Simultaneous Untangling and Smoothing of Moving Mesh

LÓPEZ, E.; NIGRO NORBERTO; STORTI MARIO

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

John Wiley & Sons Inc

Lugar: Hoboken, New Jersey; Año: 2008 vol. 76 p. 994 - 1019

0029-5981

   In this paper a useful technique for simultaneous untangling and smoothing of meshes is presented.It is based on an extension of an earlier mesh smoothing strategy developed by the authors and used tosolve the computational mesh dynamics stage in fluid-structure interaction problems. In moving gridproblems, mesh untangling is necessary when element inversion is happened due to a moving domainboundary. The original smoothing strategy is defined in terms of the minimization of a functionalassociated with the mesh distortion using an indicator of the element geometric quality. This functionalbecomes discontinuous when an element has null volume, making impossible to obtain a valid meshfrom an invalid one. To circumvent this drawback, the original functional is transformed in order toguarantee its continuity for the whole space of nodal coordinates, achieving the untangling technique.The regularization depends on one parameter, allowing the recovery of the original functional whenthis parameter tends to zero. This feature is very important because at first it is necessary to regularizethe functional in order to make the mesh valid, but then, it is advisable to use the original functionalto make the smoothing optimal. This technique is applied to several test cases, including 2D and 3Dmeshes with simplicial elements. An additional example shows how this technique