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Upwind skewed radial basis functions (USRBF) for solution of highly convective problems over meshfree nodes

Upwind skewed radial basis functions (USRBF) for solution of highly convective problems over meshfree nodes
Upwind skewed radial basis functions (USRBF) for solution of highly convective problems over meshfree nodes
An upwind skewed radial basis function (USRBF)-based solution scheme is presented for stabilized solutions of convection-dominated problems over meshfree nodes. The conventional, radially symmetric radial basis functions (RBFs) are multiplied with an upwinding factor which skews the RBFs toward the upwind direction. The upwinding factor is a function of flow direction, intensity of convection, size of local support domain, and nodal distribution. The use of USRBFs modifies the weight values such that the necessary artificial diffusion is added only along the flow direction, whereas the crosswind diffusion is avoided. Subsequently, these skewed radial basis functions are employed in finite difference mode (RBF-FD) for derivative approximation. The performance and accuracy of the proposed scheme is studied by solving convection–diffusion problems over uniform and random distribution of meshfree nodes with various convection intensities. The upwinding effectively suppresses non-physical perturbation in numerical solution of convection-dominated problems. The results show that significant improvement in accuracy can be achieved by using the proposed USRBF-based solution scheme, particularly at higher convection intensities.
0177-0667
Djidjeli, Kamal
94ac4002-4170-495b-a443-74fde3b92998
Javed, Ali
651c9b09-c3dd-4ea0-a826-beb391e7f497
Baig, Ali Asadullah
4053d253-6cf1-416c-a67d-741a4cc9bb2b
Shahzad, Aamer
887ffc22-1a98-49a0-a64b-0644c8fd9a0a
Hammed, Asad
366b053b-e33d-4f84-8b5c-4795d6464725
Djidjeli, Kamal
94ac4002-4170-495b-a443-74fde3b92998
Javed, Ali
651c9b09-c3dd-4ea0-a826-beb391e7f497
Baig, Ali Asadullah
4053d253-6cf1-416c-a67d-741a4cc9bb2b
Shahzad, Aamer
887ffc22-1a98-49a0-a64b-0644c8fd9a0a
Hammed, Asad
366b053b-e33d-4f84-8b5c-4795d6464725

Djidjeli, Kamal, Javed, Ali, Baig, Ali Asadullah, Shahzad, Aamer and Hammed, Asad (2019) Upwind skewed radial basis functions (USRBF) for solution of highly convective problems over meshfree nodes. Engineering With Computers. (doi:10.1007/s00366-019-00873-3).

Record type: Article

Abstract

An upwind skewed radial basis function (USRBF)-based solution scheme is presented for stabilized solutions of convection-dominated problems over meshfree nodes. The conventional, radially symmetric radial basis functions (RBFs) are multiplied with an upwinding factor which skews the RBFs toward the upwind direction. The upwinding factor is a function of flow direction, intensity of convection, size of local support domain, and nodal distribution. The use of USRBFs modifies the weight values such that the necessary artificial diffusion is added only along the flow direction, whereas the crosswind diffusion is avoided. Subsequently, these skewed radial basis functions are employed in finite difference mode (RBF-FD) for derivative approximation. The performance and accuracy of the proposed scheme is studied by solving convection–diffusion problems over uniform and random distribution of meshfree nodes with various convection intensities. The upwinding effectively suppresses non-physical perturbation in numerical solution of convection-dominated problems. The results show that significant improvement in accuracy can be achieved by using the proposed USRBF-based solution scheme, particularly at higher convection intensities.

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More information

Accepted/In Press date: 9 October 2019
e-pub ahead of print date: 30 October 2019

Identifiers

Local EPrints ID: 437491
URI: http://eprints.soton.ac.uk/id/eprint/437491
ISSN: 0177-0667
PURE UUID: 92fc91f2-6a91-4435-90db-47c75a10dfc9

Catalogue record

Date deposited: 31 Jan 2020 17:36
Last modified: 06 Oct 2020 21:51

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