Efficient symmetric discretization for the Poisson, heat and Stefan-type problems with Robin boundary conditions

DOI10.1016/j.jcp.2009.10.017zbMath1182.65140OpenAlexW1998883579MaRDI QIDQ2655676

Joseph Papac, Frédéric Gibou, Christian Ratsch

Publication date: 25 January 2010

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2009.10.017

zbMATH Keywords

heat equationnumerical examplesdiffusion equationStefan problemlevel set methodPoisson equationRobin boundary conditionirregular domainsCrank-Nicolson finite difference method

Mathematics Subject Classification ID

Stefan problems, phase changes, etc. (80A22) Heat equation (35K05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Free boundary problems for PDEs (35R35) Finite difference methods for boundary value problems involving PDEs (65N06) Finite difference methods applied to problems in thermodynamics and heat transfer (80M20)

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Cites Work

• Unnamed Item
• Unnamed Item
• Crystal growth of pure substances: phase-field simulations in comparison with analytical and experimental results
• A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem
• Robust second-order accurate discretizations of the multi-dimensional Heaviside and Dirac delta functions
• An efficient fluid-solid coupling algorithm for single-phase flows
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Crystal growth and dendritic solidification
• A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
• A level set approach for computing solutions to incompressible two-phase flow
• A simple level set method for solving Stefan problems
• A partial differential equation approach to multidimensional extrapolation.
• A level set approach for the numerical simulation of dendritic growth
• A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
• Island dynamics and the level set method for epitaxial growth
• Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids
• The ghost fluid method for deflagration and detonation discontinuities
• Computation of three dimensional dendrites with finite elements
• Geometric integration over irregular domains with application to level-set methods
• An Adaptive Finite Element Method for Two-Phase Stefan Problems in Two Space Dimensions. II: Implementation and Numerical Experiments
• Numerical Simulations of Unsteady Crystal Growth
• Geometric Level Set Methods in Imaging, Vision, and Graphics
• Quantitative phase-field modeling of dendritic growth in two and three dimensions
• Directions in Condensed Matter Physics
• Radially symmetric phase growth controlled by diffusion
• A numerical method for two-phase flow consisting of separate compressible and incompressible regions
• A semi-Lagrangian high-order method for Navier-Stokes equations
• A boundary condition capturing method for incompressible flame discontinuities.

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