An Overview of the Numerical Approaches to Water Hammer Modelling: The Ongoing Quest for Practical and Accurate Numerical Approaches

Here, recent developments in the key numerical approaches to water hammer modelling are summarized and critiqued. This paper summarizes one-dimensional modelling using the finite difference method (FDM), the method of characteristics (MOC), and especially the more recent finite volume method (FVM). The discussion is briefly extended to two-dimensional modelling, as well as to computational fluid dynamics (CFD) approaches. Finite volume methods are of particular note, since they approximate the governing partial differential equations (PDEs) in a volume integral form, thus intrinsically conserving mass and momentum fluxes. Accuracy in transient modelling is particularly important in certain (typically more nuanced) applications, including fault (leakage and blockage) detection. The FVM, first advanced using Godunov’s scheme, is preferred in cases where wave celerity evolves over time (e.g., due to the release of air) or due to spatial changes (e.g., due to changes in wall thickness). Both numerical and experimental studies demonstrate that the first-order Godunov’s scheme compares favourably with the MOC in terms of accuracy and computational speed; with further advances in the FVM schemes, it progressively achieves faster and more accurate codes. The current range of numerical methods is discussed and illustrated, including highlighting both their limitations and their advantages.

PADME – new code for modeling of planet georesources formation on heterogeneous computing systems

Many planets were detected in last few years, but there is no clear understanding of how they are formed. The fairly clear understanding of Solar system formation was founded with time, but there are some doubts yet because we don’t know what was at the beginning of the process, and what was acquired afterward. Moreover, formed ideas often couldn’t explain some features of other systems. Searching for Earth-like terrestrial planets is another very important problem. Even if any of found exoplanets will be similar to Earth, we couldn’t say that it is a “second Earth” exactly because its internal, geological, composition could be different – Venus is a vivid example. A new method for modelling of the planet formation process in a 3D2V formulation based on two-phase approach is presented in the paper. Fluids-in-cells method by Belotserkovskii-Davydov, modified with using the Godunov’s scheme, is used to model the gas component. The dust component is described by N-body system solved with the Particle-Mesh method. The method was accelerated by using of Nvidia CUDA technology. Gas-dust disk modelling results with the formation of sealing of gas and dust that could be interpreted as potential exoplanet are given.