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A 6th Order Mehrstellen Finite Volume Discretization of Poisson's Equation in Three Dimensions

Technical Report ·
DOI:https://doi.org/10.2172/1844490· OSTI ID:1844490
 [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

We discuss the derivation of a new, sixth-order finite volume scheme for Poisson’s equation on 3D Cartesian equispaced grids. The scheme is based on a discretization of the Laplace operator with a compact (Mehrstellen) 27-point stencil. To achieve sixth order convergence the right hand side of the equation is replaced with a discrete operator that involves the discrete Laplace and Biharmonic operators and the sum of discrete fourth-order cross derivatives applied to the charge function. Numerical tests demonstrate the superiority of the proposed method compared to the well known schemes associated with the 7-point and 19-point discretizations of the Laplacian.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
DOE Contract Number:
AC52-07NA27344
OSTI ID:
1844490
Report Number(s):
LLNL-TR-831628; 1048768
Country of Publication:
United States
Language:
English

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