An efficient, high-order method for solving Poisson equation for immersed boundaries: combination of compact difference and multiscale multigrid methods

DOI10.1016/j.jcp.2018.08.006zbMath1416.65498OpenAlexW2887276356WikidataQ129415769 ScholiaQ129415769MaRDI QIDQ2312153

Shirzad Hosseinverdi, Hermann F. Fasel

Publication date: 4 July 2019

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2018.08.006

zbMATH Keywords

Poisson equationcompact finite difference methodhigh-order methodimmersed boundarymultiscale multigrid method

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (11)

A high-order immersed interface method free of derivative jump conditions for Poisson equations on irregular domains ⋮ An immersed interface method for the 2D vorticity-velocity Navier-Stokes equations with multiple bodies ⋮ A novel sharp interface immersed boundary framework for viscous flow simulations at arbitrary Mach number involving complex and moving boundaries ⋮ An efficient extrapolation multigrid method based on a HOC scheme on nonuniform rectilinear grids for solving 3D anisotropic convection-diffusion problems ⋮ Optimal local truncation error method to solution of 2‐D time‐independent elasticity problems with optimal accuracy on irregular domains and unfitted Cartesian meshes ⋮ High-order adaptive mesh refinement multigrid Poisson solver in any dimension ⋮ A high-order numerical approach with Cartesian meshes for modeling of wave propagation and heat transfer on irregular domains with inhomogeneous materials ⋮ Compact finite difference schemes of arbitrary order for the Poisson equation in arbitrary dimensions ⋮ A new numerical approach to the solution of the 2-D Helmholtz equation with optimal accuracy on irregular domains and Cartesian meshes ⋮ A high-order embedded domain method combining a predictor-corrector-Fourier-continuation-Gram method with an integral Fourier pseudospectral collocation method for solving linear partial differential equations in complex domains ⋮ An efficient Poisson solver for complex embedded boundary domains using the multi-grid and fast multipole methods

Cites Work

• Multigrid method based on the transformation-free HOC scheme on nonuniform grids for 2D convection diffusion problems
• A simple multigrid scheme for solving the Poisson equation with arbitrary domain boundaries
• A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem
• Compact finite difference schemes of sixth order for the Helmholtz equation
• Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
• A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries
• The Shortley-Weller embedded finite-difference method for the 3D Poisson equation with mixed boundary conditions
• Sixth order compact scheme combined with multigrid method and extrapolation technique for 2D Poisson equation
• An immersed boundary technique for simulating complex flows with rigid boundary
• Numerical analysis of blood flow in the heart
• A ghost-cell immersed boundary method for flow in complex geometry.
• An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
• A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains
• A compact difference scheme for the Navier-Stokes equations in vorticity-velocity formulation
• A new high-order immersed interface method for solving elliptic equations with imbedded interface of discontinuity
• High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
• Flow patterns around heart valves: A numerical method
• Sharp interface Cartesian grid method. I: An easily implemented technique for 3D moving boundary computations
• High-order compact solvers for the three-dimensional Poisson equation
• Parallel versions of Stone's strongly implicit algorithm
• IMMERSED BOUNDARY METHODS
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• Interface tracking finite volume method for complex solid-fluid interactions on fixed meshes
• A Multigrid Tutorial, Second Edition
• The Explicit-Jump Immersed Interface Method: Finite Difference Methods for PDEs with Piecewise Smooth Solutions
• The Immersed Interface Method
• A novel velocity-vorticity formulation of the Navier-Stokes equations with applications to boundary layer disturbance evolution.
• A sharp interface Cartesian grid method for simulating flows with complex moving boundaries

This page was built for publication: An efficient, high-order method for solving Poisson equation for immersed boundaries: combination of compact difference and multiscale multigrid methods