2011/11/29 by David Salač, Salac, David
Computer Science · Engineering · #35G30 #65K05 #65N06 #65N12 #65N22 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Lattice Boltzmann Simulation Studies #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1111.6903
openalex publication_date 2011/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Including derivative information in the modelling of moving interfaces has been proposed as one method to increase the accuracy of numerical schemes with minimal additional cost. Here a new level set reinitialization technique using the fast marching method is presented. This augmented fast marching method will calculate the signed distance function and up to the second-order derivatives of the signed distance function for arbitrary interfaces. In addition to enforcing the condition |∇ϕ|2=1, where ϕ is the level set function, the method ensures that ∇(|∇ϕ|)2=0 and ∇∇(|∇ϕ|)2=0 are also satisfied. Results indicate that for both two- and three-dimensional interfaces the resulting level set and curvature field are smooth even for coarse grids. Convergence results show that using first-order upwind derivatives and the augmented fast marching method result in a second-order accurate level set and gradient field and a first-order accurate curvature field.