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Local maximum entropy approximation-based streamline upwind Petrov–Galerkin meshfree method for convection–diffusion problem

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Abstract

Local maximum entropy (LME) meshfree basis functions are among the few approximants that possess the Kronecker delta property on the boundary, which enable to impose the essential boundary conditions directly like FEM. This study presents the potential of a meshfree method based on LME approximation for the Convection–Diffusion problem via well-celebrated SUPG. The present LME based Streamline Upwind Petrov–Galerkin meshfree method (SUPGM) benefits from the advantages emanated from both methods. LME approximants accounts for the disposal of the elements and direct imposition of boundary conditions and the SUPGM technique to deal with the issues associated with the non-self-adjoint convective term. Two standard benchmark problems are considered to validate the LME-SUPGM. The effect of different priors and radius of support that defines the LME basis are studied to test their importance in the present method. It is found that a balance between stability and accuracy is possible with ease by tuning the effective radius of support for LME for the given problem. The present method converges faster than FEM-SUPG and provides a smooth solution relatively.

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  1. School of Mechanical Engineering, SASTRA Deemed to be University, Thanjavur, 613401, India

    Sreehari Peddavarapu & Raghuraman Srinivasan

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  1. Sreehari Peddavarapu
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Peddavarapu, S., Srinivasan, R. Local maximum entropy approximation-based streamline upwind Petrov–Galerkin meshfree method for convection–diffusion problem. J Braz. Soc. Mech. Sci. Eng. 43, 326 (2021). https://doi.org/10.1007/s40430-021-03038-w

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