Meshfree Finite Differences for Vector Poisson and Pressure Poisson Equations with Electric Boundary Conditions
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1312.4223.pdf
Size
1.19 MB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Zhou, Dong
Seibold, Benjamin
Shirokoff, David
Chidyagwai, Prince
Rosales, Rodolfo
Date Issued
2015
Journal
Meshfree Methods for Partial Differential Equations VII
Publisher
Springer
Citation
Zhou, Dong et al. “Meshfree Finite Differences for Vector Poisson and Pressure Poisson Equations with Electric Boundary Conditions.” Meshfree Methods for Partial Differential Equations VII (November 2014): 223–246 © 2015 Springer International Publishing Switzerland
Version
Original manuscript
Abstract
We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the incompressibility of the vector field are prescribed at the boundary. Even on irregular domains with only convex corners, canonical nodalbased finite elements may converge to the wrong solution due to a version of the Babuška paradox. In turn, straightforward meshfree finite differences converge to the true solution, and even high-order accuracy can be achieved in a simple fashion. The methodology is then extended to a specific pressure Poisson equation reformulation of the Navier-Stokes equations that possesses the same type of boundary conditions. The resulting numerical approach is second order accurate and allows for a simple switching between an explicit and implicit treatment of the viscosity terms. Keywords: Meshfree Finite-differences; Navier-Stokes; Incompressible; Vector Poisson equation; Pressure Poisson equation; Reformulation; Manufactured solution; High-order
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/978-3-319-06898-5_12
