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An efficient meshless technique for 2-D hyperbolic convection-diffusion problem
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DOI：10.1016/j.apnum.2026.01.020.png)
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Abstract
En 中文
In this work, a meshless technique has been proposed to demonstrate the numerical study of the 2-dimensional hyperbolic convection-diffusion equation. The proposed method is based on radial basis and trigonometric basis functions. The objective of the work is to perform numerical investigation for the considered problem in both regular and irregular domains. The equation is discretized using the Crank-Nicolson method for temporal derivative, and then the proposed method is used for the solution. The stability of the time semi-discrete scheme is determined using the energy technique, revealing that the proposed approach is H1-norm stable. The convergence of the proposed scheme is discussed using the energy technique and found to be of the second order. The numerical experiments are performed for both regular and irregular domains, which confirm the theoretical claim of quadratic convergence for both cases. Efficiency and accuracy of the method are demonstrated through numerical examples. The study is performed on regular and irregular domains with Dirichlet, Neumann, and Robin boundary conditions. The excellent performance of the proposed method makes its applications promising for the other complex problems as well.
Keywords:
Convection-diffusion equation
Radial basis function
Meshless method
Trigonometric basis function
Least-square method
Journal
IF:
2.4
Papers:
77
Citations:
6.7K