A Cartesian grid embedded boundary method for Poisson`s equation on irregular domains

Journal Article · Fri Nov 20 04:00:00 EST 1998 · Journal of Computational Physics

DOI:https://doi.org/10.1006/jcph.1998.5965· OSTI ID:320965

Johansen, H ^[1]; Colella, P ^[1]

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1. Univ. of California, Berkeley, CA (United States). Dept. of Mechanical Engineering

The authors present a numerical method for solving Poisson`s equation, with variable coefficients and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a finite-volume discretization, which embeds the domain in a regular Cartesian grid. They treat the solution as a cell-centered quantity, even when those centers are outside the domain. Cells that contain a portion of the domain boundary use conservative differencing of second-order accurate fluxes on each cell volume. The calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes. This allows us to use multigrid iterations with a simple point relaxation strategy. They have combined this with an adaptive mesh refinement (AMR) procedure. They provide evidence that the algorithm is second-order accurate on various exact solutions and compare the adaptive and nonadaptive calculations.

• Sponsoring Organization: USDOE, Washington, DC (United States); Department of the Air Force, Washington, DC (United States)
• DOE Contract Number: FG03-94ER25205; FG03-92ER25140; AC03-76SF00098
• OSTI ID: 320965
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 147; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
CARTESIAN COORDINATES
DIRICHLET PROBLEM
MESH GENERATION
NUMERICAL SOLUTION
POISSON EQUATION