Pseudo-divergence-free element free Galerkin method for incompressible fluid flow
Computer Methods in Applied Mechanics and Engineering, 193 (12-14):
1119--1136 (2004)Meshfree Methods: Recent Advances and New Applications.DOI: DOI: 10.1016/j.cma.2003.12.010
Abstract
Incompressible modeling in finite elements has been a major concern since its early developments and has been extensively studied. However, incompressibility in mesh-free methods is still an open topic. Thus, instabilities or locking can preclude the use of mesh-free approximations in such problems. Here, a novel mesh-free formulation is proposed for incompressible flow. It is based on defining a pseudo-divergence-free interpolation space. That is, the finite dimensional interpolation space approaches a divergence-free space when the discretization is refined. Note that such an interpolation does not include any overhead in the computations. The numerical evaluations are performed using the inf-sup numerical test and two well-known benchmark examples for Stokes flow.
Description
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