scholarly journals Exact Time Domain Solutions of 1-D Transient Dynamic Piezoelectric Problems with Nonlinear Damper Boundary Conditions

2017 ◽  
Vol 05 (04) ◽  
pp. 873-888
Author(s):  
Naum M. Khutoryansky ◽  
Vladimir Genis
Keyword(s):  
Boundary Conditions ◽  
Time Domain ◽  
Transient Dynamic ◽  
Exact Time

On the Development of a Synchronized Harmonic Balance Method for Multiple Frequencies and its Application to LPT Flows

2020 ◽  
Author(s):  
Javier Crespo ◽  
Jesús Contreras
Keyword(s):  
Boundary Conditions ◽  
Time Domain ◽  
Harmonic Balance ◽  
Fourier Transforms ◽  
Harmonic Balance Method ◽  
Single Passage ◽  
Computational Performance ◽  
Runge Phenomenon ◽  
Numerical Instabilities ◽  
The Impact

Abstract The aim of this paper is to describe the development and application of a multi-frequency harmonic balance solver for GPUs, particularly suitable for the simulation of periodic unsteadiness in nonlinear turbomachinery flows comprised of a few dominant frequencies, with an unsteady multistage coupling that bolsters the flow continuity across the rotor/stator interface. The formulation is addressed with the time-domain reinterpretation, where several non-equidistant time instants conveniently selected are solved simultaneously. The set of required frequencies in each row is driven into the governing equations with the help of almost-periodic Fourier transforms for time derivatives and time shifted boundary conditions. The spatial repetitiveness inside each row can be exploited to perform single-passage simulations and the relative circumferential positioning of the rotors or stators and the different blade or vane counts is tackled by means of adding fictitious frequencies referring to non-adjacent rows therefore taking into account clocking and indexing effects. Existing multistage row coupling techniques of harmonic methods rely on the use of non-reflecting boundary conditions, based on linearizations, or time interpolation, which may lead to Runge phenomenon with the resulting numerical instabilities and non-preserving flux exchange. Different sets of time instants might be selected in each row but the interpolation in space and time across their interfaces gives rise to robustness issues due to this phenomenon. The so-called synchronized approach, developed in this work, consist of having the same time instances among the whole ensemble of rows, ensuring that flux transfer at sliding planes is applied more robustly. The combination of a set of shared non-equidistant time instances plus the use of unequal frequencies (real and fictitious) may spoil the Fourier transforms conditioning but this can be dramatically improved with the help of oversampling and instants selection optimization. The resulting multistage coupling naturally addresses typical numerical issues such as flow that might reverse locally across the row interfaces by means of not using boundary conditions but a local flux conservation scheme in the sliding planes. Some examples will be given to illustrate the ability of this new approach to preserve accuracy and robustness while resolving them. A brief analysis of results for a fan stage and a LPT multi-row case is presented to demonstrate the correctness of the method, assessing the impact in the modeling accuracy of the present approach compared with a time-domain conventional analysis. Regarding the computational performance, the speedup compared to a full annulus time-domain unsteady simulation is a factor of order 30 combining the use of single-passage rows and time spectral accuracy.

Statement of absorbing Mur boundary conditions of the first order of accuracy for solving problems of electrodynamics by the method of finite differences in the time domain

2021 ◽  
Vol 8 ◽  
pp. 57-68
Author(s):  
R.Yu. Borodulin ◽  
N.O. Lukyanov
Keyword(s):  
Boundary Conditions ◽  
Time Domain ◽  
Correct Choice ◽  
Absorbing Boundary Conditions ◽  
Practical Significance ◽  
Stable Operation ◽  
Absorbing Boundary ◽  
Spherical Waves ◽  
The One ◽  
The Time Domain

Problem statement. The accuracy and convergence of calculations for solving problems of electrodynamics by the finite difference method in the time domain significantly depends on the correct choice of parameters and the correct setting of the absorbing boundary conditions (ABC). Two main types of absorbing boundary conditions are known: Mur ABC; Beranger ABC. It is believed that the Mur ABC is less effective at absorbing spherical waves than the Beranger ABC, but they do not require the introduction of additional parameters (the so-called "Beranger fields"), which simplifies the implementation of program code and saves computer RAM. Calculations have shown that the efficiency of the Mur ABC will depend on their thickness. On the one hand, an increase in the thickness of the ABC layers will lead to an increase in the accuracy of calculations, on the other hand, to an increase in the size of the calculation area and, as a result, an increase in RAM. The problem arises of determining the criterion for evaluating the efficiency of ABC to determine their optimal thickness. Goal. Identification of new factors that make it possible to use the Mur ABC as efficiently as the Beranger ABC, while significantly saving computer resources. Result. The expressions for the ABC are presented, taking into account the interaction of all components of the electromagnetic field within a single cell of the FDTD. Calculations of the reflection coefficient – a criterion for evaluating the efficiency of the ABC, are presented. Practical significance. Calculations are presented that allow automating the selection of ABC parameters for their stable operation in solving electrodynamic problems.

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