A physically consistent particle method for incompressible fluid flow calculation
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A physically consistent particle method for incompressible fluid flow calculation Masahiro Kondo1 Received: 30 July 2019 / Revised: 21 November 2019 / Accepted: 23 December 2019 © The Author(s) 2020
Abstract In general, mechanical energy monotonically decreases in a physically consistent system, constructed with conservative force and dissipative force. This feature is important in designing a particle method, which is a discrete system approximating continuum fluid with particles. When the discretized system can be fit into a framework of analytical mechanics, it will be a physically consistent system which prevents instability like particle scattering along with unphysical mechanical energy increase. This is the case also in incompressible particle methods. However, most incompressible particle methods do not satisfy the physical consistency, and they need empirical relaxations to suppress the system instability due to the unphysical energy behavior. In this study, a new incompressible particle method with the physical consistency, moving particle full-implicit (MPFI) method, is developed, where the discretized interaction forces are related to an analytical mechanical framework for the systems with dissipation. Moreover, a new pressure evaluation technique based on the virial theorem is proposed for the system. Using the MPFI method, static pressure, droplet extension, standing wave and dam break calculations were conducted. The capability to predict pressure and motion of incompressible free surface flow was presented, and energy dissipation property depending on the particle size and time step width was studied through the calculations. Keywords Particle method · Incompressible fluid flow · Physical consistency · Numerical stability · Full-implicit algorithm · MPS · SPH · Analytical mechanics · Extended Lagrangian mechanics · Energy dissipation · Virial theorem
1 Introduction Particle methods are widely used to calculate the complex motion of free surface flows in various engineering fields. Smoothed particle hydrodynamics (SPH) for weakly compressible free surface flow was proposed by Monaghan [1] as an extension from astrophysics, while moving particle semi-implicit (MPS) was developed by Koshizuka and Oka [2, 3] to calculate strictly incompressible free surface flows in the nuclear engineering field. In designing a numerical methodology for physical simulation, it is important to take fundamental physics into consideration. In general, continuum mechanics, e.g., fluid dynamics, satisfies the fundamental laws of physics such as the second law of thermodynamics, which claims a * Masahiro Kondo [email protected] 1
National Institute of Advanced Industrial Science and Technology (AIST), Central 2, 1‑1‑1 Umezono, Tsukuba, Ibaraki 305‑8568, Japan
monotonic decrease in mechanical energy. However, it is not always satisfied in a discrete system approximating the continuum equations. When a discrete particle system does not satisfy the second law of thermodynamics, the mechanical energy may increase
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