Meshless finite difference method with B-splines for numerical solution of coupled advection-diffusion-reaction problems

Hidayat, Mas Irfan P.

doi:10.1016/j.ijthermalsci.2021.106933

Cited by 21 publications

(13 citation statements)

References 55 publications

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“…In Figures 4 and 5, the relative error value changes irregularly with the change of d max and α, and we can only choose appropriate parameters through continuous attempts. As can be seen from the figures, the computational accuracy is higher when d max is set to 1.01 ∼ 1.2, and α is set to 1 × 10 3 ∼ 4 × 10 6 .…”

Section: Examplementioning

confidence: 96%

“…An alternate strategy is the meshless technique, which may successfully handle some challenging issues related to mesh distortion by using a set of discrete points [4]. After decades of unremitting research by researchers, many meshless methods have emerged [5][6][7][8]. In order to facilitate the comparison of the advantages and disadvantages of various meshless methods, many widely used meshless algorithms have been compared and summarized in certain review studies [9,10].…”

Section: Introductionmentioning

confidence: 99%

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A Hybrid Reproducing Kernel Particle Method for Three-Dimensional Helmholtz Equation

Peng,

Wang,

Cheng

2024

Mathematics

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The reproducing kernel particle method (RKPM) is one of the most universal meshless methods. However, when solving three-dimensional (3D) problems, the computational efficiency is relatively low because of the complexity of the shape function. To overcome this disadvantage, in this study, we introduced the dimension splitting method into the RKPM to present a hybrid reproducing kernel particle method (HRKPM), and the 3D Helmholtz equation is solved. The 3D Helmholtz equation is transformed into a series of related two-dimensional (2D) ones, in which the 2D RKPM shape function is used, and the Galerkin weak form of these 2D problems is applied to obtain the discretized equations. In the dimension-splitting direction, the difference method is used to combine the discretized equations in all 2D domains. Three example problems are given to illustrate the performance of the HRKPM. Moreover, the numerical results show that the HRKPM can improve the computational efficiency of the RKPM significantly.

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Section: Examplementioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

A Hybrid Reproducing Kernel Particle Method for Three-Dimensional Helmholtz Equation

Peng,

Wang,

Cheng

2024

Mathematics

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“…The Runge-Kutta approach offers advantages in terms of computational speed and its ability to handle initial value problems. Various numerical techniques are used to solve the boundary values problem numerically using different numerical methods (Hidayat, 2021;Hidayat, 2023). It efficiently addresses the issue of finding the missing initial value through a shooting strategy, which is particularly important in real-world applications.…”

Section: Numerical Proceduresmentioning

confidence: 99%

Coaxially swirled porous disks flow simultaneously induced by mixed convection with morphological effect of metallic/metallic oxide nanoparticles

et al. 2023

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This study focuses on the numerical modeling of coaxially swirling porous disk flow subject to the combined effects of mixed convection and chemical reactions. We conducted numerical investigations to analyze the morphologies of aluminum oxide (Al2O3) and copper (Cu) nanoparticles under the influence of magnetohydrodynamics. For the flow of hybrid nanofluids, we developed a model that considers the aggregate nanoparticle volume fraction based on single-phase simulation, along with the energy and mass transfer equations. The high-order, nonlinear, ordinary differential equations are obtained from the governing system of nonlinear partial differential equations via similarity transformation. The resulting system of ordinary differential equations is solved numerically by the Runge–Kutta technique and the shooting method. This is one of the most widely used numerical algorithms for solving differential equations in various fields, including physics, engineering, and computer science. This study investigated the impact of various nanoparticle shape factors (spherical, platelet and laminar) subject to relevant physical quantities and their corresponding distributions. Our findings indicate that aluminum oxide and copper (Al2O3-Cu/H2O) hybrid nanofluids exhibit significant improvements in heat transfer compared to other shape factors, particularly in laminar flow. Additionally, the injection/suction factor influences the contraction/expansion phenomenon, leading to noteworthy results concerning skin friction and the Nusselt number in the field of engineering. Moreover, the chemical reaction parameter demonstrates a remarkable influence on Sherwood’s number. The insights gained from this work hold potential benefits for the field of lubricant technology, as they contribute valuable knowledge regarding the behavior of hybrid nanofluids and their associated characteristics.

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“…Due to the advantages of the meshless method, some meshless methods have been developed for the CDR problems [48,49]. Zhang and Xiang discussed the numerical solutions of the CDR equation with small diffusion by the VMEFG method [50,51].…”

Section: Introductionmentioning

confidence: 99%

A Dimension Splitting Generalized Interpolating Element-Free Galerkin Method for the Singularly Perturbed Steady Convection–Diffusion–Reaction Problems

et al. 2021

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By introducing the dimension splitting method (DSM) into the generalized element-free Galerkin (GEFG) method, a dimension splitting generalized interpolating element-free Galerkin (DS-GIEFG) method is presented for analyzing the numerical solutions of the singularly perturbed steady convection–diffusion–reaction (CDR) problems. In the DS-GIEFG method, the DSM is used to divide the two-dimensional CDR problem into a series of lower-dimensional problems. The GEFG and the improved interpolated moving least squares (IIMLS) methods are used to obtain the discrete equations on the subdivision plane. Finally, the IIMLS method is applied to assemble the discrete equations of the entire problem. Some examples are solved to verify the effectiveness of the DS-GIEFG method. The numerical results show that the numerical solution converges to the analytical solution with the decrease in node spacing, and the DS-GIEFG method has high computational efficiency and accuracy.

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Meshless finite difference method with B-splines for numerical solution of coupled advection-diffusion-reaction problems

Cited by 21 publications

References 55 publications

A Hybrid Reproducing Kernel Particle Method for Three-Dimensional Helmholtz Equation

A Hybrid Reproducing Kernel Particle Method for Three-Dimensional Helmholtz Equation

Coaxially swirled porous disks flow simultaneously induced by mixed convection with morphological effect of metallic/metallic oxide nanoparticles

A Dimension Splitting Generalized Interpolating Element-Free Galerkin Method for the Singularly Perturbed Steady Convection–Diffusion–Reaction Problems

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