CUED Publications database

Improved multislope MUSCL reconstruction on unstructured grids for shallow water equations

Zhao, J and Özgen, I and Liang, D and Hinkelmann, R (2018) Improved multislope MUSCL reconstruction on unstructured grids for shallow water equations. International Journal for Numerical Methods in Fluids, 87. pp. 401-436. ISSN 0271-2091

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Abstract

Copyright © 2018 John Wiley & Sons, Ltd. In shallow water flow and transport modeling, the monotonic upstream-centered scheme for conservation laws (MUSCL) is widely used to extend the original Godunov scheme to second-order accuracy. The most important step in MUSCL-type schemes is MUSCL reconstruction, which calculate-extrapolates the values of independent variables from the cell center to the edge. The monotonicity of the scheme is preserved with the help of slope limiters that prevent the occurrence of new extrema during reconstruction. On structured grids, the calculation of the slope is straightforward and usually based on a 2-point stencil that uses the cell centers of the neighbor cell and the so-called far-neighbor cell of the edge under consideration. On unstructured grids, the correct choice for the upwind slope becomes nontrivial. In this work, 2 novel total variation diminishing schemes are developed based on different techniques for calculating the upwind slope and the downwind slope. An additional treatment that stabilizes the scheme is discussed. The proposed techniques are compared to 2 existing MUSCL reconstruction techniques, and a detailed discussion of the results is given. It is shown that the proposed MUSCL reconstruction schemes obtain more accurate results with less numerical diffusion and higher efficiency.

Item Type: Article
Subjects: UNSPECIFIED
Divisions: UNSPECIFIED
Depositing User: Cron Job
Date Deposited: 14 Feb 2018 20:06
Last Modified: 11 Jun 2019 03:12
DOI: 10.1002/fld.4499