Solving linear systems from dynamical energy analysis - using and reusing preconditioners

2021 ◽  
Vol 263 (5) ◽  
pp. 1041-1052
Author(s):  
Martin Richter ◽  
Gregor Tanner ◽  
Bruno Carpentieri ◽  
David J. Chappell
Keyword(s):  
Wave Equations ◽  
Energy Analysis ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Iterative Solvers ◽  
Computational Method ◽  
Computational Time ◽  
Shell Elements ◽  
Finite Dimensional ◽  
Large Matrix

Dynamical energy analysis (DEA) is a computational method to address high-frequency vibro-acoustics in terms of ray densities. It has been used to describe wave equations governing structure-borne sound in two-dimensional shell elements as well as three-dimensional electrodynamics. To describe either of those problems, the wave equation is reformulated as a propagation of boundary densities. These densities are expressed by finite dimensional approximations. All use-cases have in common that they describe the resulting linear problem using a very large matrix which is block-sparse, often real-valued, but non-symmetric. In order to efficiently use DEA, it is therefore important to also address the performance of solving the corresponding linear system. We will cover three aspects in order to reduce the computational time: The use of preconditioners, properly chosen initial conditions, and choice of iterative solvers. Especially the aspect of potentially reusing preconditioners for different input parameters is investigated.

An Investigation Into Nonlinear Growth Rate of Two-Dimensional and Three-Dimensional Single-Mode Richtmyer–Meshkov Instability Using an Arbitrary-Lagrangian–Eulerian Algorithm

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Mike Probyn ◽  
Ben Thornber ◽  
Dimitris Drikakis ◽  
David Youngs ◽  
Robin Williams
Keyword(s):  
Growth Rate ◽  
Numerical Scheme ◽  
Initial Conditions ◽  
Numerical Study ◽  
Three Dimensional ◽  
Single Mode ◽  
Computational Time ◽  
Initial Growth ◽  
Arbitrary Lagrangian Eulerian ◽  
Layer Width

This paper presents an investigation into the use of a moving mesh algorithm for solving unsteady turbulent mixing problems. The growth of a shock induced mixing zone following reshock, using an initial setup comparable to that of existing experimental work, is used to evaluate the behavior of the numerical scheme for single-mode Richtmyer–Meshkov instability (SM-RMI). Subsequently the code is used to evaluate the growth rate for a range of different initial conditions. The initial growth rate for three-dimensional (3D) SM Richtmyer–Meshkov is also presented for a number of different initial conditions. This numerical study details the development of the mixing layer width both prior to and after reshock. The numerical scheme used includes an arbitrary Lagrangian–Eulerian grid motion which is successfully used to reduce the mesh size and computational time while retaining the accuracy of the simulation results. Varying initial conditions shows that the growth rate after reshock is independent of the initial conditions for a SM provided that the initial growth remains in the linear regime.

The Characteristics Research of Tube Vortex Based on Large Eddy Simulation

2011 ◽  
Vol 121-126 ◽  
pp. 3657-3661
Author(s):  
Dun Zhang ◽  
Yuan Zheng ◽  
Ying Zhao ◽  
Jian Jun Huang
Keyword(s):  
Large Eddy Simulation ◽  
Turbulent Flow ◽  
Complex Geometry ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Computational Method ◽  
Francis Turbine ◽  
Eddy Simulation ◽  
Large Eddy

Numerical simulation of three-dimensional transient turbulent flow in the whole flow passage of a Francis turbine were based upon the large eddy simulation(LES) technique on Smargorinsky model and sliding mesh technology. The steady flow data simulated with the standard k-εmodel was used as the initial conditions for the unsteady simulation. The results show that LES can do well transient turbulent flow simulation in a Francis turbine with complex geometry. The computational method provides some reference for exploring the mechanism of eddy formation in a complex turbulent of hydraulic machinery.

Moving least-squares finite element method

2007 ◽  
Vol 221 (9) ◽  
pp. 1019-1036 ◽  
Author(s):  
M Musivand-Arzanfudi ◽  
H Hosseini-Toudeshky
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Three Dimensional ◽  
Meshless Methods ◽  
Computational Method ◽  
Computational Time ◽  
Moving Least Squares ◽  
Shape Functions ◽  
Element Method

A new computational method here called moving least-squares finite element method (MLSFEM) is presented, in which the shape functions of the parametric elements are constructed using moving least-squares approximation. While preserving some excellent characteristics of the meshless methods such as elimination of the volumetric locking in near-incompressible materials and giving accurate strains and stresses near the boundaries of the problem, the computational time is decreased by constructing the meshless shape functions in the stage of creating parametric elements and then utilizing them for any new problem. Moreover, it is not necessary to have knowledge about the full details of the shape function generation method in future uses. The MLSFEM also eliminates another drawback of meshless methods associated with the lack of accordance between the integration cells and the problem boundaries. The method is described for two-dimensional problems, but it is extendable for three-dimensional problems too. The MLSFEM does not require the complex mesh generation. Excellent results can be obtained even using a simple mesh. A technique is also presented for isoparametric mapping which enables best possible mapping via a constrained optimization criterion. Several numerical examples are analysed to show the efficiency and convergence of the method.

An Approximate Three-Dimensional Solution for Melting or Freezing Around a Buried Pipe Beneath a Free Surface

1986 ◽  
Vol 108 (4) ◽  
pp. 900-906 ◽  
Author(s):  
G.-P. Zhang ◽  
S. Weinbaum ◽  
L. M. Jiji
Keyword(s):  
Approximate Solution ◽  
Free Surface ◽  
Phase Change ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Computational Time ◽  
Buried Pipe ◽  
Dimensional Solution ◽  
Pipe Surface

This paper presents a quasi-steady-state approximate solution for small Stefan number for the three-dimensional melting or freezing around a fluid-carrying pipe buried in a semi-infinite phase change medium (PCM). The two-dimensional quasi-steady approximate solution method, the virtual free surface technique [18], has been extended to three dimensions where axial thermal interaction between the moving fluid and the PCM is considered. Of particular interest in the motion of the phase change interface and the time variation of the axial temperature distribution in the fluid. Due to the singularities of the differential equations along the pipe surface, an axisymmetric analytic solution is provided for the region near the pipe wall. Solutions are presented for several representative dimensionless pipe burial depths and initial conditions. The computational time to predict the three-dimensional interface location up to 10 years is several minutes on an IBM 4341 computer.

Mixed-dimensional coupling modeling for laser forming process

2014 ◽  
Vol 228 (16) ◽  
pp. 2950-2959
Author(s):  
Hong Shen ◽  
Jun Hu ◽  
Zhenqiang Yao
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Shell Element ◽  
Element Model ◽  
Thermomechanical Analysis ◽  
Coupling Method ◽  
Computational Time ◽  
Laser Forming ◽  
Forming Process ◽  
Shell Elements

Efficient laser forming modeling for industrial application is still in the developing stage and many researchers are in the process of modifying it. Conventional three-dimensional finite element models are still expensive on computational time. In this paper, a finite element model adopting a shell-solid coupling technique is developed for the thermomechanical analysis of laser forming process. In the shell-solid coupling method, an additional shell element plane is utilized to transfer heat flux and displacement from the solid elements to the shell elements. The effects of the additional interface shell element thickness on temperature distribution and final distortion are investigated. The presented shell-solid coupling method is evaluated by the results of three-dimensional simulations and experimental data.

scholarly journals Vibration Control of Nonlinear Three‐dimensional Marine Riser Model with Output Constraints

2021 ◽  
Author(s):  
Min Wan ◽  
Yanxia Yin ◽  
Jun Liu ◽  
Xiaoqiang Guo
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
External Disturbance ◽  
Three Dimensional ◽  
Distributed Parameter ◽  
Marine Riser ◽  
Control Laws ◽  
Finite Dimensional ◽  
Output Constraints ◽  
The Stability

Abstract A typical three-dimensional flexible marine riser which is described by a distributed parameter system with several partial differential equations and ordinary differential equations is considered in this paper, we are aiming at limiting the top displacement of riser within restricted ranges. Appropriate boundary controls by integrating finite-dimensional backstepping technique with barrier Lyapunov functions are put forwarded to suppress the vibration of flexible riser under the external disturbance. The stability of the closed-loop system with the designed boundary control laws is proved by Lyapunov’s synthetic method without any discretization or simplification of the dynamic in the time and space when the initial conditions are satisfied. Furthermore, in order to illustrate the effectiveness of proposed controls laws, numerical simulation studies are carried.

On Computation of the Motion of Elastic Rods

1974 ◽  
Vol 41 (3) ◽  
pp. 777-780 ◽  
Author(s):  
R. P. Nordgren
Keyword(s):  
Initial Conditions ◽  
Three Dimensional ◽  
Free Fall ◽  
Finite Amplitude ◽  
Computational Method ◽  
Elastic Rods ◽  
Explicit Method ◽  
Finite Difference Approximations ◽  
Method Of Solution ◽  
Rigid Plane

A computational method is developed for the finite-amplitude three-dimensional motion of inextensible elastic rods with equal principal stiffnesses. The method also applies to the two-dimensional motion of such rods with unequal principal stiffnesses. For these two classes of problems the equations of the classical theory of rods are reduced to a non-linear vector equation of motion together with the inextensibility condition and appropriate boundary and initial conditions. Consistent finite-difference approximations are introduced and a semi-explicit method of solution is devised. The approximate limitation for numerical stability of the method is shown to be the same as for the usual explicit method in linear beam dynamics. By way of example the method is applied to the free fall of a circular pipe through water onto a rigid plane from a suspended initial configuration.

scholarly journals A Proof-of-Concept Algorithm for the Retrieval of Total Column Amount of Trace Gases in a Multi-Dimensional Atmosphere

2021 ◽  
Vol 13 (2) ◽  
pp. 270
Author(s):  
Adrian Doicu ◽  
Dmitry S. Efremenko ◽  
Thomas Trautmann
Keyword(s):  
Trace Gases ◽  
Three Dimensional ◽  
Principal Component ◽  
Radiative Transfer Model ◽  
Computational Time ◽  
Transfer Model ◽  
Proof Of Concept ◽  
Discrete Ordinate ◽  
Distribution Method ◽  
Total Column

An algorithm for the retrieval of total column amount of trace gases in a multi-dimensional atmosphere is designed. The algorithm uses (i) certain differential radiance models with internal and external closures as inversion models, (ii) the iteratively regularized Gauss–Newton method as a regularization tool, and (iii) the spherical harmonics discrete ordinate method (SHDOM) as linearized radiative transfer model. For efficiency reasons, SHDOM is equipped with a spectral acceleration approach that combines the correlated k-distribution method with the principal component analysis. The algorithm is used to retrieve the total column amount of nitrogen for two- and three-dimensional cloudy scenes. Although for three-dimensional geometries, the computational time is high, the main concepts of the algorithm are correct and the retrieval results are accurate.

scholarly journals Finite-dimensional boundary uniform stabilization of the Boussinesq system in Besov spaces by critical use of Carleman estimate-based inverse theory

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Irena Lasiecka ◽  
Buddhika Priyasad ◽  
Roberto Triggiani
Keyword(s):  
Besov Space ◽  
Internal Control ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Critical Role ◽  
Boussinesq System ◽  
Heat Equations ◽  
Fluid Equation ◽  
Low Regularity ◽  
Finite Dimensional

Abstract We consider the 𝑑-dimensional Boussinesq system defined on a sufficiently smooth bounded domain and subject to a pair { v , u } \{v,\boldsymbol{u}\} of controls localized on { Γ ~ , ω } \{\widetilde{\Gamma},\omega\} . Here, 𝑣 is a scalar Dirichlet boundary control for the thermal equation, acting on an arbitrarily small connected portion Γ ~ \widetilde{\Gamma} of the boundary Γ = ∂ ⁡ Ω \Gamma=\partial\Omega . Instead, 𝒖 is a 𝑑-dimensional internal control for the fluid equation acting on an arbitrarily small collar 𝜔 supported by Γ ~ \widetilde{\Gamma} . The initial conditions for both fluid and heat equations are taken of low regularity. We then seek to uniformly stabilize such Boussinesq system in the vicinity of an unstable equilibrium pair, in the critical setting of correspondingly low regularity spaces, by means of an explicitly constructed, finite-dimensional feedback control pair { v , u } \{v,\boldsymbol{u}\} localized on { Γ ~ , ω } \{\widetilde{\Gamma},\omega\} . In addition, they will be minimal in number and of reduced dimension; more precisely, 𝒖 will be of dimension ( d - 1 ) (d-1) , to include necessarily its 𝑑-th component, and 𝑣 will be of dimension 1. The resulting space of well-posedness and stabilization is a suitable, tight Besov space for the fluid velocity component (close to L 3 ⁢ ( Ω ) \boldsymbol{L}^{3}(\Omega) for d = 3 d=3 ) and a corresponding Besov space for the thermal component, q > d q>d . Unique continuation inverse theorems for suitably over-determined adjoint static problems play a critical role in the constructive solution. Their proof rests on Carleman-type estimates, a topic pioneered by M. V. Klibanov since the early 80s.

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