A streamline tracking algorithm for semi-Lagrangian advection schemes based on the analytic integration of the velocity field

Journal article (2005)
Department
Hydraulic Engineering (CEG) (TU Delft)
Copyright: Elsevier
DOI: https://doi.org/doi:10.1016/j.cam.2005.04.055
Computational fluid dynamics Unstructured mesh Finite volume Advection Semi-Lagrangian Streamlines
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Published Date

31-12-2005

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Source:

Journal of Computational and Applied Mathematics, 192 (1), 2006

ISSN:

0377-0427

Faculty

Civil Engineering and Geosciences

Department

Hydraulic Engineering

Abstract

A new scheme for the construction on an unstructured grid of the streamlines of the three-dimensional shallow water equations is presented. The qualitative advantages of the scheme, notably closed streamlines and realistic treatment of closed boundaries, are derived and the spatial accuracy is demonstrated. Semi-Lagrangian advection schemes offer the computational cost advantage of being explicit but also unconditionally stable with respect to time step. However, semi-Lagrangian methods based on the numerical integration of the discretised velocity field frequently have difficulty in meeting physically significant criteria such as the closure of streamlines and the inviolability of closed boundaries. Here a streamline tracking scheme based on the analytic integration of the discretised velocity field is presented.

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