ADI method based on C2-continuous two-node integrated-RBF elements for viscous flows
Article
Article Title | ADI method based on C2-continuous two-node integrated-RBF elements for viscous flows |
---|---|
ERA Journal ID | 48 |
Article Category | Article |
Authors | An-Vo, D.-A. (Author), Mai-Duy, N. (Author), Tran, C.-D. (Author) and Tran-Cong, T. (Author) |
Journal Title | Applied Mathematical Modelling: simulation and computation for engineering and environmental systems |
Journal Citation | 37 (7), pp. 5184-5203 |
Number of Pages | 20 |
Year | 2013 |
Publisher | Elsevier |
Place of Publication | United States |
ISSN | 0307-904X |
1872-8480 | |
Digital Object Identifier (DOI) | https://doi.org/10.1016/j.apm.2012.10.034 |
Web Address (URL) | https://www.sciencedirect.com/science/article/pii/S0307904X12006397 |
Abstract | We propose a C2-continuous alternating direction implicit (ADI) method for the solution of the streamfunction-vorticity equations governing steady 2D incompressible viscous fluid flows. Discretisation is simply achieved with Cartesian grids. Local two-node integrated radial basis function elements (IRBFEs) [D.-A. An-Vo, N. Mai-Duy, T. Tran-Cong, A C2-continuous control-volume technique based on Cartesian grids and two-node integrated-RBF elements for second-order elliptic problems, CMES: Computer Modeling in Engineering & Sciences 72 (2011) 299-334] are used for the discretisation of the diffusion terms, and then the convection terms are incorporated into system matrices by treating nodal derivatives as unknowns. ADI procedure is applied for the time integration. Following ADI factorisation, the two-dimensional problem becomes a sequence of one-dimensional problems. The solution strategy consists of multiple use of a one-dimensional sparse matrix algorithm that helps saving the computational cost. High levels of accuracy and efficiency of the present methods are demonstrated with solutions of several benchmark problems defined on rectangular and non-rectangular domains. |
Keywords | Navier-Stokes equations; integrated-radial-basis-function elements; C2-continuous solutions; Cartesian grid; ADI method; local RBF approximation |
ANZSRC Field of Research 2020 | 490303. Numerical solution of differential and integral equations |
490101. Approximation theory and asymptotic methods | |
401706. Numerical modelling and mechanical characterisation | |
Public Notes | File reproduced in accordance with the copyright policy of the publisher/author. |
Byline Affiliations | Computational Engineering and Science Research Centre |
Institution of Origin | University of Southern Queensland |
https://research.usq.edu.au/item/q2375/adi-method-based-on-c2-continuous-two-node-integrated-rbf-elements-for-viscous-flows
Download files
1948
total views277
total downloads1
views this month2
downloads this month
Export as
Related outputs
Potential for greenhouse gas (GHG) emissions savings from replacing short motorcycle trips with active travel modes in Vietnam
Tong, Yen Dan, Maraseni, Tek, Nguyen, Phuong-Duy, An-Vo, Duc-Anh, Mancuso Tradenta, Julio and Tran, Thuy Ai Dong. 2023. "Potential for greenhouse gas (GHG) emissions savings from replacing short motorcycle trips with active travel modes in Vietnam." Transportation. https://doi.org/10.1007/s11116-023-10394-0Electrohydrodynamic Nebuliser (eNEB) for Direct Pulmonary Drug Delivery Application
Vu, Trung-Hieu, Mai, Luan Ngoc, Nguyen, Tuan-Hung, Tran, Dang Ngoc, Nguyen, Tuan-Khoa, Nguyen, Thanh, Fastier-Woollel, Jarred, Tran, Canh-Dung, Dinh, Toan, Nguyen, Hong-Quan, Dao, Dzung Viet and Dau, Van Thanh. 2023. "Electrohydrodynamic Nebuliser (eNEB) for Direct Pulmonary Drug Delivery Application." 2023 IEEE 36th International Conference on Micro Electro Mechanical Systems (MEMS). Munich, Germany 15 - 19 Jan 2023 United States. IEEE Computer Society. https://doi.org/10.1109/MEMS49605.2023.10052181A new high-order nine-point stencil, based on integrated-RBF approximations, for the first biharmonic equation
Mai-Duy, N., Strunin, D. and Karunasena, W.. 2022. "A new high-order nine-point stencil, based on integrated-RBF approximations, for the first biharmonic equation." Engineering Analysis with Boundary Elements. 143, pp. 687-699. https://doi.org/10.1016/j.enganabound.2022.07.014Groundwater-surface water interactions at wetland interface: Advancement in catchment system modeling
Rafiei, Vahid, Nejadhashemi, A. Pouyan, Mushtaq, Shahbaz, Bailey, Ryan T. and An-Vo, Duc-Anh. 2022. "Groundwater-surface water interactions at wetland interface: Advancement in catchment system modeling." Environmental Modelling and Software. 152, pp. 1-15. https://doi.org/10.1016/j.envsoft.2022.105407Electric Field-Enhanced Electrohydrodynamic Process For Fabrication of Highly Sensitive Piezoelectric Sensor
Vu, Trung-Hieu, Nguyen, Hang Thu, Fastier-Wooller, Jarred W., Tran, Dang D. H., Nguyen, Tuan-Hung, Nguyen, Thanh, Nguyen, Tuan-Khoa, Tran, Canh-Dung, Abbasi, Naghmeh, Bui, Tung T., Dao, Dzung V. and Dau, Van Thanh. 2022. "Electric Field-Enhanced Electrohydrodynamic Process For Fabrication of Highly Sensitive Piezoelectric Sensor." 35th IEEE International Conference on Micro Electro Mechanical Systems (MEMS 2022). Tokyo, Japan 09 - 13 Jan 2022 Japan. https://doi.org/10.1109/MEMS51670.2022.9699674NEXUS project: pathways for greenhouse gas emissions mitigation and climate change adaptation of Australian Livestock Industries
Cullen, Brendan R., Harrison, Matthew T., Mayberry, Dianne, Cobon, David H., An-Vo, Duc-Anh, Christie, Karen M., Bilotto, Franco, Talukder, Saranika, Perry, Lindsey, Eckard, Richard J. and Davison, Thomas M.. 2022. "NEXUS project: pathways for greenhouse gas emissions mitigation and climate change adaptation of Australian Livestock Industries." 8th International Greenhouse Gas and Animal Agriculture Conference (GGAA 2022). Orlando, United States 05 - 09 Jun 2022 Florida, United States.Nuanced assessment of livelihood resilience through the intersectional lens of gender and ethnicity: evidence from small-scale farming communities in the upland regions of Vietnam
Tran, Van Thanh, An-Vo, Duc-Anh, Mushtaq, Shahbaz and Cockfield, Geoff. 2022. "Nuanced assessment of livelihood resilience through the intersectional lens of gender and ethnicity: evidence from small-scale farming communities in the upland regions of Vietnam." Journal of Rural Studies. 92, pp. 68-78. https://doi.org/10.1016/j.jrurstud.2022.03.011The concept of light-harvesting, self-powered mechanical sensors using a monolithic structure
Nguyen, Thanh, Dinh, Toan, Dau, Van Thanh, Nguyen, Hung, Vu, Trung Hieu, Tran, Canh-Dung, Song, Pingan, Bell, John, Nguyen, Nam-Trung and Dao, Dzung Viet. 2022. "The concept of light-harvesting, self-powered mechanical sensors using a monolithic structure." Nano Energy. 96, pp. 1-9. https://doi.org/10.1016/j.nanoen.2022.107030An improved calibration technique to address high dimensionality and non-linearity in integrated groundwater and surface water models
Rafiei, Vahid, Nejadhashemi, A. Pouyan, Mushtaq, Shahbaz, Bailey, Ryan T. and An-Vo, Duc-Anh. 2022. "An improved calibration technique to address high dimensionality and non-linearity in integrated groundwater and surface water models." Environmental Modelling and Software. 149, pp. 1-15. https://doi.org/10.1016/j.envsoft.2022.105312A framework for assessing the value of seasonal climate forecasting in key agricultural decisions
An-Vo, Duc-Anh, Radanielson, Ando Mariot, Mushtaq, Shahbaz, Reardon-Smith, Kate and Hewitt, Chris. 2021. "A framework for assessing the value of seasonal climate forecasting in key agricultural decisions." Climate Services. 22, pp. 1-14. https://doi.org/10.1016/j.cliser.2021.100234
The value of seasonal climate forecasting in agricultural decision-making
Reardon-Smith, Kate and An-Vo, Duc-Anh. 2022. "The value of seasonal climate forecasting in agricultural decision-making." African Technical Workshop on Crop Models and coupling with Numerical Weather and Seasonal to Sub-seasonal Forecasts. Niamey, Niger 13 - 15 Jun 2022Limit state analysis of reinforced concrete slabs using an integrated radial basis function based mesh-free method
Ho, Phuc L. H., Le, Canh V. and Tran-Cong, T.. 2018. "Limit state analysis of reinforced concrete slabs using an integrated radial basis function based mesh-free method." Applied Mathematical Modelling: simulation and computation for engineering and environmental systems. 53, pp. 1-11. https://doi.org/10.1016/j.apm.2017.08.006Enhanced electro-hydrodynamics for electrospinning a highly sensitive flexible fiber-based piezoelectric sensor
Vu, Trung-Hieu, Nguyen, Hang Thu, Fastier-Wooller, Jarred W., Tran, Canh-Dung, Nguyen, Tuan-Hung, Nguyen, Hong-Quan, Nguyen, Thanh, Nguyen, Tuan-Khoa, Dinh, Toan, Bui, Tung T., Zhong, Yulin, Phan, Hoang-Phuong, Nguyen, Nam-Trung, Dao, Dzung V. and Dau, Van Thanh. 2022. "Enhanced electro-hydrodynamics for electrospinning a highly sensitive flexible fiber-based piezoelectric sensor." ACS Applied Electronic Materials. 4 (3), pp. 1301-1310. https://doi.org/10.1021/acsaelm.2c00030Simulation of non‑dilute fibre suspensions using RBF‑based macro–micro multiscale method
Nguyen, Hung Quoc and Tran, Canh‑Dung. 2022. "Simulation of non‑dilute fibre suspensions using RBF‑based macro–micro multiscale method." Korea-Australia Rheology Journal. 34 (1), pp. 1-15. https://doi.org/10.1007/s13367-022-00022-1Innovative value assessment for seasonal climate forecasting
An-Vo, Duc-Anh. 2021. "Innovative value assessment for seasonal climate forecasting." 2nd Asia-Pacific Agriculture Climate Services Week. Bangkok, Thailand Bangkok, Thailand.Computing high-order derivatives in compact integrated-RBF stencils
Mai-Duy, N., Strunin, D. and Karunasena, W.. 2022. "Computing high-order derivatives in compact integrated-RBF stencils." Engineering Analysis with Boundary Elements. 135, pp. 369-381. https://doi.org/10.1016/j.enganabound.2021.11.025