Behavioral Study of Various Radial Basis Functions for Approximation and Interpolation Purposes

Cervenka, Martin; Skala, Václav

doi:10.1109/sami48414.2020.9108712

Cited by 6 publications

(3 citation statements)

References 19 publications

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“…As a perspective, we endeavor to investigate the limitation of the Hermitian finite differences method to treat the 3D jet flow simulation. Besides, to inspect the capability of spectral methods [38], and meshless methods [39][40][41][42][43] to deal with the jet problem at higher Reynolds number.…”

Section: Discussionmentioning

confidence: 99%

Numerical Modeling of Jet at the Bottom of Tank at Moderate Reynolds Number Using Compact Hermitian Finite Differences Method

Loukili

Kotrasová

Dutykh

2021

Fluids

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In this manuscript, the injection of a homogeneous jet in a numerical tank is considered to revolve around discussing the limitation of the direct numerical simulation (DNS), to resolve the equations governing the problem of a jet emitted from the bottom of a numerical tank. The investigation has been made in the context of an unsteady, viscous, and incompressible fluid. The numerical resolution of the equations governing the problem is made by the compact Hermitian finite differences method (HFDM) high accuracy Oh2,h4 First, the numerical code used in this work is validated by comparing the profiles of the velocity components at the median of the lid-driven cavity with the results of the literature. Furthermore, to confirm the validity of the present numerical code, an evaluation of mesh domain sensitivity is assessed by comparing the numerical vertical velocity profiles for different steps of y-direction (flow direction) with the analytical solution. Afterward, the aim is to perform the nonlinear simulations of the Navier–Stokes equations in a large computational domain. Next, the goal is to characterize the instabilities associated with high Reynolds numbers when a jet is emitted from the bottom of the numerical tank.

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Section: Discussionmentioning

confidence: 99%

Numerical Modeling of Jet at the Bottom of Tank at Moderate Reynolds Number Using Compact Hermitian Finite Differences Method

Loukili

Kotrasová

Dutykh

2021

Fluids

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“…It should be noted that the problem of improving the quality of approximation is very important and interesting. In this regard, we should note that finding points of importance in an interpolation problem were considered in papers [14]- [15].…”

Section: Introductionmentioning

confidence: 99%

Application of Non-polynomial Splines to Solving Differential Equations

Бурова

2020

Wseas Transactions on Mathematics

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The application of the local polynomial and non-polynomial to the construction of methods for numerically solving the heat conduction problem is discussed. The non-polynomial splines are used here to approximate the partial derivatives. Formulas for numerical differentiation based on the application of the nonpolynomial splines of the fourth order of approximation are constructed. Particular attention is paid to polynomial, trigonometric, exponential, polynomial-trigonometric and polynomial-exponential splines. This approach allows us to construct explicit and implicit difference schemes. The main focus of the paper is on implicit difference scheme. New approximations with splines of the Lagrange and Hermite type with new properties are obtained. These approximations take into account the first and second derivatives of the function being approximated. Numerical examples are given.

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“…The RBF has a simple structure and easy to be implemented. It is almost independent of dimensionality of problems, which avoids the complex and time-consuming algorithms caused by the higher dimension [14]. Additionally, as each solid can be represented by an independent isosurface equation, the RBF method is also appropriate for solving multi-body problems.…”

Section: Introductionmentioning

confidence: 99%

An RBF-Based h-Adaptive Cartesian Grid Refinement Method for Arbitrary Single/Multi-Body Hull Modeling and Reconstruction

2020

Symmetry

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Complex single/multi-body structures are generally found in ship and ocean engineering. They have the smooth, sharp, concave, and convex surface features in common. Precise modeling of the structures is the basis of numerical simulation. However, the most widely used explicit modeling method requires considerable manual operations. The result is also difficult to reproduce. Therefore, this paper presents a Radial basis function (RBF) based hierarchical (h-) adaptive Cartesian grid method. The RBF is introduced for arbitrary implicit modeling over the Cartesian framework. Thanks to its natural properties, the RBF is easy to use, highly automated, and only needs a set of scatter points for modeling. The block-based h-adaptive mesh refinement (AMR) combined with the RBF aims to enhance the local grid resolution. It accelerates the calculation of intersecting points compared with the uniform Cartesian grid. The accuracy, efficiency, and robustness of the proposed method are validated by the simulation of the 3D analytical ellipsoidal surface and the unclosed conic surface. To select suitable parameters, we thoroughly investigated the uncertainty factors including sample points, RBF functions, and h-AMR grids. The simulation results of the single/multi-body Wigley hull and KCS hull forms verified the proper selection of the factors and the feasibility of our method to solve practical problems.

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Behavioral Study of Various Radial Basis Functions for Approximation and Interpolation Purposes

Cited by 6 publications

References 19 publications

Numerical Modeling of Jet at the Bottom of Tank at Moderate Reynolds Number Using Compact Hermitian Finite Differences Method

Numerical Modeling of Jet at the Bottom of Tank at Moderate Reynolds Number Using Compact Hermitian Finite Differences Method

Application of Non-polynomial Splines to Solving Differential Equations

An RBF-Based h-Adaptive Cartesian Grid Refinement Method for Arbitrary Single/Multi-Body Hull Modeling and Reconstruction

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