Numerical Solution of Natural Convection Problems by a Meshless Method

Kosec, Gregor; Šarler, Božidar

doi:10.5772/23816

Cited by 15 publications

(13 citation statements)

References 38 publications

(14 reference statements)

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“…Recently, a number of meshless (or mesh-free) techniques were proposed for solving convection-diffusion problems with arbitrarily shaped cavities [7][8][9]. They became popular due to their simplicity, flexibility, and independence from a complicated domain geometry.…”

Section: Introductionmentioning

confidence: 99%

Thermal Accelerometer Simulation by the R‑Functions Method

2020

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As well as many modern devices, thermal accelerometers (TAs) need a sophisticated mathematical simulation to find the ways for their performance optimization. In the paper, a novel approach for solving computational fluid dynamics (CFD) problems in the TA’s cavity is proposed (MQ-RFM), which is based on the combined use of Rvachev’s R-functions method (RFM) and the Galerkin technique with multiquadric (MQ) radial basis functions (RBFs). The semi-analytical RFM takes an intermediate position between traditional analytical approaches and numerical methods, such as the finite-element method (FEM), belonging to the family of the so-called meshless techniques which became popular in the last decades in solving various CFD problems in complex-shaped cavities. Mathematical simulation of TA by using the MQ-RFM was carried out with the purpose to simulate the temperature response of the device and to study and improve its performance. The results of numerical experiments were compared with well-known analytical and numerical benchmark solutions for the circular annulus geometry and it demonstrated the effectiveness of the MQ-RFM for solving the convective heat-transfer problem in the TA’s cavity. The use of solution structures allows one to take a relatively small number of expansion terms to achieve an appropriate accuracy of the approximate solution satisfying at the same time the given boundary conditions exactly. The application of the MQ-RFM gives the possibility to obtain semi-analytical solutions to the diffusion-convection problems and to identify the main thermal characteristics of the TA, that allows one to improve the device performance.

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Section: Introductionmentioning

confidence: 99%

Thermal Accelerometer Simulation by the R‑Functions Method

2020

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“…meshless) методами решения крае-вых задач, например методом коллокации с функциями радиального базиса RBF (англ. Radial-Basis Functions) [6]. Вместе с тем данный под-ход по-прежнему характеризуется необходимостью выбора относи-тельно большого числа базисных функций, а также нахождения их параметров (тип RBF, центр и ширина каждой RBF).…”

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Solving stationary two-dimensional problems of natural convection in enclosed cavities by the R-functions method

Басараб¹

2013

EJSI

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“…Besides, the localization in the LRBFCM can alleviate the problems of ill-conditioning matrix and form a system of sparse matrix. Recently, many researchers [4][5][6] have successfully applied the LRBFCM to analyze various engineering problems. Thus, we adopted the LRBFCM for spatial discretization of the potential problems of the sloshing phenomenon at every time step.…”

Section: Introductionmentioning

confidence: 99%

“…Because the computational domain and the profile of free surface change at every time step, the local radial basis function collocation method (LRBFCM) [4][5][6] is used to efficiently deal with the potential problem with mixed boundary conditions at every time step. Recently, various meshless methods have been proposed to analyze engineering applications in order to avoid the time-consuming tasks of mesh generation and numerical quadrature.…”

Section: Introductionmentioning

confidence: 99%

Local Radial Basis Function Collocation Method for Numerical Solutions of Sloshing Phenomenon

Fan¹,

Lai²

2015

Proceedings of the 2015 International Conference on Applied Science and Engineering Innovation

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Abstract.A promising domain-type meshless method is adopted to analyze the moving-boundary problems of sloshing phenomenon in a horizontally-excited numerical tank. When a tank partially filled with liquid is excited, the flow fields and the evolutionary profiles of free surface are known as the sloshing phenomenon. The local radial basis function collocation method is a newly-developed domain-type meshless method, so the time-consuming tasks of mesh generation and numerical quadrature can be avoided. The spatial derivatives at every node can be expressed as linear combination of nearby function values with different weighting, since the interpolation within every subdomain is achieved by function expansion of radial basis functions. Some numerical results and comparisons are provided to verify the merits of the proposed meshless scheme.

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Numerical Solution of Natural Convection Problems by a Meshless Method

Cited by 15 publications

References 38 publications

Thermal Accelerometer Simulation by the R‑Functions Method

Thermal Accelerometer Simulation by the R‑Functions Method

Solving stationary two-dimensional problems of natural convection in enclosed cavities by the R-functions method

Local Radial Basis Function Collocation Method for Numerical Solutions of Sloshing Phenomenon

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