Modelling Convection-Diffusion Phenomena by Direct and Indirect Meshless Methods
Abstract
Time-dependent convection-diffusion problems, prevalent in science and engineering, present significant analytical challenges. The limitations of traditional mesh-based numerical methods necessitate alternative approaches. Meshless methods emerge as a pivotal solution, offering precision where conventional techniques falter. This research centers on applying meshless methods to such problems, emphasizing their critical role in accurately modelling complex phenomena across various applications. Methodologically, the research compares two specific meshless methods: the Direct method and the Indirect method. Both methods are implemented using the multiquadric radial basis function within a global collocation framework. The Direct method is derivative-based, while Indirect adopts an integration-based approach. The comparison is conducted over four different test cases, which are designed to assess the sensitivity of Direct and Indirect to the multiquadric shape parameter and node density, their effectiveness under varying convection forces, and their computational efficiency.The findings of the study are twofold. Firstly, the Direct method exhibits superior accuracy overall, particularly in scenarios with intense convection and in capturing boundary layers characterized by steep flow variable gradients. Secondly, the Indirect method demonstrates notable computational efficiency, requiring approximately half the computational time needed by the Direct method. However, this efficiency comes with a trade-off in accuracy, particularly under conditions of high convection. The research concludes that the choice between the Direct and Indirect methods should be based on the specific demands of the problem, considering factors such as the desired level of accuracy, available computational resources, and the complexity of the scenario. This study offers valuable insights for professionals in fields like environmental science and pollution control, aiding in the selection of the most suitable meshless method for effectively tackling convection-diffusion challenges.
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