1998

P.A. Sleigh, M. Berzins, P.H. Gaskell, N.G. Wright.
**“An Unstructured Finite Volume Algorithm for Predicting Flow in Rivers and Estuaries,”** In *Computers and Fluids*, Vol. 27, No. 4, pp. 479--508. 1998.

N. Touheed, P. Selwood, P.K. Jimack, M. Berzins.
**“Parallel Dynamic Load-Balancing for the Solution of Transient CFD Problems Using Adaptive Tetrahedral Meshes,”** In *Parallel Computational Fluid Dynamics - Recent Developments and Advances Using Parallel Computers*, Edited by D.R. Emerson and A. Ecer and J. Periaux and N. Satufoka and P. Fox, Elsevier Science, pp. 81--88. 1998.

1997

I. Ahmad, M. Berzins.
**“An Algorithm for ODEs from Atmospheric Dispersion Problems,”** In *Applied Numerical Mathematics*, Vol. 25, pp. 137--149. 1997.

M. Berzins, S.V. Pennington, P.R. Pratt, J.M. Ware.
**“SPRINT2D Software for Convection Dominated PDEs,”** In *Modern Software Tools in Scientific Computing*, Edited by E. Arge and A.M. Bruaset and H.P. Langtangen, Birkhauser Press, 1997.

SPRINT2D is a set of software tools for solving time-dependent partial differential equations in two space variables. The software uses unstructured triangular meshes and adaptive error control in both space and time. This chapter describes the software and shows how the adaptive techniques may be used to increase the reliability of the solution procedure for a challenging combustion problem. The recent construction of a problem solving environment (PSE) has partially automated the use of SPRINT2D. This PSE consists of tools such as a visual domain specification tool, which helps ease the input of complex geometries, and a visual problem specification tool. After describing these components an evaluation will be made of SPRINT2D and its associated PSE.

M. Berzins, P.J. Capon, P.K. Jimack.
**“On Spatial Adaptivity and Interpolation when Using the Method of Lines,”** In *Applied Numerical Mathematics: Transactions of IMACS*, Vol. 26, No. 1--2, pp. 117--133. 1997.

D.J. Creasey, D.E. Heard, M. Pilling, B.J. Whitaker, M. Berzins, R. Fairlie.
**“Visualisation of a Supersonic Free-Jet Expansion Using Laser-Induced Fluorescence Spectroscopy: Application to the Measurement of Rate Constants at Ultralow Temperatures,”** In *Applied Physics B: Lasers and Optics*, Vol. 65, pp. 375--391. 1997.

P. Selwood, N.A. Verhoeven, J.M. Nash, M. Berzins, N.P. Weatherill, P.M. Dew, K. Morgan.
**“Parallel Mesh Generation and Adaptivity : Partitioning and Analysis,”** In *Parallel C.F.D.- Proc. of Parallel CFD 96 Conference*, Capri, Italy, Edited by A.Ecer and J.Periaux and N.Satufoka and P.Schiano, Elesvier Science BV, May, 1997.

ISBN: 0-444 823271

P. Selwood, M. Berzins, P.M. Dew.
**“3D Parallel Mesh Adaptivity: Data Structures and Algorithms,”** In *Proc. of SIAM Conf. on Parallel Processing for Scientific Computing*, Minneapolis, MN, USA, pp. (CD-Rom). March, 1997.

ISBN: 0-89871-395-1

W. Speares, M. Berzins.
**“A 3D Unstructured Mesh Adaptation Algorithm for Time Dependent Shock Dominated Problems,”** In *Int. Jour Numerical Methods in Fluids*, Vol. 25, pp. 81--104. 1997.

A. Tomlin, M. Berzins, J.M. Ware, J. Smith, M. Pilling.
**“On the use of adaptive gridding methods for modelling chemical transport from multi-scale sources,”** In *Atmospheric Env.*, Vol. 31, No. 18, pp. 2945--2959. 1997.

1996

M. Berzins, T.H.C. Childs, G.R. Ryder.
**“The Selective Laser Sintering of Polycarbonate,”** In *CIRP Annals*, Vol. 45, No. 1, pp. 187--190. 1996.

ISSN: 0007-8506

DOI: 10.1016/S0007-8506(07)63044-3

M. Berzins, J.M. Ware.
**“Solving Convection and Convection Reaction Problems Using the M.O.L.,”** In *Applied Numerical Mathematics*, Vol. 20, pp. 83--99. 1996.

E. Nurgat, M. Berzins.
**“A new relaxation scheme for solving EHL Problems,”** In *23rd Leeds-Lyon Symposium on Tribology, Tribology Series*, Vol. 32, Edited by D.Dowson et al., Elsevier, pp. 125a-134. 1996.

ISBN: 0444828095

A New Relaxation Scheme (NRS) is presented in this paper to solve Elasto Hydrodynamic Lubrication (EHL) point contact problems. The solutions obtained are compared with those obtained by Ehret [6] who employed the Distributive Relaxation Scheme (DRS) of Venner [2]. Results obtained using the two schemes are in close agreement which is very encouraging although it is too early to draw any conclusions. The new relaxation scheme thus provides an alternative approach to the distributive relaxation scheme.

E. Nurgat, M. Berzins.
**“A new relaxation scheme for solving EHL Problems,”** In *Proceedings of 23rd Leeds-Lyon Symposium on Tribology*, Tribology Series, Vol. 32, Edited by D.Dowson et al., Elsevier, pp. 125A--134. 1996.

ISBN: 0444828095

P. Pratt, M. Berzins.
**“Shock preserving quadratic interpolation for visualization on triangular meshes,”** In *Computers & Graphics*, Vol. 20, No. 5, pp. 723--730. 1996.

DOI: 10.1016/S0097-8493(96)00046-5

A new interpolation method for visualizing shock-type solutions on triangular meshes is presented. The method combines standard linear and quadratic interpolants in such a way as to avoid supurious numerical values. The effectiveness of the method is demonstrated on test problems.

G.J. Ryder, M. Berzins, T.H.C. Childs.
**“Modelling Simple Feature Creation in Selective Laser Sintering,”** In *Proc 7th Symposium on Solid Free Form Fabrication*, University of Texas at Austin, Edited by J.W. Barlow et al., pp. 567--574. 1996.

P.A. Sleigh, M. Berzins, P.H. Gaskell.
**“A Reliable and Accurate Technique for the Modelling of Complex Hydraulic Flows,”** In *Proceedings of the First International Symposium on Finite Volumes for Complex Applications*, Hermes, Paris, pp. 635--642. 1996.

ISBN: 2-86601-556-8

J.D.B. Smith, A.S. Tomlin, M. Berzins, V. Pennington, M.J. Pilling.
**“Modelling the effects of Concentrated Emissions Sources on Tropospheric Ozone,”** In *Proceedings of the 3rd Workshop on Modelling of Chemical Reaction Systems*, Heidelberg, Germany, Published on CD-ROM, July, 1996.

ISBN: 3-932217-00-4

Numerical models that describe the chemical processes occurring in the troposphere, in the main, are still using fixed or telescopic grids to provide greater detail where it is required, such as near large emissions sources. While the use of adaptive grids has become well accepted in the fields of aeronautical and mechanical engineering, the adoption of adaptive gridding techniques in atmospheric modelling has been somewhat slower. Tomlin et al [1] recently demonstrated the use of time-dependent adaptive mesh gridding techniques applied to the investigation of a single power station plume, with regards to regional ozone levels. The results of that paper highlighted the differences in the total and peak concentrations of ozone arising from using fixed grids, as opposed to using adaptive grids.

Ozone concentrations in the atmospheric boundary layer, the bottom kilometre of the troposphere, are dependent on the interactions of nitrogen oxides and the volatile organic compounds (VOCs) that are emitted from both anthropogenic and biogenic sources. There are many more chemical species involved in the processes of the atmospheric boundary layer than in the stratosphere. This makes the use of detailed chemical mechanisms with fine mesh resolution difficult in two space dimensions, and prohibitively expensive for three space dimensions.

This paper investigates the effects of multiple point sources interacting with the more diffuse area sources arising from urban emissions, and will show the differences arising from the use of adaptive gridding techniques rather than fixed grids. The numerical code, SPRINT2D, provides spatial and temporal error controls for limiting the adaptation of the grid for a length scale ranging from a few hundred metres to a few hundred kilometres.

Comparisons will also be made between a systematically reduced mechanism, CBMLeeds[2], and the Generic Reaction Set (GRS) of Azzi et al [3] to see the advantages of the two approaches. CBMLeeds originates from the CBM-Ex scheme of Gery et al [4], which uses lumped organic species, as opposed to the heavily parameterised organic chemistry of the GRS.

1995

M. Berzins, J.M. Ware.
**“Positive Cell Centered Finite Volume Discretisation Methods for Hyperbolic Equations on Irregular Meshes,”** In *Applied Numerical Mathematics*, Vol. 16, pp. 417--438. 1995.

The conditions sufficient to ensure positivity and linearity preservation for a cell-centered finite volume schemefor time-dependent hyperbolic equations using irregular one-dimensional and triangular two-dimensional meshes arederived. The conditions require standard flux limiters to be modified and also involve possible constraints on themeshes. The accuracy of this finite volume scheme is considered and is illustrated by two simple numerical examples.

M. Berzins, P. Gaskell, A. Sleigh, A.S. Tomlin, J. Ware.
**“An adaptive CFD solver for time-dependent environmental flow problems,”** In *Proceedings of the Institute of Computational Fluid Dynamics Conference*, Edited by K.W. Morton, M.J. Baines, Oxford University Press, pp. 311-317. 1995.