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An implicit gradient meshfree formulation for convection-dominated problems. (English) Zbl 1356.76235
Bazilevs, Yuri (ed.) et al., Advances in computational fluid-structure interaction and flow simulation. New methods and challenging computations. Based on the presentations at the conference, AFSI, Tokyo, Japan, March 19–21, 2014. Basel: Birkhäuser/Springer (ISBN 978-3-319-40825-5/hbk; 978-3-319-40827-9/ebook). Modeling and Simulation in Science, Engineering and Technology, 25-37 (2016).
Summary: 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.
For the entire collection see [Zbl 1356.76009].
MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76R99 Diffusion and convection
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