Dundee Tunnel Research

Academic Research - Numerical Analysis

Dundee Tunnel Research (DTR) prides itself on the efficiency with which its numerical algorithms solve the analytical equations used to represent tunnel airflows. In addition to being unusually accurate, the algorithms are robust and fast. Historically, much of their development has been undertaken at DTR and the expertise has subsequently been fed into university-related research.  Naturally, however, there has also been valuable information transfer in the opposite direction.

A by-product of this self-belief in practical numerical analysis is a keen awareness of general skill levels demonstrated in practical applications and evidenced in published work.  Numerical methods are so widely used in engineering that few engineering predictions are made without them.  It is generally assumed that the users of the relevant software will have sufficient understanding and professionalism to ensure that their designs are not unduly influenced by numerical deficiencies. Sadly, however, there is extensive information to the contrary.  Surprisingly few published papers state clearly what has been done to ensure that numerical errors have been tamed and even these are often unconvincing. Grid-size dependence is often ignored or assessed poorly.

It is easy to argue that this is a reflection of bad practice, that it is symptomatic of only the poorer end of the spectrum and that better education should be able to cure it. There is some truth in this, but it leaves open such questions as “Will engineers have more time in future?” and “Will their work be supervised and checked more effectively?”.  It is not obvious why this should be so in a world with increasing demands on everyone’s time.  Perhaps, therefore, a different approach is needed.

Dundee’s contribution

In a collaborative research project, Alan Vardy and Professor Masashi Shimada at the University of Tokyo (latterly at Tsukuba University) seek to eliminate the need for individual engineers to become expert in the use of numerical methods.  Today, users need to prescribe numerical grid structures and to take responsibility for their suitability.  The aim of our research is to move to a position where users prescribe the degree of accuracy they require and the software is responsible for choosing grid structures that will achieve this.

There are several ways in which this aim can be realised. At the coarsest level, the software could simply mimic best existing practice by performing simulations with different grid structures and different numerical algorithms and then assessing accuracy in a post-processing mode.  At a more advanced level, the software could have built-in expert-knowledge of the frequency-accuracy characteristics of particular approaches.  This is the method that Shimada, Vardy and Brown have followed to date.  As computers become ever more powerful, it should be possible for the software to generate its own expert-knowledge.

The transfer of responsibility from the user to the software does not, of course, change the fundamental link between the numerical method and the resulting accuracy.  If a user asks for excessively high accuracy or high detail, the software will need excessive resources to satisfy the demand.  Nevertheless, the transfer of responsibility will force users to acknowledge explicitly that the predictions are not exact and it will provide a useful yardstick for presentation to persons who will need to use the predictions in some form.

Masashi Shimada in harmony
Masashi Shimada in harmony

Selected References

Shimada M, Brown JMB, Leslie DJ & Vardy AE (2006) Time-line interpolation errors in pipe networks, Journal of Hydraulic Engineering, ASCE, 132(3), 294-306

Shimada M, Brown JMB & Vardy AE (2007) Estimating friction errors in MOC analyses of unsteady pipe flows, Computers & Fluids, 32, 1235-1246

Shimada M, Brown JMB & Vardy AE (2008) Interpolation errors in rectangular and diamond characteristic grids,Journal of Hydraulic Engineering, ASCE, 134(10), 1480-1490

Shimada M & Vardy AE (2013) Non-linear interaction of friction and interpolation errors in unsteady flow analyses, Journal of Hydraulic Engineering, ASCE, 139(4), 397-409

Vardy AE (2008) Method of characteristics in quasi-steady compressible flows, Proc 10th int conf on Pressure Surges, Edinburgh UK, 14-16 May 2008, BHR Group, 505-518

Vardy AE & Pan Z (1997) Quasi-steady friction in polytropic flow, Computers & Fluids, 26(8), 793-809

Vardy AE & Pan Z (1998) Interpolation in transient polytropic flow, Computers & Fluids, 27(7), 783-796

Vardy AE & Pan Z (2000) Wave paths in transient polytropic flow, Computers and Fluids, 29(3), 235-259

Vardy AE & Tijsseling AS (2015) Method of characteristics: (Why) is it so good?, Proc 12th int conf on Pressures Surges, Dublin, Eire, 18-20 Nov 2015, BHR Group, 327-341