Back and forth error compensation and correction methods for removing errors induced by uneven gradients of the level set function

DOI10.1016/S0021-9991(03)00276-6zbMath1031.65110MaRDI QIDQ1408436

Yingjie Liu, Todd F. Dupont

Publication date: 15 September 2003

Published in: Journal of Computational Physics (Search for Journal in Brave)

zbMATH Keywords

stabilitycomparison of methodsnumerical exampleslevel set methodfront trackingerror reductiontranslation equationflux corrected transportlinear advection equationsbackward error compensation methodforward error compensation methodZalesak's problem

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Initial value problems for first-order hyperbolic systems (35L45)

Related Items

An adaptive numerical method for free surface flows passing rigidly mounted obstacles, A new incompressibility discretization for a hybrid particle MAC grid representation with surface tension, A ghost-fluid method for large eddy simulations of premixed combustion in complex geometries, An enhanced non-oscillatory BFECC algorithm for finite element solution of advective transport problems, A finite difference method on irregular grids with local second order ghost point extension for solving Maxwell's equations around curved PEC objects, An embedded strategy for the analysis of fluid structure interaction problems, Accuracy enhancing interface treatment algorithm: the back and forth error compensation and correction method, An unconditionally stable MacCormack method, Out-of-core computations of high-resolution level sets by means of code transformation, A ghost-point based second order accurate finite difference method on uniform orthogonal grids for electromagnetic scattering around curved perfect electric conductors with corners, Back and forth error compensation and correction method for linear hyperbolic systems with application to the Maxwell's equations, A Simple Implementation of the Semi-Lagrangian Level-Set Method, A splitting method for free surface flows over partially submerged obstacles, Geometric advection and its application in the emulation of high aspect ratio structures, Discrete Lie advection of differential forms, An unconditionally stable fully conservative semi-Lagrangian method, A MODIFIED SUB-CELL-FIX METHOD FOR RE-INITIALIZATION OF LEVEL-SET DISTANCE FUNCTION AND ITS DEPENDENCE TESTS ON GRID STRETCHING, An enriched finite element/level-set method for simulating two-phase incompressible fluid flows with surface tension, A limiting strategy for the back and forth error compensation and correction method for solving advection equations, On the evolution of vector distance functions of closed curves, THE LATTICE BOLTZMANN METHOD BASED ON QUADTREE MESH, Assessment and modification of sub-cell-fix method for re-initialization of level-set distance function, Back and forth error compensation and correction methods for semi-lagrangian schemes with application to level set interface computations

Uses Software

• SHASTA

Cites Work

• Fully multidimensional flux-corrected transport algorithms for fluids
• Uniformly high order accurate essentially non-oscillatory schemes. III
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
• Motion of multiple junctions: A level set approach
• A level set approach for computing solutions to incompressible two-phase flow
• Weighted essentially non-oscillatory schemes
• A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows
• A hybrid particle level set method for improved interface capturing
• A fast level set method for propagating interfaces
• A variational level set approach to multiphase motion
• An Efficient, Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow
• Finite Difference WENO Schemes with Lax--Wendroff-Type Time Discretizations
• Flux-corrected transport. I: SHASTA, a fluid transport algorithm that works