Multiscale Calculations Using an Adaptive Wavelet Algorithm

2002 ◽  
Author(s):  
Yevgenii A. Rastigejev ◽  
Samuel Paolucci
Keyword(s):  
Degrees Of Freedom ◽  
Computational Cost ◽  
Reynolds Numbers ◽  
Adaptive Wavelet ◽  
Great Ability ◽  
Driven Cavity ◽  
Multiresolution Representation ◽  
Order Of Magnitude ◽  
Comparable Accuracy ◽  
Solution Accuracy

We present a new wavelet-based adaptive multiresolution representation (WAMR) algorithm for the numerical solution of multiscale evolution problems. Key features of the algorithm are fast procedures for grid rearrangement, computation of derivatives, as well as the ability to minimize the degrees of freedom for a prescribed solution accuracy. To demonstrate the efficiency and accuracy of the algorithm, we use it to solve the two-dimensional benchmark problem of incompressible fluid-flow in a lid-driven cavity at large Reynolds numbers. The numerical experiments demonstrate the great ability of the algorithm to adapt to different scales at different locations and at different times so as to produce accurate solutions at low computational cost. Specifically, we show that solutions of comparable accuracy as the benchmarks are obtained with more than an order of magnitude reduction in degrees of freedom.

WAVELET ADAPTIVE MULTIRESOLUTION REPRESENTATION: APPLICATIONS TO VISCOUS MULTISCALE FLOW SIMULATIONS

2006 ◽  
Vol 04 (02) ◽  
pp. 333-343 ◽  
Author(s):  
YEVGENII A. RASTIGEJEV ◽  
SAMUEL PAOLUCCI
Keyword(s):  
Degrees Of Freedom ◽  
Computational Cost ◽  
Reynolds Numbers ◽  
Great Ability ◽  
Driven Cavity ◽  
Multiresolution Representation ◽  
Order Of Magnitude ◽  
Comparable Accuracy ◽  
Solution Accuracy ◽  
Low Computational Cost

We present a new wavelet-based adaptive multiresolution representation (WAMR) algorithm for the numerical solution of multiscale evolution problems. Key features of the algorithm are fast procedures for grid rearrangement, computation of derivatives, as well as the ability to minimize the degrees-of-freedom for a prescribed solution accuracy. To demonstrate the efficiency and accuracy of the algorithm, we use it to solve the two-dimensional benchmark problem of incompressible fluid-flow in a lid-driven cavity at large Reynolds numbers. The numerical experiments demonstrate the great ability of the algorithm to adapt to different scales at different locations and at different times so as to produce accurate solutions at low computational cost. Specifically, we show that solutions of comparable accuracy as the benchmarks are obtained with more than an order of magnitude reduction in degrees-of-freedom.

A 3D Complexity-Adaptive Approach to Exploit Sparsity in Elastic Wave Propagation

Geophysics ◽  
2021 ◽  
pp. 1-64
Author(s):  
Claudia Haindl ◽  
Kuangdai Leng ◽  
Tarje Nissen-Meyer
Keyword(s):  
Degrees Of Freedom ◽  
Computational Cost ◽  
Parameter Tuning ◽  
Performance Limits ◽  
Absorbing Boundary ◽  
Adaptive Approach ◽  
Order Of Magnitude ◽  
Speed Up ◽  
Complex Settings ◽  
Close Fit

We present an adaptive approach to seismic modeling by which the computational cost of a 3D simulation can be reduced while retaining resolution and accuracy. This Azimuthal Complexity Adaptation (ACA) approach relies upon the inherent smoothness of wavefields around the azimuth of a source-centered cylindrical coordinate system. Azimuthal oversampling is thereby detected and eliminated. The ACA method has recently been introduced as part of AxiSEM3D, an open-source solver for global seismology. We employ a generalization of this solver which can handle local-scale Cartesian models, and which features a combination of an absorbing boundary condition and a sponge boundary with automated parameter tuning. The ACA method is benchmarked against an established 3D method using a model featuring bathymetry and a salt body. We obtain a close fit where the models are implemented equally in both solvers and an expectedly poor fit otherwise, with the ACA method running an order of magnitude faster than the classic 3D method. Further, we present maps of maximum azimuthal wavenumbers that are created to facilitate azimuthal complexity adaptation. We show how these maps can be interpreted in terms of the 3D complexity of the wavefield and in terms of seismic resolution. The expected performance limits of the ACA method for complex 3D structures are tested on the SEG/EAGE salt model. In this case, ACA still reduces the overall degrees of freedom by 92% compared to a complexity-blind AxiSEM3D simulation. In comparison with the reference 3D method, we again find a close fit and a speed-up of a factor 7. We explore how the performance of ACA is affected by model smoothness by subjecting the SEG/EAGE salt model to Gaussian smoothing. This results in a doubling of the speed-up. ACA thus represents a convergent, versatile and efficient method for a variety of complex settings and scales.

scholarly journals GEOMETRICAL EVALUATION OF RECTANGULAR FIN MOUNTED IN LATERAL SURFACE OF LID-DRIVEN CAVITY FORCED CONVECTIVE FLOWS

2019 ◽  
Vol 18 (2) ◽  
pp. 98
Author(s):  
E. D. dos Santos ◽  
P. M. Rodrigues ◽  
L. A. Isoldi ◽  
J. F. Prolo Filho ◽  
L. A. O. Rocha ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Thermal Performance ◽  
Degrees Of Freedom ◽  
Reynolds Numbers ◽  
Cavity Surface ◽  
Square Cavity ◽  
Driven Cavity ◽  
Convective Flows ◽  
Constructal Design ◽  
Volume Method

In this work, it is investigated the geometric effect of rectangular fin inserted in a lid-driven square cavity over thermal performance of laminar, incompressible, steady and forced convective flows. This study is performed by applying Constructal Design to maximize the heat transfer between the fin and the cavity flow. For that, the problem is subjected to two constraints: area of the cavity and area of rectangular fin, and two degrees of freedom: height/length ratio of rectangular fin (H1/L1) and its position in upstream surface of the cavity (S/A1/2). It is considered here some fixed parameters, as the ratio between the fin and cavity areas (ϕ = 0.05), the aspect ratio of the cavity dimensions (H/L = 1.0) and Prandtl number (Pr = 0.71). The fin aspect ratio (H1/L1) was varied for three different placements of the fin at the upstream cavity surface (S/A1/2 = 0.1, 0.5 and 0.9) which represents a lower, intermediate and upper positions of the fin. The effects of the fin geometry over the spatial-averaged Nusselt number ( ) is investigated for three different Reynolds numbers (ReH = 10, 102 and 103). The conservation equations of mass, momentum and energy were numerically solved with the Finite Volume Method. Results showed that both degrees of freedom (H1/L1 and S/A1/2) had a strong influence over , mainly for higher magnitudes of Reynolds number. Moreover, the best thermal performance is reached when the fin is placed near the upper surface of the cavity for an intermediate ratio between height and length of rectangular fin, more precisely when (S/A1/2)o = 0.9 and (H1/L1)oo = 2.0.

Verification of Length Scale Effects on Solution Accuracy of Hybrid RANS-LES Methods

2016 ◽  
Author(s):  
Gaurav Kumar ◽  
Harish Gopalan ◽  
Dominic Chandar ◽  
Vinh-Tan Nguyen ◽  
Ashoke De
Keyword(s):  
Bluff Body ◽  
Scale Effects ◽  
Computational Cost ◽  
Separated Flow ◽  
Reynolds Numbers ◽  
Test Problems ◽  
Length Scale ◽  
High Reynolds ◽  
Solution Accuracy ◽  
Bluff Body Flows

Hybrid RANS-LES methods are gaining popularity for the simulation of the complex bluff body flows at high Reynolds numbers due to their reduced computational cost and good accuracy. A number of such methods have been proposed in the literature. Each of these methods have enjoyed varying degree of success for different applications. One of the most important parameter which determines the switching between near-wall RANS region and off-body LES region is the length scale parameter. This parameter can be grid based or physics based and numerous choices exist for defining this parameter. This study proposes to investigate the effect of this parameter on the size of the RANS and LES regions and also on the solution accuracy. Four test problems are chosen covering attached, mildly separated and massively separated flow regimes. Results will help us to identify length scale definitions to be used for different flow scenarios.

Driving Torsion Scans with Wavefront Propagation

2020 ◽  
Author(s):  
Yudong Qiu ◽  
Daniel Smith ◽  
Chaya Stern ◽  
mudong feng ◽  
Lee-Ping Wang
Keyword(s):  
Potential Energy ◽  
Force Field ◽  
Degrees Of Freedom ◽  
Computational Cost ◽  
Initial Guess ◽  
Field Development ◽  
Force Field Development ◽  
Wavefront Propagation ◽  
Open Source Software Package

<div>The parameterization of torsional / dihedral angle potential energy terms is a crucial part of developing molecular mechanics force fields.</div><div>Quantum mechanical (QM) methods are often used to provide samples of the potential energy surface (PES) for fitting the empirical parameters in these force field terms.</div><div>To ensure that the sampled molecular configurations are thermodynamically feasible, constrained QM geometry optimizations are typically carried out, which relax the orthogonal degrees of freedom while fixing the target torsion angle(s) on a grid of values.</div><div>However, the quality of results and computational cost are affected by various factors on a non-trivial PES, such as dependence on the chosen scan direction and the lack of efficient approaches to integrate results started from multiple initial guesses.</div><div>In this paper we propose a systematic and versatile workflow called \textit{TorsionDrive} to generate energy-minimized structures on a grid of torsion constraints by means of a recursive wavefront propagation algorithm, which resolves the deficiencies of conventional scanning approaches and generates higher quality QM data for force field development.</div><div>The capabilities of our method are presented for multi-dimensional scans and multiple initial guess structures, and an integration with the MolSSI QCArchive distributed computing ecosystem is described.</div><div>The method is implemented in an open-source software package that is compatible with many QM software packages and energy minimization codes.</div>

scholarly journals Nebula: ultra-efficient mapping-free structural variant genotyper

2021 ◽  
Author(s):  
Parsoa Khorsand ◽  
Fereydoun Hormozdiari
Keyword(s):  
Large Scale ◽  
Structural Variants ◽  
Sequencing Technologies ◽  
Generic Framework ◽  
Common Genetic Variants ◽  
Order Of Magnitude ◽  
Complex Events ◽  
Comparable Accuracy ◽  
Using Data ◽  
Computational Resources

Abstract Large scale catalogs of common genetic variants (including indels and structural variants) are being created using data from second and third generation whole-genome sequencing technologies. However, the genotyping of these variants in newly sequenced samples is a nontrivial task that requires extensive computational resources. Furthermore, current approaches are mostly limited to only specific types of variants and are generally prone to various errors and ambiguities when genotyping complex events. We are proposing an ultra-efficient approach for genotyping any type of structural variation that is not limited by the shortcomings and complexities of current mapping-based approaches. Our method Nebula utilizes the changes in the count of k-mers to predict the genotype of structural variants. We have shown that not only Nebula is an order of magnitude faster than mapping based approaches for genotyping structural variants, but also has comparable accuracy to state-of-the-art approaches. Furthermore, Nebula is a generic framework not limited to any specific type of event. Nebula is publicly available at https://github.com/Parsoa/Nebula.

The two-sided lid-driven cavity: experiments on stationary and time-dependent flows

2002 ◽  
Vol 450 ◽  
pp. 67-95 ◽  
Author(s):  
CH. BLOHM ◽  
H. C. KUHLMANN
Keyword(s):  
Three Dimensional ◽  
Standing Waves ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Flow State ◽  
Incompressible Fluid Flow ◽  
Velocity Measurements ◽  
Driven Cavity ◽  
Rectangular Container ◽  
Hot Film

The incompressible fluid flow in a rectangular container driven by two facing sidewalls which move steadily in anti-parallel directions is investigated experimentally for Reynolds numbers up to 1200. The moving sidewalls are realized by two rotating cylinders of large radii tightly closing the cavity. The distance between the moving walls relative to the height of the cavity (aspect ratio) is Γ = 1.96. Laser-Doppler and hot-film techniques are employed to measure steady and time-dependent vortex flows. Beyond a first threshold robust, steady, three-dimensional cells bifurcate supercritically out of the basic flow state. Through a further instability the cellular flow becomes unstable to oscillations in the form of standing waves with the same wavelength as the underlying cellular flow. If both sidewalls move with the same velocity (symmetrical driving), the oscillatory instability is found to be tricritical. The dependence on two sidewall Reynolds numbers of the ranges of existence of steady and oscillatory cellular flows is explored. Flow symmetries and quantitative velocity measurements are presented for representative cases.

A Dynamic Adaptive Wavelet Method for Solution of the Schrodinger Equation

2015 ◽  
Vol 06 (01) ◽  
pp. 1450001 ◽  
Author(s):  
Ratikanta Behera ◽  
Mani Mehra
Keyword(s):  
Schrödinger Equation ◽  
Computational Efficiency ◽  
Schrodinger Equation ◽  
Computational Cost ◽  
Two Dimensional ◽  
Wavelet Method ◽  
Adaptive Wavelet ◽  
One Dimensional ◽  
Grid Adaptation ◽  
Adaptive Wavelet Method

In this paper, we present a dynamically adaptive wavelet method for solving Schrodinger equation on one-dimensional, two-dimensional and on the sphere. Solving one-dimensional and two-dimensional Schrodinger equations are based on Daubechies wavelet with finite difference method on an arbitrary grid, and for spherical Schrodinger equation is based on spherical wavelet over an optimal spherical geodesic grid. The method is applied to the solution of Schrodinger equation for computational efficiency and achieve accuracy with controlling spatial grid adaptation — high resolution computations are performed only in regions where a solution varies greatly (i.e., near steep gradients, or near-singularities) and a much coarser grid where the solution varies slowly. Thereupon the dynamic adaptive wavelet method is useful to analyze local structure of solution with very less number of computational cost than any other methods. The prowess and computational efficiency of the adaptive wavelet method is demonstrated for the solution of Schrodinger equation on one-dimensional, two-dimensional and on the sphere.

Development of an Inverse Plume Model for Mass Eruption Rate in Unsteady Conditions

2021 ◽  
Author(s):  
Stephen A Solovitz
Keyword(s):  
Laboratory Data ◽  
Model Performance ◽  
Volcanic Eruptions ◽  
Reynolds Numbers ◽  
Model Parameters ◽  
Plume Height ◽  
Eruption Rate ◽  
Mass Eruption Rate ◽  
Downstream Effects ◽  
Order Of Magnitude

Abstract Following volcanic eruptions, forecasters need accurate estimates of mass eruption rate (MER) to appropriately predict the downstream effects. Most analyses use simple correlations or models based on large eruptions at steady conditions, even though many volcanoes feature significant unsteadiness. To address this, a superposition model is developed based on a technique used for spray injection applications, which predicts plume height as a function of the time-varying exit velocity. This model can be inverted, providing estimates of MER using field observations of a plume. The model parameters are optimized using laboratory data for plumes with physically-relevant exit profiles and Reynolds numbers, resulting in predictions that agree to within 10% of measured exit velocities. The model performance is examined using a historic eruption from Stromboli with well-documented unsteadiness, again providing MER estimates of the correct order of magnitude. This method can provide a rapid alternative for real-time forecasting of small, unsteady eruptions.

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