A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation

Adams, T.; Giani, S.; Coombs, W.M.

Abstract

In this paper, an efficient, high-order accurate, level set reinitialisation method is proposed, based on the elliptic reinitialisation method (Basting and Kuzmin, 2013 [1]), which is discretised spatially using the discontinuous Galerkin (DG) symmetric interior penalty method (SIPG). In order to achieve this a number of improvements have been made to the elliptic reinitialisation method including; reformulation of the underlying minimisation problem driving the solution; adoption of a Lagrange multiplier approach for enforcing a Dirichlet boundary condition on the implicit level set interface; and adoption of a narrow band approach. Numerical examples confirm the high-order accuracy of the resultant method by demonstrating experimental orders of convergence congruent with optimal convergence rates for the SIPG method, that is and in the and DG norms respectively. Furthermore, the degree to which the level set function satisfies the Eikonal equation improves proportionally to , and the often ignored homogeneous Dirichlet boundary condition on the interface is shown to be satisfied accurately with a rate of convergence of at least for all polynomial orders.

Citation

Adams, T., Giani, S., & Coombs, W. (2019). A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation. Journal of Computational Physics, 379, 373-391. https://doi.org/10.1016/j.jcp.2018.12.003

• Journal Article Type: Article
• Acceptance Date: Dec 5, 2018
• Online Publication Date: Dec 12, 2018
• Publication Date: Feb 15, 2019
• Deposit Date: Dec 6, 2018
• Publicly Available Date: Dec 12, 2019
• Journal: Journal of Computational Physics
• Print ISSN: 0021-9991
• Electronic ISSN: 1090-2716
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 379
• Pages: 373-391
• DOI: https://doi.org/10.1016/j.jcp.2018.12.003
• Keywords: Level set, Reinitialisation, Discontinuous Galerkin
• Public URL: https://durham-repository.worktribe.com/output/1341707