Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session KP1: Poster Session (3:20-4:05pm)
Monday, November 19, 2018
Georgia World Congress Center Room: Level 1, Exhibit Hall B2 by the GFM videos
Abstract ID: BAPS.2018.DFD.KP1.72
Abstract: KP1.00072 : Semi-Extrapolated Finite Difference Schemes: Accuracy and Consistency
When solving partial differential equations, finite difference methods are a popular choice. Several factors come into play when choosing a finite difference method, such as stability, computational cost, accuracy, and consistency. In response to the small stability regions of explicit methods and the computational cost of implicit methods, we’ve developed a novel discretization technique (semi-extrapolation) that generates explicit schemes from implicit schemes by applying extrapolation to the implicit schemes in an unconventional fashion. Semi-extrapolating can lead to improved stabilities as compared to the stabilities of analogous explicit schemes, however, consistency and accuracy can be affected by semi-extrapolation. In our presentation, we’ll discuss our semi-extrapolation technique and introduce several semi-extrapolated discretizations of the Advection Equation and the Advection-Diffusion Equation. We’ll then analyze the consistency of these semi-extrapolated discretizations, compare their accuracies against the accuracies of several common discretizations, and discuss how stability constraints and choice of extrapolation stencil both influence the consistency and accuracy of semi-extrapolated schemes.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2018.DFD.KP1.72
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