Parallel Computation Using Non-Overlapping Domain Decomposition Coupled with Compact Local Integrated RBF for Navier-Stokes Equations

Article

Pham-Sy, Nam and Tran, Canh-Dung. 2022. "Parallel Computation Using Non-Overlapping Domain Decomposition Coupled with Compact Local Integrated RBF for Navier-Stokes Equations." International Journal of Computational Fluid Dynamics. 36 (10), pp. 835-856. https://doi.org/10.1080/10618562.2023.2229250
Article Title

Parallel Computation Using Non-Overlapping Domain Decomposition Coupled with Compact Local Integrated RBF for Navier-Stokes Equations

ERA Journal ID3464
Article CategoryArticle
AuthorsPham-Sy, Nam and Tran, Canh-Dung
Journal TitleInternational Journal of Computational Fluid Dynamics
Journal Citation36 (10), pp. 835-856
Number of Pages22
Year2022
PublisherTaylor & Francis
Place of PublicationSwitzerland
ISSN1029-0257
1061-8562
Digital Object Identifier (DOI)https://doi.org/10.1080/10618562.2023.2229250
Web Address (URL)https://www.tandfonline.com/doi/full/10.1080/10618562.2023.2229250
AbstractA non-overlapping domain decomposition-based parallel algorithm coupled with a compact local integrated radial basis function (CLIRBF) method is developed for solving Navier-Stokes equations. For this approach, a problem is divided into subdomains. In each sub-domain, a CLIRBF scheme is applied to solve the Navier-Stokes equations of flows. A relaxation factor is used at the interface between sub-domains to ensure the quick convergence of the present method. The Bitmap termination detection technique is introduced to complete the global termination. The present approach is verified using two fluid flow problems: the lid-driven cavity and the natural convection in concentric annuli flow. The numerical results have demonstrated the efficiency of the present parallel method compared with the corresponding sequential one and other published methods. Especially, super-linear speed-up was achieved for several CPUs. In terms of accuracy, the obtained results are in very good agreement with benchmark results.
KeywordsParallel algorithm; non-overlapping domain; decomposition method; compact local integrated; radial basis function; Navier–Stokes equations
ANZSRC Field of Research 2020490399. Numerical and computational mathematics not elsewhere classified
Byline AffiliationsSchool of Engineering
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Dinh, Toan, Phan, Hoang-Phuong, Nguyen, Tuan-Khoa, Qamar, Afzaal, Foisal, Abu Riduan Md, Nguyen, Thanh Viet, Tran, Canh-Dung, Zhu, Yong, Nguyen, Nam-Trung and Dao, Dzung Viet. 2016. "Environment-friendly carbon nanotube based flexible electronics for noninvasive and wearable healthcare." Journal of Materials Chemistry C. 4 (42), pp. 10061-10068. https://doi.org/10.1039/c6tc02708c
RBFN stochastic coarse-grained simulation method: Part I - Dilute polymer solutions using bead-spring chain models
Nguyen, H. Q., Tran, C.-D. and Tran-Cong, T.. 2015. "RBFN stochastic coarse-grained simulation method: Part I - Dilute polymer solutions using bead-spring chain models." CMES Computer Modeling in Engineering and Sciences. 105 (5), pp. 399-439. https://doi.org/10.3970/cmes.2015.105.399
A three-point coupled compact integrated RBF scheme for second-order differential problems
Tien, C. M. T., Thai-Quang, N., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2015. "A three-point coupled compact integrated RBF scheme for second-order differential problems." CMES Computer Modeling in Engineering and Sciences. 104 (6), pp. 425-469. https://doi.org/10.3970/cmes.2015.104.425
Corona based air-flow using parallel discharge electrodes
Dau, Van Thanh, Dinh, Thien Xuan, Bui, Tung Thanh, Tran, Canh-Dung, Phan, Hoa Thanh and Terebessy, Tibor. 2016. "Corona based air-flow using parallel discharge electrodes." Experimental Thermal and Fluid Science. 79, pp. 52-56. https://doi.org/10.1016/j.expthermflusci.2016.06.023
Simulation of flow of fibre suspensions using an IRBF-BCF based multiscale approach
Nguyen, H. Q., Tran, C.-D. and Tran-Cong, T.. 2015. "Simulation of flow of fibre suspensions using an IRBF-BCF based multiscale approach." Solnordal, C. B., Liovic, P., Delaney, G. W., Cummins, S. J., Schwarz, M. P. and Witt, P. J. (ed.) 11th International Conference on Computational Fluid Dynamics in the Minerals and Process Industries (CFD2015). Melbourne, Australia 07 - 09 Dec 2015 Australia.
Stable integrated RBF calculation using preconditioning and high-order compact approximation for second-order PDEs
Tien, C. M. T., Mai-Duy, N., Ngo-Cong, D., Tran, C. D. and Tran-Cong, T.. 2015. "Stable integrated RBF calculation using preconditioning and high-order compact approximation for second-order PDEs." Witt, Peter (ed.) Eleventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries 2015. Melbourne, Victoria 07 - 09 Dec 2015 Australia.
Incompressible smoothed particle hydrodynamics-moving IRBFN method for viscous flow problems
Ngo-Cong, D., Tran, C.-D., Mai-Duy, N. and Tran-Cong, T.. 2015. "Incompressible smoothed particle hydrodynamics-moving IRBFN method for viscous flow problems." Engineering Analysis with Boundary Elements. 59, pp. 172-186. https://doi.org/10.1016/j.enganabound.2015.06.006
High-order fully coupled scheme based on compact integrated RBF approximation for viscous flows in regular and irregular domains
Tien, C. M. T., Thai-Quang, N., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2015. "High-order fully coupled scheme based on compact integrated RBF approximation for viscous flows in regular and irregular domains." CMES Computer Modeling in Engineering and Sciences. 105 (4), pp. 301-340. https://doi.org/10.3970/cmes.2015.105.301
A multiscale method based on the fibre configuration field, IRBF and DAVSS for the simulation of fibre suspension flows
Nguyen, H. Q., Tran, C.-D. and Tran-Cong, T.. 2015. "A multiscale method based on the fibre configuration field, IRBF and DAVSS for the simulation of fibre suspension flows." CMES: Computer Modeling in Engineering and Science. 109 (4), pp. 361-403. https://doi.org/10.3970/cmes.2015.109.361
A high-order coupled compact integrated RBF approximation based domain decomposition algorithm for second-order differential problems
Tien, C. M. T., Pham-Sy, N., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2015. "A high-order coupled compact integrated RBF approximation based domain decomposition algorithm for second-order differential problems." CMES Computer Modeling in Engineering and Sciences. 104 (4), pp. 251-304. https://doi.org/10.3970/cmes.2015.104.251
Parallel computations based on domain decompositions and integrated radial basis functions for fluid flow problems
Pham-Sy, Nam. 2015. Parallel computations based on domain decompositions and integrated radial basis functions for fluid flow problems. PhD Thesis Doctor of Philosophy. University of Southern Queensland.
Parallel control-volume method based on compact local integrated RBFs for the solution of fluid flow problems
Pham-Sy, N., Tran, C.-D., Mai-Duy, N. and Tran-Cong, T.. 2014. "Parallel control-volume method based on compact local integrated RBFs for the solution of fluid flow problems." CMES Computer Modeling in Engineering and Sciences. 100 (5), pp. 363-397. https://doi.org/10.3970/cmes.2014.100.363
A fully coupled scheme for viscous flows in regular and irregular domains using compact integrated RBF approximation
Tien, C. M. T., Thai-Quang, N., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2014. "A fully coupled scheme for viscous flows in regular and irregular domains using compact integrated RBF approximation." Applied Mechanics and Materials. 553, pp. 138-143. https://doi.org/10.4028/www.scientific.net/AMM.553.138
A numerical solution based on the Fokker-Planck equation for dilute polymer solutions using high order RBF methods
Nguyen, H. Q., Tran, C.-D., Pham-Sy, N. and Tran-Cong, T.. 2014. "A numerical solution based on the Fokker-Planck equation for dilute polymer solutions using high order RBF methods." Applied Mechanics and Materials. 553, pp. 187-192. https://doi.org/10.4028/www.scientific.net/AMM.553.187
ADI method based on C2-continuous two-node integrated-RBF elements for viscous flows
An-Vo, D.-A., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2013. "ADI method based on C2-continuous two-node integrated-RBF elements for viscous flows." Applied Mathematical Modelling: simulation and computation for engineering and environmental systems. 37 (7), pp. 5184-5203. https://doi.org/10.1016/j.apm.2012.10.034
A direct forcing immersed boundary method employed with compact integrated RBF approximations for heat transfer and fluid flow problems
Thai-Quang, N., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2013. "A direct forcing immersed boundary method employed with compact integrated RBF approximations for heat transfer and fluid flow problems." CMES Computer Modeling in Engineering and Sciences. 96 (1), pp. 49-90. https://doi.org/10.3970/cmes.2013.096.049
Compact local IRBF and domain decomposition method for solving PDEs using a distributed termination detection based parallel algorithm
Pham-Sy, N., Tran, C.-D., Hoang-Trieu, T.-T., Mai-Duy, N. and Tran-Cong, T.. 2013. "Compact local IRBF and domain decomposition method for solving PDEs using a distributed termination detection based parallel algorithm." CMES Computer Modeling in Engineering and Sciences. 92 (1), pp. 1-31. https://doi.org/10.3970/cmes.2013.092.001
A finite-volume method based on compact local integrated radial basis function approximations for second-order differential problems
Hoang-Trieu, T.-T., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2013. "A finite-volume method based on compact local integrated radial basis function approximations for second-order differential problems." CMES Computer Modeling in Engineering and Sciences. 91 (6), pp. 485-516. https://doi.org/10.3970/cmes.2013.091.485
A numerical scheme based on compact integrated-RBFs and Adams-Bashforth/Crank-Nicolson algorithms for diffusion and unsteady fluid flow problems
Thai-Quang, N., Le-Cao, K., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2013. "A numerical scheme based on compact integrated-RBFs and Adams-Bashforth/Crank-Nicolson algorithms for diffusion and unsteady fluid flow problems." Engineering Analysis with Boundary Elements. 37 (12), pp. 1653-1667. https://doi.org/10.1016/j.enganabound.2013.09.011
Dry spinning carbon nanotubes into continuous yarns: progress, processing and applications
Tran, Canh-Dung. 2013. "Dry spinning carbon nanotubes into continuous yarns: progress, processing and applications." Schulz, Mark J., Shanov, Vesselin N. and Yin, Zhangzhang (ed.) Nanotube superfiber materials: changing engineering design. Oxford, United Kingdom. Elsevier. pp. 211-242
RBF computation of multiscale elliptic problems [Keynote paper]
An-Vo, D.-A., Tran, C.-D., Mai-Duy, N. and Tran-Cong, T.. 2012. "RBF computation of multiscale elliptic problems [Keynote paper]." Atluri, S. N., Vusanovic, I. and Sarler, B. (ed.) 8th ICCES Special Symposium on Meshless & Other Novel Computational Methods (ICCES MM 2012). Budva, Montenegro 02 - 06 Sep 2012 Montenegro.
Computation of a Fokker-Planck-equation-based multi-scale model for complex flows using the IRBFN method
Tran, Canh-Dung, Mai-Duy, Nam and Tran-Cong, Thanh. 2012. "Computation of a Fokker-Planck-equation-based multi-scale model for complex flows using the IRBFN method." Eberhardsteiner, J., Böhm, H. J. and Rammerstorfer, F. G. (ed.) 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012). Vienna, Austria Vienna, Austria.
Numerical solution of Fokker-Planck equation using the integral radial basis function networks
Tran, C.-D., Mai-Duy, N. and Tran-Cong, T.. 2012. "Numerical solution of Fokker-Planck equation using the integral radial basis function networks." Pimenta, P. M. and Campello, E. M. B. (ed.) 10th World Congress on Computational Mechanics (WCCM 2012). Sao Paulo, Brazil 08 - 13 Jul 2012 Sao Paulo, Brazil. https://doi.org/10.5151/10.5151/meceng-wccm2012-19433
Modeling strain localisation in a segmented bar by a C2-continuous two-node integrated-RBF element formulation
An-Vo, D.-A., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2012. "Modeling strain localisation in a segmented bar by a C2-continuous two-node integrated-RBF element formulation." Brebbia, C. A. and Poljak, D. (ed.) 34th International Conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM 2012). Split, Croatia 25 - 27 Jun 2012 United Kingdom. https://doi.org/10.2495/BE120011
Development of parallel algorithm for boundary value problems using compact local integrated RBFN and domain decomposition
Pham-Sy, N., Hoang-Trieu, T.-T., Tran, C.-D., Mai-Duy, N. and Tran-Cong, T.. 2012. "Development of parallel algorithm for boundary value problems using compact local integrated RBFN and domain decomposition." Gu, Y. T. and Saha, Suvash C. (ed.) 4th International Conference on Computational Methods (ICCM 2012). Gold Coast, Australia 25 - 28 Nov 2012 Brisbane, Australia.
A high-order compact integrated-RBF scheme for time-dependent problems
Thai-Quang, N., Le-Cao, K., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2012. "A high-order compact integrated-RBF scheme for time-dependent problems." Gu, Y. T. and Saha, Suvash C. (ed.) 4th International Conference on Computational Methods (ICCM 2012). Gold Coast, Australia 25 - 28 Nov 2012 Brisbane, Australia.
Compact local integrated RBF stencil based on finite volume formulation for second-order differential problems
Hoang-Trieu, T.-T., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2012. "Compact local integrated RBF stencil based on finite volume formulation for second-order differential problems." Gu, Y. T. and Saha, Suvash C. (ed.) 4th International Conference on Computational Methods (ICCM 2012). Gold Coast, Australia 25 - 28 Nov 2012 Brisbane, Australia.
High-order alternating direction implicit method based on compact integrated-RBF approximations for unsteady/steady convection-diffusion equations
Thai-Quang, N., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2012. "High-order alternating direction implicit method based on compact integrated-RBF approximations for unsteady/steady convection-diffusion equations." CMES Computer Modeling in Engineering and Sciences. 89 (3), pp. 189-220. https://doi.org/10.3970/cmes.2012.089.189
RBF-based multiscale control volume method for second order elliptic problems with oscillatory coefficients
An-Vo, D.-A., Tran, C.-D., Mai-Duy, N. and Tran-Cong, T.. 2012. "RBF-based multiscale control volume method for second order elliptic problems with oscillatory coefficients." CMES Computer Modeling in Engineering and Sciences. 89 (4), pp. 303-359. https://doi.org/10.3970/cmes.2012.089.303
A continuum-microscopic method based on IRBFs and control volume scheme for viscoelastic fluid flows
Tran, C.-D., Mai-Duy, N., Le-Cao, K. and Tran-Cong, T.. 2012. "A continuum-microscopic method based on IRBFs and control volume scheme for viscoelastic fluid flows." CMES Computer Modeling in Engineering and Sciences. 85 (6), pp. 499-519. https://doi.org/10.3970/cmes.2012.085.499
Processing the CNTs' interaction in web using an electro-static field based process
Tran, Canh-Dung, Tran-Cong, Thanh, Le-Cao, K. and Ho-Minh, D.. 2012. "Processing the CNTs' interaction in web using an electro-static field based process." Griffin, Brendan, Faraone, Lorenzo and Martyniuk, Mariusz (ed.) 2012 International Conference on Nanoscience and Nanotechnology (ICONN 2012). Perth, Australia 05 - 09 Feb 2012 Piscataway, NJ. United States.
IRBFN-based multiscale solution of a model 1D elliptic equation
An-Vo, D.-A., Tran, C.-D., Mai-Duy, N. and Tran-Cong, T.. 2011. "IRBFN-based multiscale solution of a model 1D elliptic equation." Brebbia, C. A. and Popov, V. (ed.) 33rd International Conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM 2011). New Forest, United Kingdom 28 - 30 Jun 2011 Southampton, United Kingdom. https://doi.org/10.2495/BE110211
Numerical study of stream-function formulation governing flows in multiply-connected domains by integrated RBFs and Cartesian grids
Le-Cao, K., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2011. "Numerical study of stream-function formulation governing flows in multiply-connected domains by integrated RBFs and Cartesian grids." Computers and Fluids. 44 (1), pp. 32-42. https://doi.org/10.1016/j.compfluid.2010.11.027
An integrated RBFN-based macro-micro multi-scale method for computation of visco-elastic fluid flows
Tran, C.-D., An-Vo, D.-A., Mai-Duy, N. and Tran-Cong, T.. 2011. "An integrated RBFN-based macro-micro multi-scale method for computation of visco-elastic fluid flows." CMES Computer Modeling in Engineering and Sciences. 82 (2), pp. 137-162. https://doi.org/10.3970/cmes.2011.082.137
Manufacturing polymer/carbon nanotube composite using a novel direct process
Tran, C.-D., Lucas, S., Phillips, D. G., Randeniya, L. K., Baughman, R. H. and Tran-Cong, T.. 2011. "Manufacturing polymer/carbon nanotube composite using a novel direct process." Nanotechnology. 22 (14), pp. 1453021-1453029. https://doi.org/10.1088/0957-4484/22/14/145302
Spinning CNT based composite yarns using a dry spinning process
Tran, Canh-Dung, Smith, Shaun M., Higgerson, G., Bui, Anh, Randeniya, Lakshman K. and Tran-Cong, Thanh. 2010. "Spinning CNT based composite yarns using a dry spinning process." Dzurak, Andrew (ed.) 2010 International Conference on Nanoscience and Nanotechnology (ICONN 2010). Sydney, Australia 22 - 26 Feb 2010 Piscataway, NJ. United States. https://doi.org/10.1109/ICONN.2010.6045159
Element-free simulation of dilute polymeric flows using Brownian configuration fields
Tran, Canh-Dung and Tran-Cong, Thanh. 2004. "Element-free simulation of dilute polymeric flows using Brownian configuration fields." Korea-Australia Rheology Journal. 16 (1), pp. 1-15.
Composite yarns of multi-walled carbon nanotubes with metallic electrical conductivity
Randeniya, Lakshman K., Bendavid, Avi, Martin, Philip J. and Tran, Canh-Dung. 2010. "Composite yarns of multi-walled carbon nanotubes with metallic electrical conductivity." Small. 6 (16), pp. 1806-1811. https://doi.org/10.1002/smll.201000493
Issues in processing unstable twisted fibre assemblies
Tran, Canh-Dung, van der Heijden, G. H. M. and Phillips, David G.. 2006. "Issues in processing unstable twisted fibre assemblies." Genco, Alessandro, Gentile, Antonio and Sorce, Salvatore (ed.) 4th International Industrial Simulation Conference (ISC 2006). Palermo, Italy 05 - 07 Jun 2006 Italy.
Computation of viscoelastic flow using neural networks and stochastic simulation
Tran, Canh-Dung and Tran-Cong, Thanh. 2002. "Computation of viscoelastic flow using neural networks and stochastic simulation." Korea-Australia Rheology Journal. 14 (4), pp. 161-174.
BEM-NN computation of generalised Newtonian flows
Tran, Canh-D. and Tran-Cong, T.. 2002. "BEM-NN computation of generalised Newtonian flows." Engineering Analysis with Boundary Elements. 26 (1), pp. 15-28. https://doi.org/10.1016/S0955-7997(01)00085-6
Predicting torque of worsted singles yarn using an efficient radial basis function network-based method
Tran, Canh-Dung and Phillips, David G.. 2007. "Predicting torque of worsted singles yarn using an efficient radial basis function network-based method." Journal of the Textile Institute. 98 (5), pp. 387-396. https://doi.org/10.1080/00405000701475650
Application of topological conservation to model key features of zero-torque multi-ply yarns
Tran, Canh-Dung, van der Heijden, G. H. M. and Phillips, David G.. 2008. "Application of topological conservation to model key features of zero-torque multi-ply yarns." Journal of the Textile Institute. 99 (4), pp. 325-337. https://doi.org/10.1080/00405000701442635
Improving the tensile strength of carbon nanotube spun yarns using a modified spinning process
Tran, Canh-Dung, Humphries, William, Smith, Shaun M., Huynh, Chi and Lucas, Stuart. 2009. "Improving the tensile strength of carbon nanotube spun yarns using a modified spinning process." Carbon. 47 (11), pp. 2662-2670. https://doi.org/10.1016/j.carbon.2009.05.020
Computation of dilute polymer solution flows using BCF-RBFN based method and domain decomposition technique
Tran, Canh-Dung, Phillips, David G. and Tran-Cong, Thanh. 2009. "Computation of dilute polymer solution flows using BCF-RBFN based method and domain decomposition technique." Korea-Australia Rheology Journal. 21 (1), pp. 1-12.
Towards an analysis of shear suspension flows using radial basis functions
Le-Cao, K., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2010. "Towards an analysis of shear suspension flows using radial basis functions." CMES Computer Modeling in Engineering and Sciences. 67 (3), pp. 265-294. https://doi.org/10.3970/cmes.2010.067.265
Stationary solution of the ring-spinning balloon in zero air drag using a RBFN based mesh-free method
Tran, Canh-Dung, Phillips, David G. and Fraser, W. Barrie. 2010. "Stationary solution of the ring-spinning balloon in zero air drag using a RBFN based mesh-free method." Journal of the Textile Institute. 101 (2), pp. 101-110. https://doi.org/10.1080/00405000802273632
Torsional properties of staple fibre plied yarns
Phillips, D. G., Tran, Canh-Dung, Fraser, W. B. and van der Heijden, G. H. M.. 2010. "Torsional properties of staple fibre plied yarns." Journal of the Textile Institute. 101 (7), pp. 595-612. https://doi.org/10.1080/00405000802632886
A new integrated-RBF-based domain-embedding scheme for solving fluid-flow problems
Le-Cao, K., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2010. "A new integrated-RBF-based domain-embedding scheme for solving fluid-flow problems." Khalili, N., Valliappan, S., Li, Q. and Russell, A. (ed.) 9th World Congress on Computational Mechanics and 4th Asian-Pacific Congress on Computational Mechanics (WCCM/APCOM 2010). Sydney, Australia 19 - 23 Jul 2010 United Kingdom. Informa UK(IOP Books). https://doi.org/10.1088/1757-899X/10/1/012021
Simulating the flow of some non-Newtonian fluids with neural-like networks and stochastic processes
Tran, Canh-Dung. 2004. Simulating the flow of some non-Newtonian fluids with neural-like networks and stochastic processes. PhD Thesis Doctor of Philosophy. University of Southern Queensland.
Use of a microplate reader for protein assays and a fixed-time kinetic assay
Powers, JL, Kiesman, N., Tran, Canh-Dung, Jain, Jain, Brown, J and Bevilacqua, VLH. 2005. "Use of a microplate reader for protein assays and a fixed-time kinetic assay." The FASEB Journal. 19 (5), pp. A1395-A1395.
Parallel meshfree TPSRBFN-BCF method for dilute polymer solution
Tran, CD and Tran-Cong, T.. 2003. "Parallel meshfree TPSRBFN-BCF method for dilute polymer solution." The 2nd Korean-Australian Rheology Conference 2003. Gyeongju , Korea 24 - 26 Sep 2003 Korea .
Comparison of BEM-FFNN and BEM-RBFN methods for GNF flow analysis
Tran, C., Mai-Duy, N. and Tran-Cong, T.. 2000. "Comparison of BEM-FFNN and BEM-RBFN methods for GNF flow analysis." The XIIIth International Congress on Rheology. Cambridge, United Kingdom 20 - 25 Aug 2000 United Kingdom.