A sixth order Mehrstellen scheme with an application to the Method of Local Corrections for the 3D Poisson equation
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
We present a sixth order finite difference scheme for Poisson’s equation when discretized with the compact 27-point stencil based on Mehrstellen corrections of the forcing function term f. Our approach results in a sixth order accurate solution error as opposed to a fourth-order error imposed by the classical Mehrstellen correction for the 19-point and 27-point stencils. The present study is a continuation of former work of Spotz and Carey (1996) on compact finite difference schemes for Poisson’s equation where sixth order convergence may be obtained under the assumption that the fourth order derivatives of f are determined analytically. Specifically, we show that sixth order convergence can still be attained when only values of f at grid points are available. The sixth order Mehrstellen scheme is further coupled with a Method of Local Corrections (MLC) 3D Poisson solver improving to sixth order accuracy the results reported in Kavouklis and Colella (2019). The MLC test case considered involves an adaptive grid that comprises 7.5 billion cells.
- Research Organization:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- DOE Contract Number:
- AC52-07NA27344; AC02-05CH11231
- OSTI ID:
- 1879264
- Report Number(s):
- LLNL-TR-838195; 1058576
- Country of Publication:
- United States
- Language:
- English
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