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Upwind compact implicit and explicit high-order finite difference schemes for level set technique

Nouri Borujerdi, A ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1080/15502287.2012.682198
  3. Publisher: 2012
  4. Abstract:
  5. This paper investigates implementation of upwind compact implicit and explicit high-order finite difference schemes for solution of the level set equation. The upwind compact implicit and explicit high-order finite difference schemes are well-known techniques to descritize spatial derivatives for convection term in hyperbolic equations. Applying of upwind high-order schemes on the level set equation leads to less error and CPU time reduction compared to essential non-oscillatory (ENO), weighted essential non-oscillatory schemes (WENO), and even different particle level set methods. The results indicate the error based on area loss decreases drastically with applying high-order upwind, especially implicit schemes compared to ENO and WENO schemes. In addition, CPU time is reduced compared to these methods. Hence, the upwind high-order schemes are suggested as excellent alternatives for the previous schemes to calculate spatial derivatives in the level set equation
  6. Keywords:
  7. High-order compact finite difference scheme ; Numerical method ; CPU time ; High-order ; High-order compact finite difference ; High-order finite differences ; High-order scheme ; Hyperbolic equations ; Implicit schemes ; Level Set ; Level-set equation ; Level-set techniques ; Particle level set ; Spatial derivatives ; Upwind technique ; WENO schemes ; Numerical methods ; Partial differential equations ; Finite difference method
  8. Source: International Journal of Computational Methods in Engineering Science and Mechanics ; Volume 13, Issue 4 , 2012 , Pages 308-318 ; 15502287 (ISSN)
  9. URL: http://www.tandfonline.com/doi/abs/10.1080/15502287.2012.682198#.Vp9oxy6Hi-E