Global Versus Localized RBF Meshless Methods for Solving Incompressible Fluid Flow with Heat Transfer

Abstract:A localized meshless method is used to simulate 3-D atmospheric wind fields for wind energy assessment and emergency response. The meshless (or mesh-free) method with radial basis functions (RBFs) alleviates the need to create a mesh required by finite difference, finite volume, and finite element methods. The method produces a fast solution that converges with high accuracy, establishing 3-D wind estimates over complex terrain. The method does not require discretization of the domain or boundary and removes the need for domain integration. The meshless method converges exponentially for smooth boundary shapes and boundary data, and is insensitive to dimensional constraints. Coding of the method is very easy and can be done using MATLAB or MAPLE. By employing a localized RBF procedure, 3-D wind fields can be established from sparse meteorological data. The meshless method can be easily run on PCs and hand-held mobile devices. This article summarizes previous work where the meshless method has successfully simulated 3D wind fields over various environments, along with the equations used to obtain the simulations.

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“…The analytical solution is given as Figure 5. Steady-state conduction in a two-dimensional plate (from Waters, J., et al [24]). …”

Section: Comparison Resultsmentioning

confidence: 99%

“…Pepper et al [23] describes the use of the global RBF approach for 3-D wind fields. More detailed discussion on implementation of the local approach is given in Waters and Pepper [24]. Since the localized RBF method collocates a small number of points for each subdomain, the method is ideal for use as an app on mobile devices.…”

Section: Local Rbf Approachmentioning

confidence: 99%

A Localized Meshless Technique for Generating 3-D Wind Fields

Pepper

Gonzalez

2018

Computation

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“…In this paper an implementation of the Radial Basis Function-generated Finite Difference (RBF-FD) meshless method [4,[7][8][9][10][11] is used to solve thermo-fluid problems over 3D geometries. The main advantages of this method is that no connectivity information is stored or processed, this implies the overcoming of all the limitations of the mesh-based methods enumerated so far.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of thermo-fluid problems in 3D domains by means of the RBF-FD meshless method

Zamolo

Miotti

2022

J. Phys.: Conf. Ser.

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The use of CAE (Computer Aided Engineering) software, commonly applied to the design and verification of a great variety of manufactured products, is totally reliant on accurate numerical simulations. Classic mesh-based methods, e.g., Finite Element (FEM) and Finite Volume (FVM), are usually employed for such simulations, where the role of the mesh is crucial for both accuracy and time consumption issues. This is especially true for complex 3D domains which are typically encountered in most practical problems. Meshless, or meshfree, methods have been recently introduced in order to replace the usual mesh with much simpler node distributions, thus purifying the data structures of any additional geometric information. Radial Basis Function-Finite Difference (RBF-FD) meshless methods have been shown to be able to easily solve problems of engineering relevance over complex-shaped domains with great accuracy, with particular reference to fluid flow and heat transfer problems. In this paper the RBF-FD method is employed to solve heat transfer problems with incompressible, steady-state laminar flow over 3D complex-shaped domains. The required node distributions are automatically generated by using a meshless node generation algorithm, which has been specifically developed to produce high quality node arrangements over arbitrary 3D geometries. The presented strategy represents therefore a fully-meshless approach for the accurate and automatic simulation of thermo-fluid problems over 3D domains of practical interest.

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“…The radial basis function interpolation along with the barycentric rational interpolation has been used to 2D viscoelastic wave equation [ 9 ]. The global and local meshless method has been used for solving problems of incompressible fluid flow with heat transfer where radial basis functions have been used [ 10 ]. Kernel Techniques have also been used for meshless methods [ 11 ].…”

Section: Introductionmentioning

confidence: 99%

Selection of Radial Basis Functions for the Accuracy of Meshfree Galerkin Method in Rotating Euler–Bernoulli Beam Problem

Panchore

2022

Int. J. Appl. Comput. Math

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In this work, the radial basis function approximations are used to improve the accuracy of meshfree Galerkin method. The method is applied to the free vibration problems of non-rotating and rotating Euler–Bernoulli beams. The stiffness and mass matrices are derived by using conventional methods. In this meshfree method, only six nodes are considered within a single sub-domain. The parameters are varied for different approximations; the results are obtained with different approximations and found accurate. Two new basis function have been developed which are relatively accurate than conventional basis function: the first new basis function is obtained by multiplication of linear function to radial basis function and second new basis function is obtained by multiplying cubuic radial basis function to Gaussian radial basis function. The first few modes show same result that is available in literature using finite element method and higher modes are found very accurate as well. The result are found to be more accurate for first three modes of non-rotating and rotating Euler–Bernoulli beams where the cantilever beam boundary conditions are used; the first three modes do not change with the change in the parameter c of radial basis function.

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Global Versus Localized RBF Meshless Methods for Solving Incompressible Fluid Flow with Heat Transfer

Cited by 22 publications

References 32 publications

A Localized Meshless Technique for Generating 3-D Wind Fields

A Localized Meshless Technique for Generating 3-D Wind Fields

Numerical analysis of thermo-fluid problems in 3D domains by means of the RBF-FD meshless method

Selection of Radial Basis Functions for the Accuracy of Meshfree Galerkin Method in Rotating Euler–Bernoulli Beam Problem

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