An implicit gradient meshfree formulation for convection-dominated problems

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Meshfree approximations are ideal for the gradient-type stabilized Petrov-Galerkin methods used for solving Eulerian conservation laws due to their ability to achieve arbitrary smoothness,however,the gradient terms are computationally demanding for meshfree methods. To address this issue,a stabilization technique that avoids high order differentiation of meshfree shape functions is introduced by employing implicit gradients under the reproducing kernel approximation framework. The modification to the standard approximation introduces virtually no additional computational cost,and its implementation is simple. The effectiveness of the proposed method is demonstrated in several benchmark problems.

Original languageEnglish (US)
Title of host publicationModeling and Simulation in Science, Engineering and Technology
PublisherSpringer Basel
Pages25-37
Number of pages13
DOIs
StatePublished - Jan 1 2016

Publication series

NameModeling and Simulation in Science, Engineering and Technology
ISSN (Print)2164-3679
ISSN (Electronic)2164-3725

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Engineering(all)
  • Fluid Flow and Transfer Processes
  • Computational Mathematics

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  • Cite this

    Hillman, M. C., & Chen, J. S. (2016). An implicit gradient meshfree formulation for convection-dominated problems. In Modeling and Simulation in Science, Engineering and Technology (pp. 25-37). (Modeling and Simulation in Science, Engineering and Technology). Springer Basel. https://doi.org/10.1007/978-3-319-40827-9_3