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

Technical Report · Fri Jan 31 04:00:00 EST 1997

DOI:https://doi.org/10.2172/459443· OSTI ID:459443

Johansen, H ^[1]; Colella, P ^[2]

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1. Univ. of California, Berkeley, CA (United States). Dept. of Mechanical Engineering
2. Lawrence Berkeley National Lab., CA (United States). Center for Computational Sciences and 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 conservation 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 them to use multi-grid 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 non-adaptive calculations.

• Research Organization: Lawrence Berkeley National Lab., CA (United States); California Univ., Berkeley, CA (United States); Air Force Office of Scientific Research, Baltimore, MD (United States)
• Sponsoring Organization: USDOE Office of Energy Research, Washington, DC (United States); Department of the Air Force, Washington, DC (United States)
• DOE Contract Number: AC03-76SF00098; FG03-94ER25205; FG03-92ER25140
• OSTI ID: 459443
• Report Number(s): LBNL--39908; ON: DE97004174; CNN: AASERT Grant F49620-93-1-0521
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ACCURACY
ALGORITHMS
BOUNDARY CONDITIONS
ITERATIVE METHODS
MESH GENERATION
NUMERICAL SOLUTION
POISSON EQUATION