High resolution sharp computational methods for elliptic and parabolic problems in complex geometries
type: Item
instance of: scholarly article
title: High resolution sharp computational methods for elliptic and parabolic problems in complex geometries
zbMATH Open document ID: 1263.65093
author: Frédéric Gibou
author: Chohong Min
author: Ron Fedkiw
published in: Journal of Scientific Computing
publication date: 2013-04-08T00:00:00Z
Mathematics Subject Classification ID: 65M50
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 80A22
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 6151368
zbMATH Keywords: level-set method
zbMATH Keywords: quadtree
zbMATH Keywords: octree
zbMATH Keywords: ghost-fluid method
zbMATH Keywords: Poisson equation
zbMATH Keywords: free boundary problem
zbMATH Keywords: Crank-Nicolson method
zbMATH Keywords: Stefan problem
zbMATH Keywords: diffusion equation
zbMATH Keywords: adaptive mesh refinement
zbMATH Keywords: numerical experiments
describes a project that uses: PROST
describes a project that uses: IIMPACK
describes a project that uses: SLIC
describes a project that uses: KRAKEN
describes a project that uses: Gerris
describes a project that uses: p4est
MaRDI profile type: Publication
full work available at URL: s10915-012-9660-1
OpenAlex ID: W1992566117
cites work: A fast level set method for propagating interfaces
cites work: The fast construction of extension velocities in level set methods
cites work: Adaptive moment-of-fluid method
cites work: The formation of a solid nucleus in supercooled liquid. I
cites work: Variational algorithms and pattern formation in dendritic solidification
cites work: A partial differential equation approach to multidimensional extrapolation.
cites work: A geometrical area-preserving volume-of-fluid advection method
cites work: A method of constructing adaptive hexahedral moving grids
cites work: A second order virtual node method for elliptic problems with interfaces and irregular domains
cites work: Computational methods in Lagrangian and Eulerian hydrocodes
cites work: Local adaptive mesh refinement for shock hydrodynamics
cites work: Adaptive mesh refinement for hyperbolic partial differential equations
cites work: Analysis of a One-Dimensional Model for the Immersed Boundary Method
cites work: The pricing of options and corporate liabilities
cites work: A Robust Front Tracking Method: Verification and Application to Simulation of the Primary Breakup of a Liquid Jet
cites work: On the properties and limitations of the height function method in two-dimensional Cartesian geometry
cites work: A local level-set method using a hash table data structure
cites work: p4est : Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
cites work: Island dynamics and the level set method for epitaxial growth
cites work: A numerical method for two-phase flow consisting of separate compressible and incompressible regions
cites work: Three-dimensional, fully adaptive simulations of phase-field fluid models
cites work: A supra-convergent finite difference scheme for the Poisson and heat equations on irregular domains and non-graded adaptive Cartesian grids
cites work: A numerical scheme for the Stefan problem on adaptive Cartesian grids with supralinear convergence rate
cites work: A simple level set method for solving Stefan problems
cites work: Second-order accurate computation of curvatures in a level set framework using novel high-order reinitialization schemes
cites work: Redistancing by flow of time dependent eikonal equation
cites work: A Cartesian grid embedded boundary method for solving the Poisson and heat equations with discontinuous coefficients in three dimensions
cites work: Theory of solidification
cites work: A level set method for vapor bubble dynamics
cites work: Reconstruction of multi-material interfaces from moment data
cites work: A hybrid particle level set method for improved interface capturing
cites work: A posteriori error estimation and adaptive mesh refinement for a multiscale operator decomposition approach to fluid-solid heat transfer
cites work: A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
cites work: The ghost fluid method for deflagration and detonation discontinuities
cites work: A level set based sharp interface method for the multiphase incompressible Navier --- Stokes equations with phase change
cites work: A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem
cites work: A level set approach for the numerical simulation of dendritic growth
cites work: A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
cites work: Q3359644
cites work: Electrostatics and heat conduction in high contrast composite materials
cites work: An adaptive, formally second order accurate version of the immersed boundary method
cites work: Front-tracking finite element method for dendritic solidification
cites work: A second order virtual node method for elliptic problems with interfaces and irregular domains in three dimensions

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Volume of fluid (VOF) method for the dynamics of free boundaries

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A numerical method for solving variable coefficient elliptic equation with interfaces

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A new adaptive mesh refinement data structure with an application to detonation

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Weighted ENO Schemes for Hamilton--Jacobi Equations

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Efficient implementation of weighted ENO schemes

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A Cartesian grid embedded boundary method for Poisson's equation on irregular domains

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A front-tracking method for dendritic solidification

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Computations of boiling flows

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Feature-driven Cartesian adaptive mesh refinement for vortex-dominated flows

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Quantitative phase-field modeling of dendritic growth in two and three dimensions

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Supra-Convergent Schemes on Irregular Grids

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A memory and computation efficient sparse level-set method

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Advanced Transport Phenomena

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: High-Resolution Conservative Algorithms for Advection in Incompressible Flow

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Adjoint sensitivity analysis for time-dependent partial differential equations with adaptive mesh refinement

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: The Immersed Interface Method

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A boundary condition capturing method for Poisson's equation on irregular domains

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Spatially adaptive techniques for level set methods and incompressible flow

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: The numerical solution of second-order boundary value problems on nonuniform meshes

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A correction function method for Poisson problems with interface jump conditions

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: The Fast Solution of Poisson’s and the Biharmonic Equations on Irregular Regions

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A node-centered local refinement algorithm for Poisson's equation in complex geometries

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Local level set method in high dimension and codimension

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: On reinitializing level set functions

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A second order accurate projection method for the incompressible Navier-Stokes equations on non-graded adaptive grids

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A second order accurate level set method on non-graded adaptive Cartesian grids

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A supra-convergent finite difference scheme for the variable coefficient Poisson equation on non-graded grids

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Block structured adaptive mesh and time refinement for hybrid, hyperbolic \(+ N\)-body systems

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Crystal growth of pure substances: phase-field simulations in comparison with analytical and experimental results

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: An efficient fluid-solid coupling algorithm for single-phase flows

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A boundary condition capturing method for incompressible flame discontinuities.

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Dynamic tubular grid: an efficient data structure and algorithms for high resolution level sets

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Q4160606

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Level set methods and dynamic implicit surfaces

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Geometric Level Set Methods in Imaging, Vision, and Graphics

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Efficient symmetric discretization for the Poisson, heat and Stefan-type problems with Robin boundary conditions

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A PDE-based fast local level set method

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Flow patterns around heart valves: A numerical method

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Numerical analysis of blood flow in the heart

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: The immersed boundary method

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Gerris: A tree-based adaptive solver for the incompressible Euler equations in complex geometries.

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: An accurate adaptive solver for surface-tension-driven interfacial flows

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Adaptive mesh refinement computation of solidification microstructures using dynamic data structures

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A front tracking method for the motion of premixed flames

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method.

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A remark on computing distance functions

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Q4414855

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Q4414854

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A Parallel Geometric Multigrid Method for Finite Elements on Octree Meshes

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A fast marching level set method for monotonically advancing fronts.

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Fast Marching Methods

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Crystal growth and dendritic solidification

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Q4247633

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Adaptive mesh refinement based on high order finite difference WENO scheme for multi-scale simulations

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: The Numerical Solution of Laplace's Equation

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Efficient implementation of essentially nonoscillatory shock-capturing schemes. II

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Three-dimensional simulation of saturated film boiling on a horizontal cylinder

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Numerical simulation of melting of a horizontal substrate placed beneath a heavier liquid

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Numerical simulation of nucleate boiling on a horizontal surface at high heat fluxes

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Fast tree-based redistancing for level set computations

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Tree methods for moving interfaces

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A new adaptive local mesh refinement algorithm and its application on fourth order thin film flow problem

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: An adaptive level set approach for incompressible two-phase flows

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A level set approach for computing solutions to incompressible two-phase flow

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A level set simulation of dendritic solidification of multi-component alloys

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Modeling the growth and interaction of multiple dendrites in solidification using a level set method

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: An adaptive mesh redistribution method for nonlinear Hamilton--Jacobi equations in two- and three-dimensions.

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A multigrid method on non-graded adaptive octree and quadtree Cartesian grids

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Numerical simulation of bubble growth in film boiling using a coupled level-set and volume-of-fluid method

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A front-tracking method for the computations of multiphase flow.

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Fast Sweeping Algorithms for a Class of Hamilton--Jacobi Equations

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Rapid and accurate computation of the distance function using grids

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Efficient algorithms for globally optimal trajectories

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Multiphase dynamics in arbitrary geometries on fixed Cartesian grids

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Sharp-interface simulation of dendritic growth with convection: Benchmarks.

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A front-tracking method for viscous, incompressible multi-fluid flows

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A new volume-of-fluid method with a constructed distance function on general structured grids

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A volume of fluid based method for fluid flows with phase change

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Scale separation for implicit large eddy simulation

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A semi-Lagrangian high-order method for Navier-Stokes equations

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: The adjoint method for an inverse design problem in the directional solidification of binary alloys

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Sharp interface Cartesian grid method. III: Solidification of pure materials and binary solutions

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Modelling dendritic solidification with melt convection using the extended finite element method

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Handling solid-fluid interfaces for viscous flows: explicit jump approximation vs. ghost cell approaches

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: A fast sweeping method for Eikonal equations

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Modeling dendritic growth of a binary alloy

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (cites work)
cites work: Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method

High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (DOI)
DOI: 10.1007/S10915-012-9660-1