High-resolution finite volume computations using a novel weighted least-squares formulation

High‐resolution finite volume schemes based on a novel reconstruction technique, SDWLS (solution‐dependent weighted least squares) are considered. The SDWLS technique, originally developed for second‐order variable reconstruction by Mandal and Subramanian (Appl. Numer. Math., 2007; DOI: 10.1016/j.ap...

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Bibliographic Details
Published in:International journal for numerical methods in fluids 2008-03, Vol.56 (8), p.1425-1431
Main Authors: Mandal, J. C., Rao, S., Subramanian, J.
Format: Article
Language:English
Subjects:
Computational methods in fluid dynamics
Euler equations
Exact sciences and technology
finite volume method
Fluid dynamics
Fundamental areas of phenomenology (including applications)
high-resolution schemes
higher-order reconstruction
Physics
solution-dependent weighted least squares
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Summary:High‐resolution finite volume schemes based on a novel reconstruction technique, SDWLS (solution‐dependent weighted least squares) are considered. The SDWLS technique, originally developed for second‐order variable reconstruction by Mandal and Subramanian (Appl. Numer. Math., 2007; DOI: 10.1016/j.apnum.2007.02.003), is further extended to third‐order reconstruction with compact stencils involving only the nearest neighbors. The new schemes are applied to solve a few numerical test examples, involving scalar conservation laws and the system of non‐linear gas dynamics equations, in order to study their performance. Significant improvements in solution accuracy have been achieved with the second‐ and third‐order SDWLS reconstruction techniques. Copyright © 2007 John Wiley & Sons, Ltd.
ISSN:0271-2091
1097-0363
DOI:10.1002/fld.1707