Wide Range ◽  
Cladding Panels ◽  
Vibration Tests

Full-scale tests on a one-story steel frame structure with a typical precast cladding system using ambient and free vibration methods are described in detail. The cladding system is primarily composed of ALC (Autoclaved Lightweight Concrete) external wall cladding panels, gypsum plasterboard interior linings, and window glazing systems. Ten test cases including the bare steel frame and the steel frame with addition of different parts of the precast cladding system are prepared for detailed investigations. The amplitude-dependent dynamic characteristics of the test cases including natural frequencies and damping ratios determined from the tests are presented. The effects of the ALC external wall cladding panels, the gypsum plasterboard interior linings, and the window glazing systems on the stiffness and structural damping of the steel frame are discussed in detail. The effect of the precast cladding systems on the amplitude dependency of the dynamic characteristics and the tendencies of the dynamic parameters with respect to the structural response amplitude are investigated over a wide range. Furthermore, results estimated from the ambient vibration method are compared with those from the free vibration tests to evaluate the feasibility of the ambient vibration method.

Constrained optimal terrain following/threat avoidance trajectory planning using network flow

2014 ◽  
Vol 118 (1203) ◽  
pp. 523-539 ◽  
Author(s):  
R. Zardashti ◽  
A. A. Nikkhah ◽  
M. J. Yazdanpanah
Keyword(s):  
Cost Function ◽  
Trajectory Planning ◽  
Network Flow ◽  
Equations Of Motion ◽  
Minimum Cost ◽  
Masking Effect ◽  
Search Problem ◽  
Starting Point ◽  
Terrain Following ◽  
Threat Avoidance

AbstractThis paper focuses on the trajectory planning for a UAV on a low altitude terrain following/threat avoidance (TF/TA) mission. Using a grid-based approximated discretisation scheme, the continuous constrained optimisation problem into a search problem is transformed over a finite network. A variant of the Minimum Cost Network Flow (MCNF) to this problem is then applied. Based on using the Digital Terrain Elevation Data (DTED) and discrete dynamic equations of motion, the four-dimensional (4D) trajectory (three spatial and one time dimensions) from a starting point to an end point is obtained by minimising a cost function subject to dynamic and mission constraints of the UAV. For each arc in the grid, a cost function is considered as the combination of the arc length, fuel consumption and flight time. The proposed algorithm which considers dynamic and altitude constraints of the UAV explicitly is then used to obtain the feasible trajectory. The resultant trajectory can increase the survivability of the UAV using the threat region avoidance and the terrain masking effect. After obtaining the feasible trajectory, an improved algorithm is proposed to smooth the trajectory. The numeric results are presented to verify the capability of the proposed approach to generate admissible trajectory in minimum possible time in comparison to the previous works.

NOVEL COUPLING CONSTRAINT TECHNIQUE FOR EXPLICIT FINITE ELEMENT ANALYSIS

2004 ◽  
Vol 01 (02) ◽  
pp. 309-328
Author(s):  
R. J. HO ◽  
S. A. MEGUID ◽  
R. G. SAUVÉ
Keyword(s):  
Finite Element ◽  
Current Method ◽  
Explicit Integration ◽  
Rotation Tensor ◽  
Element Analysis ◽  
Explicit Finite Element ◽  
Explicit Finite Element Analysis ◽  
Wide Range ◽  
Large Rotations ◽  
Generalized Constraint

This paper presents a unified novel technique for enforcing nonlinear beam-to-shell, beam-to-solid, and shell-to-solid constraints in explicit finite element formulations. The limitations of classical multi-point constraint approaches are examined at length, particularly in the context of explicit solution schemes. Novel formulation of a generalized constraint method that ensures proper element coupling is then presented, and its computer implementation in explicit integration algorithms is discussed. Crucial in this regard is the accurate and efficient representation of finite rotations, accomplished using an incremental rotation tensor. The results of some illustrative test cases show the accuracy and robustness of the newly developed algorithm for a wide range of deformation, including that in which large rotations are encountered. When compared to existing works, the salient features of the current method are in evidence.

Time Integration Incorporated Sensitivity Analysis With Generalized-α Method for Multibody Dynamics Systems

2011 ◽  
Author(s):  
Guang Dong ◽  
Zheng-Dong Ma ◽  
Gregory Hulbert ◽  
Noboru Kikuchi
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Dynamic Loading ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Time Integration ◽  
Optimization Method ◽  
Sensitivity Analysis Method ◽  
System Equations ◽  
Consecutive Time

The topology optimization method is extended for the optimization of geometrically nonlinear, time-dependent multibody dynamics systems undergoing nonlinear responses. In particular, this paper focuses on sensitivity analysis methods for topology optimization of general multibody dynamics systems, which include large displacements and rotations and dynamic loading. The generalized-α method is employed to solve the multibody dynamics system equations of motion. The developed time integration incorporated sensitivity analysis method is based on a linear approximation of two consecutive time steps, such that the generalized-α method is only applied once in the time integration of the equations of motion. This approach significantly reduces the computational costs associated with sensitivity analysis. To show the effectiveness of the developed procedures, topology optimization of a ground structure embedded in a planar multibody dynamics system under dynamic loading is presented.

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

Calculation of the primary trajectories of seeds and other particles in strong winds

1983 ◽  
Vol 219 (1215) ◽  
pp. 217-217
Keyword(s):  
Equations Of Motion ◽  
Aerodynamic Resistance ◽  
Reynolds Numbers ◽  
Spherical Particles ◽  
Spores And Pollen ◽  
General Terms ◽  
Wide Range ◽  
Strong Winds ◽  
Dispersal Distances ◽  
Enormous Number

The movement of variously dense spherical particles representing a variety of seeds, fruits, spores and pollen, and released from rest into arbitrary winds and a gravitational field is discussed in general terms that account in detail for changes in the quasi-static aerodynamic resistance to motion experienced by such particles during aerial flight. A hybrid analytical-empirical law is established which describes this resistance fairly accurately for particle Reynolds numbers in the range 0—60 000 and that allows for the numerical integration of the equations of motion so as to cover a very wide range of flight conditions. This makes possible the provision of a set of four-parameter universal range tables from which the dispersal distances for an enormous number of practical cases may be estimated. One particular case of particle movement in a region of pseudo-thermal convection is also discussed and this shows how a marked degree of deposition concentration may be induced in some circumstances by such a flow. Botanists and ecologists concerned with seed and particle dispersal in the environment may find the universal range tables of particular interest and use. This is because the tables obviate the need for the integration of the equations of motion when dealing with individual cases and permit an estimation of range purely on the basis of the specified quantities of particle size, density and altitude of release, atmospheric wind speed, density and viscosity, and the acceleration due to gravity.

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