Numerical instabilities of vector-invariant momentum equations on rectangular C-grids

2016 ◽  
Vol 143 (702) ◽  
pp. 563-581 ◽  
Author(s):  
Michael J. Bell ◽  
Pedro S. Peixoto ◽  
John Thuburn
Keyword(s):  
Numerical Instabilities ◽  
Vector Invariant

Numerical Simulation of Contact Pressure Evolution in Fretting

1994 ◽  
Vol 116 (2) ◽  
pp. 247-254 ◽  
Author(s):  
L. Johansson
Keyword(s):  
Numerical Simulation ◽  
Contact Pressure ◽  
Stability Criterion ◽  
Frictional Contact ◽  
Elastic Bodies ◽  
Numerical Instabilities ◽  
Archard’S Law Of Wear ◽  
Pressure Evolution

In the present paper an algorithm for frictional contact between two elastic bodies is presented. The algorithm is applied to the calculation of the evolution of contact pressure between two elastic bodies when material is being removed by fretting. To this end Archard’s law of wear is implemented into the algorithm. It is noticed that the calculated pressures after a period of fretting differ considerably from the initial Hertz type pressures. Further, it is noted that numerical instabilities can occur in explicit type wear calculations, and a stability criterion is suggested.

CHOICE OF CONDITIONS FOR MHD SIMULATIONS ABOVE THE ACTIVE REGION, ALLOWING THE STUDY OF THE SOLAR FLARE MECHANISM

2021 ◽  
Vol 44 ◽  
pp. 92-95
Author(s):  
A.I. Podgorny ◽  
◽  
I.M. Podgorny ◽  
A.V. Borisenko ◽  
N.S. Meshalkina ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Active Region ◽  
Solar Flare ◽  
Magnetic Energy ◽  
Solar Radius ◽  
Computational Domain ◽  
Mhd Simulations ◽  
Flare Energy ◽  
Numerical Instabilities ◽  
The Magnetic Field

Primordial release of solar flare energy high in corona (at altitudes 1/40 - 1/20 of the solar radius) is explained by release of the magnetic energy of the current sheet. The observed manifestations of the flare are explained by the electrodynamical model of a solar flare proposed by I. M. Podgorny. To study the flare mechanism is necessary to perform MHD simulations above a real active region (AR). MHD simulation in the solar corona in the real scale of time can only be carried out thanks to parallel calculations using CUDA technology. Methods have been developed for stabilizing numerical instabilities that arise near the boundary of the computational domain. Methods are applicable for low viscosities in the main part of the domain, for which the flare energy is effectively accumulated near the singularities of the magnetic field. Singular lines of the magnetic field, near which the field can have a rather complex configuration, coincide or are located near the observed positions of the flare.

On numerical instabilities of Godunov-type schemes for strong shocks

2017 ◽  
Vol 350 ◽  
pp. 607-637 ◽  
Author(s):  
Wenjia Xie ◽  
Wei Li ◽  
Hua Li ◽  
Zhengyu Tian ◽  
Sha Pan
Keyword(s):  
Numerical Instabilities

scholarly journals Implicit Euler Method for Three-Dimensional Turbomachinery Flow Calculation

1993 ◽  
Author(s):  
Shih H. Chen ◽  
Anthony H. Eastland
Keyword(s):  
Three Dimensional ◽  
Prediction Method ◽  
Minimum Cost ◽  
Inviscid Flow ◽  
Turnaround Time ◽  
Euler Method ◽  
Second Order ◽  
Approximate Factorization ◽  
Implicit Euler Method ◽  
Numerical Instabilities

A compressible three-dimensional implicit Euler solution method for turbomachinery flows has been developed. The goal of the present study is to develop an efficient and reliable method that can be used to replace the semi-empirical, semi-analytical quasi-three-dimensional turbomachinery flow prediction method currently being used for multi-stage turbomachinery design at early design stages. Currently, a methodology has been developed based on an inviscid flow model (Euler solver) and tested on single blade rows for validation. The method presented here is derived from the Beam and Warming implicit approximate factorization (AF) finite difference algorithm. To avoid high frequency numerical instabilities associated with the use of central differencing schemes to obtain a spatial second order accuracy, a combined explicit and implicit artificial dissipation model is adopted. This model consists of a second order implicit dissipation and mixed second/fourth order explicit dissipation terms. A Cartesian coordinate H-grid generated by a three-dimensional interactive grid generator developed by Beach is used. Results for SSME High Pressure Fuel Turbine are presented and the comparison with experimental data is discussed. The use of the present implicit Euler method and the three-dimensional turbomachinery interactive grid generator shows that turnaround time could be as short as one day using a workstation. This allows the designers to explore optimal design configurations at minimum cost.

scholarly journals Data Augmentation Through Monte Carlo Arithmetic Leads to More Generalizable Classification in Connectomics

2020 ◽  
Author(s):  
Gregory Kiar ◽  
Yohan Chatelain ◽  
Ali Salari ◽  
Alan C. Evans ◽  
Tristan Glatard
Keyword(s):  
Monte Carlo ◽  
Data Augmentation ◽  
Learning Models ◽  
Reduction Techniques ◽  
Numerical Noise ◽  
Numerical Instabilities ◽  
Dimensionality Reduction Techniques ◽  
Improved Performance ◽  
Low Dimensional ◽  
Machine Learning Models

AbstractMachine learning models are commonly applied to human brain imaging datasets in an effort to associate function or structure with behaviour, health, or other individual phenotypes. Such models often rely on low-dimensional maps generated by complex processing pipelines. However, the numerical instabilities inherent to pipelines limit the fidelity of these maps and introduce computational bias. Monte Carlo Arithmetic, a technique for introducing controlled amounts of numerical noise, was used to perturb a structural connectome estimation pipeline, ultimately producing a range of plausible networks for each sample. The variability in the perturbed networks was captured in an augmented dataset, which was then used for an age classification task. We found that resampling brain networks across a series of such numerically perturbed outcomes led to improved performance in all tested classifiers, preprocessing strategies, and dimensionality reduction techniques. Importantly, we find that this benefit does not hinge on a large number of perturbations, suggesting that even minimally perturbing a dataset adds meaningful variance which can be captured in the subsequently designed models.

scholarly journals On physical and numerical instabilities arising in simulations of non-stationary radiatively cooling shocks

2016 ◽  
Vol 459 (2) ◽  
pp. 2188-2211 ◽  
Author(s):  
D. A. Badjin ◽  
S. I. Glazyrin ◽  
K. V. Manukovskiy ◽  
S. I. Blinnikov
Keyword(s):  
Numerical Instabilities

scholarly journals Patch-Recovery Filters for Curvature in Discontinuous Galerkin-Based Level-Set Methods

2016 ◽  
Vol 19 (2) ◽  
pp. 329-353 ◽  
Author(s):  
Florian Kummer ◽  
Tim Warburton
Keyword(s):  
Discontinuous Galerkin ◽  
Level Set ◽  
Numerical Study ◽  
Level Set Methods ◽  
Computational Cost ◽  
Pressure Jump ◽  
Two Phase ◽  
Two Fluids ◽  
Whole Process ◽  
Numerical Instabilities

AbstractIn two-phase flow simulations, a difficult issue is usually the treatment of surface tension effects. These cause a pressure jump that is proportional to the curvature of the interface separating the two fluids. Since the evaluation of the curvature incorporates second derivatives, it is prone to numerical instabilities. Within this work, the interface is described by a level-set method based on a discontinuous Galerkin discretization. In order to stabilize the evaluation of the curvature, a patch-recovery operation is employed. There are numerous ways in which this filtering operation can be applied in the whole process of curvature computation. Therefore, an extensive numerical study is performed to identify optimal settings for the patch-recovery operations with respect to computational cost and accuracy.

scholarly journals A Least Squares Computational Method for the Scattering Amplitude

1988 ◽  
Vol 41 (1) ◽  
pp. 47 ◽  
Author(s):  
JN Das
Keyword(s):  
Least Squares ◽  
Numerical Computation ◽  
Scattering Amplitude ◽  
High Accuracy ◽  
Computational Method ◽  
Partial Support ◽  
Numerical Instabilities

A new least squares computational method for the scattering amplitude is proposed. This may be applied without difficulty to atomic and other scattering computations. The approach is expected to give converged results of high accuracy and also to be free from major numerical instabilities. As an example a numerical computation is carried out following the method and some results are presented in partial support of the claim.

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.

Sign in / Sign up

Export Citation Format

Share Document