𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Semi-Lagrangian Methods for Level Set Equations

✍ Scribed by John Strain

Book ID
102970268
Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
540 KB
Volume
151
Category
Article
ISSN
0021-9991

No coin nor oath required. For personal study only.

✦ Synopsis

A new numerical method for solving geometric moving interface problems is presented. The method combines a level set approach and a semi-Lagrangian time stepping scheme which is explicit yet unconditionally stable. The combination decouples each mesh point from the others and the time step from the CFL stability condition, permitting the construction of methods which are efficient, adaptive, and modular. Analysis of a linear one-dimensional model problem suggests a surprising convergence criterion which is supported by heuristic arguments and confirmed by an extensive collection of two-dimensional numerical results. The new method computes correct viscosity solutions to problems involving geometry, anisotropy, curvature, and complex topological events.

📜 SIMILAR VOLUMES

A Semi-Lagrangian High-Order Method for
A Semi-Lagrangian High-Order Method for Navier–Stokes Equations
✍ Dongbin Xiu; George Em Karniadakis 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 323 KB

We present a semi-Lagrangian method for advection-diffusion and incompressible Navier-Stokes equations. The focus is on constructing stable schemes of secondorder temporal accuracy, as this is a crucial element for the successful application of semi-Lagrangian methods to turbulence simulations. We i

Semi-Lagrangian Schemes for Hamilton–Jac
Semi-Lagrangian Schemes for Hamilton–Jacobi Equations, Discrete Representation Formulae and Godunov Methods
✍ M. Falcone; R. Ferretti 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 379 KB

We study a class of semi-Lagrangian schemes which can be interpreted as a discrete version of the Hopf-Lax-Oleinik representation formula for the exact viscosity solution of first order evolutive Hamilton-Jacobi equations. That interpretation shows that the scheme is potentially accurate to any pres

A Monge-Ampère enhancement for semi-Lagr
A Monge-Ampère enhancement for semi-Lagrangian methods
✍ Jean-François Cossette; Piotr K. Smolarkiewicz 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 924 KB

Demanding the compatibility of semi-Lagrangian trajectory schemes with the fundamental Euler expansion formula leads to the Monge-Ampère (MA) nonlinear second-order partial differential equation. Given standard estimates of the departure points of flow trajectories, solving the associated MA problem