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A fast high-resolution algorithm for linear convection problems: particle transport method


Smolianski, A; Shipilova, O; Haario, H (2007). A fast high-resolution algorithm for linear convection problems: particle transport method. International Journal for Numerical Methods in Engineering, 70(6):655-684.

Abstract

The paper is devoted to a novel explicit technique, the particle transport method (PTM), for solving linear convection problems. While being a Lagrangian (characteristic based) method, PTM has the advantage of Eulerian methods to represent the solution on a fixed mesh. The proposed approach belongs to the class of monotone high-resolution numerical schemes, possesses the property of unconditional stability and works with structured and unstructured meshes. It is also demonstrated that the method has a linear computational complexity. The performance of the presented algorithm is tested on one- and two-dimensional benchmark problems. The numerical results confirm that the method has the 2nd-order spatial accuracy and can be significantly faster than the grid-based methods of the same order. Copyright © 2006 John Wiley & Sons, Ltd.

Abstract

The paper is devoted to a novel explicit technique, the particle transport method (PTM), for solving linear convection problems. While being a Lagrangian (characteristic based) method, PTM has the advantage of Eulerian methods to represent the solution on a fixed mesh. The proposed approach belongs to the class of monotone high-resolution numerical schemes, possesses the property of unconditional stability and works with structured and unstructured meshes. It is also demonstrated that the method has a linear computational complexity. The performance of the presented algorithm is tested on one- and two-dimensional benchmark problems. The numerical results confirm that the method has the 2nd-order spatial accuracy and can be significantly faster than the grid-based methods of the same order. Copyright © 2006 John Wiley & Sons, Ltd.

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12 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:linear convection • particle transport • monotone • high-resolution • unconditionally stable • linear complexity
Language:English
Date:2007
Deposited On:03 Nov 2009 09:50
Last Modified:06 Dec 2017 20:43
Publisher:Wiley-Blackwell
ISSN:0029-5981
Additional Information:The attached file is a preprint (accepted version) of an article published in International Journal for Numerical Methods in Engineering
Publisher DOI:https://doi.org/10.1002/nme.1899

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