scholarly journals A new hybrid adaptive mesh algorithm based on Voronoi tessellations and equi-distribution principle: Algorithms and numerical experiments

2015 ◽  
Vol 109 ◽  
pp. 137-154 ◽  
Author(s):  
Shaolin Mao
Keyword(s):  
Numerical Experiments ◽  
Adaptive Mesh ◽  
Voronoi Tessellations ◽  
Distribution Principle

COMPUTING AN ADAPTIVE MESH IN FLUID PROBLEMS USING NEURAL NETWORK AND GENETIC ALGORITHM WITH ADAPTIVE RELAXATION

2008 ◽  
Vol 17 (06) ◽  
pp. 1089-1108 ◽  
Author(s):  
NAMEER N. EL. EMAM ◽  
RASHEED ABDUL SHAHEED
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Numerical Experiments ◽  
Back Propagation ◽  
Adaptive Mesh ◽  
Learning System ◽  
Back Propagation Algorithm ◽  
Adaptive Smoothing ◽  
Different Types ◽  
Optimal Values

A method based on neural network with Back-Propagation Algorithm (BPA) and Adaptive Smoothing Errors (ASE), and a Genetic Algorithm (GA) employing a new concept named Adaptive Relaxation (GAAR) is presented in this paper to construct learning system that can find an Adaptive Mesh points (AM) in fluid problems. AM based on reallocation scheme is implemented on different types of two steps channels by using a three layer neural network with GA. Results of numerical experiments using Finite Element Method (FEM) are discussed. Such discussion is intended to validate the process and to demonstrate the performance of the proposed learning system on three types of two steps channels. It appears that training is fast enough and accurate due to the optimal values of weights by using a few numbers of patterns. Results confirm that the presented neural network with the proposed GA consistently finds better solutions than the conventional neural network.

scholarly journals Efficient Computation of Highly Oscillatory Fourier Transforms with Nearly Singular Amplitudes over Rectangle Domains

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1930
Author(s):  
Zhen Yang ◽  
Junjie Ma
Keyword(s):  
Adaptive Mesh Refinement ◽  
Numerical Experiments ◽  
Singular Integrals ◽  
Fourier Transforms ◽  
Adaptive Mesh ◽  
Oscillatory Integrals ◽  
Efficient Computation ◽  
New Approach ◽  
Highly Oscillatory ◽  
Nearly Singular Integrals

In this paper, we consider fast and high-order algorithms for calculation of highly oscillatory and nearly singular integrals. Based on operators with regard to Chebyshev polynomials, we propose a class of spectral efficient Levin quadrature for oscillatory integrals over rectangle domains, and give detailed convergence analysis. Furthermore, with the help of adaptive mesh refinement, we are able to develop an efficient algorithm to compute highly oscillatory and nearly singular integrals. In contrast to existing methods, approximations derived from the new approach do not suffer from high oscillatory and singularity. Finally, several numerical experiments are included to illustrate the performance of given quadrature rules.

scholarly journals On the hydrodynamics of crystal clustering

2019 ◽  
Vol 377 (2139) ◽  
pp. 20180015 ◽  
Author(s):  
Michael Z. McIntire ◽  
George W. Bergantz ◽  
Jillian M. Schleicher
Keyword(s):  
Numerical Experiments ◽  
Olivine Basalt ◽  
Probability Density Functions ◽  
Physical Contact ◽  
Density Functions ◽  
Crystal Mush ◽  
Voronoi Tessellations ◽  
Orientation Data ◽  
Mobile State ◽  
Reservoir Architecture

The formation of crystal clusters may influence the mechanical behaviour of magmas. However, whether clusters form largely from physical contact in a mobile state during sedimentation and stirring, or require residence in a crystal mush, is not well understood. In this paper, we use discrete-element fluid dynamics numerical experiments to illuminate the potential for clustering from both sedimentation and open-system mixing in a model olivine basalt reservoir for three different initial solid volume per cents. Crystal clustering is quantified using both bulk measures of clustering such as the R index and Ripley's L(r) and g(r) functions and with a variable scale technique called Voronoi tessellations, which also provide orientation data. Probability density functions for the likelihood of crystal clustering under freely circulating conditions indicate that there is nearly an equal likelihood for clustering and non-clustered textures in natural examples. A crystal cargo in igneous rock suites exhibiting a dominance of crystal clusters may be largely sampling magmatic materials formed in a crystal mush. This article is part of the Theo Murphy meeting issue ‘Magma reservoir architecture and dynamics’.

scholarly journals COMPARISON OF ADAPTIVE MESHES FOR A SINGULARLY PERTURBED REACTION–DIFFUSION PROBLEM

2012 ◽  
Vol 17 (5) ◽  
pp. 732-748 ◽  
Author(s):  
Andrej Bugajev ◽  
Raimondas Čiegis
Keyword(s):  
Numerical Experiments ◽  
Reaction Diffusion ◽  
Adaptive Mesh ◽  
Diffusion Problem ◽  
Adaptive Meshes ◽  
Finite Element Scheme ◽  
Differential Problem ◽  
Galerkin Finite Element ◽  
Error Estimators ◽  
Shishkin Meshes

We consider a singular second-order boundary value problem. The differential problem is approximated by the Galerkin finite element scheme. The main goal is to compare the well known apriori Bakhvalov and Shishkin meshes with the adaptive mesh based on the aposteriori dual error estimators. Results of numerical experiments are presented.

A Multi-Fluid Investigation of the Membrane Supporting Grid Effects on the Richtmyer-Meshkov Instability

2019 ◽  
Vol 390 ◽  
pp. 1-7
Author(s):  
Mohamad Al-Marouf ◽  
Ravi Samtaney
Keyword(s):  
Adaptive Mesh Refinement ◽  
Numerical Experiments ◽  
Complex Geometry ◽  
Adaptive Mesh ◽  
Circular Cylinders ◽  
Small Scale ◽  
Gas Mixture ◽  
Material Interface ◽  
Wire Grid ◽  
Thin Wires

We present results of numerical experiments performed to evaluate the effects of the material interface supporting wire grid on the Richtmyer-Meshkov instability (RMI). An air-SF6 interface initially perturbed sinusoidally supported on a number of solid circular cylinders. These cylinders are introduced along the interface to mimic the presence of the grid thin wires. The resulted mixing and growth rate of the perturbation in the presence and absence of the supporting grid were analyzed and validated with experimental measurements. The small scales perturbation imposed by the cylinders are around two orders of magnitude smaller than the interface sinusoidal perturbation wavelength requiring the adaptive mesh refinement (AMR) to adequately resolve small scale features. Furthermore, an embedded boundary technique is used to handle the complex geometry stemming from the presence of these multiple. A multi-fluid formulation is utilized to form a multi-gas species interface and compute the gas mixture properties.

A SECOND-ORDER ADAPTIVE ARBITRARY LAGRANGIAN–EULERIAN METHOD FOR THE COMPRESSIBLE EULER EQUATIONS

2009 ◽  
Vol 23 (04) ◽  
pp. 583-601
Author(s):  
Y. J. WANG ◽  
N. ZHAO ◽  
C. W. WANG ◽  
D. H. WANG
Keyword(s):  
Numerical Experiments ◽  
Adaptive Mesh ◽  
Time Discretization ◽  
Second Order ◽  
Arbitrary Lagrangian Eulerian ◽  
Finite Volume Schemes ◽  
Order Accuracy ◽  
Specific Internal Energy ◽  
Ale Methods ◽  
Lagrangian Scheme

Most of finite volume schemes in the Arbitrary Lagrangian–Eulerian (ALE) method are constructed on the staggered mesh, where the momentum is defined at the nodes and the other variables (density, pressure and specific internal energy) are cell-centered. However, this kind of schemes must use a cell-centered remapping algorithm twice which is very inefficient. Furthermore, there is inconsistent treatment of the kinetic and internal energies.1 Recently, a new class of cell-centered Lagrangian scheme for two-dimensional compressible flow problems has been proposed in Ref. 2. The main new feature of the algorithm is the introduction of four pressures on each edge, two for each node on each side of the edge. This scheme is only first-order accurate. In this paper, a second-order cell-centered conservative ENO Lagrangian scheme is constructed by using an ENO-type approach to extend the spatial second-order accuracy. Time discretization is based on a second-order Runge–Kutta scheme. Combining a conservative interpolation (remapping) method3,4 with the second-order Lagrangian scheme, a kind of cell-centered second-order ALE methods can be obtained. Some numerical experiments are made with this method. All results show that our method is effective and have second-order accuracy. At last, in order to further increase the resolution of shock regions, we use an adaptive mesh generation based on the variational principle5 as a rezoned strategy for developing a class of adaptive ALE methods. Numerical experiments are also presented to valid the performance of the proposed method.

Adaptive Mesh Refinement in 2D – An Efficient Implementation in Matlab

2020 ◽  
Vol 20 (3) ◽  
pp. 459-479 ◽  
Author(s):  
Stefan A. Funken ◽  
Anja Schmidt
Keyword(s):  
Data Structure ◽  
Adaptive Mesh Refinement ◽  
Numerical Experiments ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Two Dimensions ◽  
Efficient Implementation ◽  
Research And Education ◽  
Mesh Refinements ◽  
Implementation In Matlab

AbstractThis paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab. We give insights into different adaptive mesh refinement strategies allowing triangular and quadrilateral grids with and without hanging nodes. Throughout, the focus is on an efficient implementation by utilization of reasonable data structure, use of Matlab built-in functions and vectorization. This paper shows the transition from theory to implementation in a clear way and thus is meant to serve educational purposes of how to implement a method while keeping the code as short as possible – an implementation of an efficient adaptive mesh refinement is possible within 71 lines of Matlab. Numerical experiments underline the efficiency of the code and show the flexible deployment in different contexts where adaptive mesh refinement is in use. Our implementation is accessible and easy-to-understand and thus considered to be a valuable tool in research and education.

scholarly journals Stable Dynamical Adaptive Mesh Refinement

2021 ◽  
Vol 86 (3) ◽  
Author(s):  
Tomas Lundquist ◽  
Jan Nordström ◽  
Arnaud Malan
Keyword(s):  
Finite Difference ◽  
Adaptive Mesh Refinement ◽  
Numerical Experiments ◽  
Adaptive Mesh ◽  
Time Dependent ◽  
Inner Product ◽  
Finite Difference Schemes ◽  
Adaptive Meshes ◽  
Moving Interfaces ◽  
Interpolation Operators

AbstractWe consider accurate and stable interpolation procedures for numerical simulations utilizing time dependent adaptive meshes. The interpolation of numerical solution values between meshes is considered as a transmission problem with respect to the underlying semi-discretized equations, and a theoretical framework using inner product preserving operators is developed, which allows for both explicit and implicit implementations. The theory is supplemented with numerical experiments demonstrating practical benefits of the new stable framework. For this purpose, new interpolation operators have been designed to be used with multi-block finite difference schemes involving non-collocated, moving interfaces.

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