Commun. Comput. Phys., 8 (2010), pp. 585-609.


WENO Schemes for Mixed-Element Unstructured Meshes

V. A. Titarev 1*, P. Tsoutsanis 1, D. Drikakis 1

1 Fluid Mechanics and Computational Sciences Group, Aerospace Sciences Department, Cranfield University, Cranfield, MK43 0AL, UK.

Received 4 September 2009; Accepted (in revised version) 8 January 2010
Available online 15 April 2010
doi:10.4208/cicp.040909.080110a

Abstract

The paper extends weighted essentially non-oscillatory (WENO) schemes to two-dimensional quadrilateral and mixed-element unstructured meshes. The key element of the proposed methods is a reconstruction procedure suitable for arbitrarily-shaped cells. The resulting schemes achieve the designed uniformly high-order of accuracy and compute discontinuous solutions without spurious oscillations at interfaces between cells of two different types.

AMS subject classifications: 65M08, 76-04, 76N99

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Key words: WENO, unstructured, mixed-element, triangular, quadrilateral, finite volume.

*Corresponding author.
Email: v.a.titarev@cranfield.ac.uk, titarev@mail.ru (V. A. Titarev), takis10@hotmail.com (P. Tsoutsanis), d.drikakis@cranfield.ac.uk (D. Drikakis)
 

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