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