Imposing Boundary Conditions to Match a CAD Virtual Geometry for the Mesh Curving Problem

  • Eloi Ruiz-GironésEmail author
  • Xevi Roca
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 127)


We present a high-order mesh curving method where the mesh boundary is enforced to match a target virtual geometry. Our method has the unique capability to allow curved elements to span and slide on top of several CAD entities during the mesh curving process. The main advantage is that small angles or small patches of the CAD model do not compromise the topology, quality and size of the boundary elements. We associate each high-order boundary node to a unique group of either curves (virtual wires) or surfaces (virtual shell). Then, we deform the volume elements to accommodate the boundary curvature, while the boundary condition is enforced with a penalty method. At each iteration of the penalty method, the boundary condition is updated by projecting the boundary interpolative nodes of the previous iteration on top of the corresponding virtual entities. The method is suitable to curve meshes featuring non-uniform isotropic and highly stretched elements while matching a given virtual geometry.



This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No 715546. This work has also received funding from the Generalitat de Catalunya under grant number 2017 SGR 1731. The work of Xevi Roca has been partially supported by the Spanish Ministerio de Economía y Competitividad under the personal grant agreement RYC-2015–01633.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Computer Applications in Science and EngineeringBarcelona Supercomputing CenterBarcelonaSpain

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