Both the Wave Plan Method (WPM) and the Method of Characteristics (MOC) have both been shown to produce solutions identical to an exact solution for cases where pipe friction is not considered (this is the only situation for which an exact solution can be attained).
Both methods obtain solutions at intervals of (change in t) at all junctions and components. However, the MOC also requires solutions at all interior points within pipes for each time step in order to calculate the effects of friction and determine wave characteristics. In contrast, the WPM handles these effects by tracking pressure waves, which are modified for the effects of friction by a single calculation between junction nodes/components.
For most systems the WPM approach requires fewer calculations while producing virtually identical results. For example, for a 2517-pipe water distribution system the MOC requires 323,995 calculations per time step. The WPM requires 4267 calculations per time step while producing virtually identical solutions. This comparison depends on the accuracy of the model pipe lengths.
Over the past 40 years we at KYPipe, LLC have developed the extremely efficient and accurate WPM (aka Wave Plan Method or Wave Method) for analyzing transients in piping systems. This significant development not only provides the capability to handle distribution systems, but because it is based on the movement of pressure waves, it gives the engineer an immediate intuitive understanding of transient flow in all piping systems. The traditional MOC approach requires complex mathematical manipulations and provides no insight into the phenomena of pressure wave action. However, the really serious difficulty with the MOC approach is that the requirement for calculations at many interior locations results in orders of magnitude more calculations. Numerous examples are available in journals showing that solutions obtained by the MOC and the WPM are virtually identical (as, of course, they should be). This requirement to make internal calculations essentially limits the use of the MOC approach to transmission pipelines and relatively simple pipe networks. Analyzing extensive distribution systems using existing MOC modeling software is not an option.
There are ongoing attempts to turn the enormous computational disadvantage of the MOC into an advantage by saying the thousands of required internal calculations somehow assure the modeler that important results will not be missed. It is also said that the WPM only computes results at junctions. Let us be clear on this point – with the WPM, junction nodes can be inserted at any desired location where local pressure results are required. We recommend that modelers do this at local high and low points and in very long stretches of pipelines. This could result in adding 10% more nodes – not 20 times as many nodes (or more) and the results are comprehensive – nothing of significance is missed. We are proud of our very significant development of the Wave Plan Method which opens the door to transient modeling of distribution systems. Low pressure transients in drinking water systems pose a real health hazard (pathogen intrusion) and it is imperative that engineers have the tools to address this and other pressure surge problems in these systems, no matter how simple or complex the networks are.
See also Dr. Wood’s blog post on this subject, co-authored with Dr. Srinivasa Lingireddy, which provides numerical solution sets for three different modeling problems as examples of how WPM and MOC both produce accurate results. Blog post link.
Dr. Lingireddy has published a 2021 text which describes surge modeling in general, and compares and contrasts WPM with MOC. This book is available as a hardcover book (Book link), and as an e-book (E-Book Link).
Dr. Wood explains the WPM in this video.
