A note on the stability of cut cells and cell merging

DOI10.1016/j.apnum.2015.05.003zbMath1321.65137OpenAlexW591344257MaRDI QIDQ492938

Marsha J. Berger

Publication date: 21 August 2015

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2015.05.003

zbMATH Keywords

stabilitynumerical examplesfinite volumelinear advectionembedded boundarycell mergingcut cellfirst-order upwind scheme

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Initial value problems for first-order hyperbolic equations (35L03)

Related Items (7)

An explicit algorithm for imbedding solid boundaries in Cartesian grids for the reactive Euler equations ⋮ A Two-Dimensional Stabilized Discontinuous Galerkin Method on Curvilinear Embedded Boundary Grids ⋮ A state redistribution algorithm for finite volume schemes on cut cell meshes ⋮ A weighted state redistribution algorithm for embedded boundary grids ⋮ An implicit Cartesian cut-cell method for incompressible viscous flows with complex geometries ⋮ An explicit implicit scheme for cut cells in embedded boundary meshes ⋮ A novel supermesh method for computing solutions to the multi-material Stefan problem with complex deforming interfaces and microstructure

Cites Work

• An adaptive multilevel multigrid formulation for Cartesian hierarchical grid methods
• Time step restrictions for Runge-Kutta discontinuous Galerkin methods on triangular grids
• Group velocity interpretation of the stability theory of Gustafsson, Kreiss, and Sundstroem
• Developments in Cartesian cut cell methods
• An analysis of the spectrum of the discontinuous Galerkin method. II: Nonuniform grids
• Cartesian cut cell approach for simulating incompressible flows with rigid bodies of arbitrary shape
• Stability Theory of Difference Approximations for Mixed Initial Boundary Value Problems. II
• H-Box Methods for the Approximation of Hyperbolic Conservation Laws on Irregular Grids

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