Research
Development of particle-based simulation method for strongly nonlinear free surface flow
When the wave height is significantly smaller than the wavelength of water waves, it is possible to accurately predict the behavior of water waves using the linear potential theory. However, in situations involving strongly nonlinear phenomena, such as the generation of spray, obtaining analytical solutions becomes exceedingly challenging.
In such cases, Computational Fluid Dynamics (CFD) comes to the forefront as a numerical method for discretizing and solving the governing equations of fluid flow, known as the Navier-Stokes equations, with the computational power of computers. Our laboratory, with a strong background in the linear potential theory, has focused on a particle-based simulation method, particularly well-suited for replicating fluid phenomena with splashing, and has been working on its high-precision refinement.
The particle-based simulation method treats fluid as an assembly of particles and calculates the behavior of each individual particle. This method, due to its ability to "realistically" reproduce phenomena like splashes, finds applications not only in the field of analysis but also in computer graphics. The following video is a numerical experiment simulating the behavior of fluids when a dam collapses (slow playback and the contours represent the pressure field).
Through numerical computations, the simulation successfully reproduces the flow of water as it pours out of the collapsing dam, splashes against walls, and forms sprays in a manner that appears realistic.
However, it's important to note that while the particle-based simulation method can "realistically" simulate fluid behavior, it may not excel at quantitatively and accurately calculating pressure fields. Small variations in particle positions can have a significant impact on pressure calculations, leading to unnatural oscillations (disturbances) when viewed over time. Additionally, the chosen numerical simulation conditions, such as particle size and time step, can greatly influence the results.
This experiment was conducted based on the work of Lobovský et al. (2014), where actual tank experiments were performed, and pressure results from sensors attached to the right wall were obtained. The figure below compares the time series of pressure and numerical calculation results using several methods (the horizontal axis represents time, and the vertical axis represents dimensionless pressure values). Our laboratory proposes a novel calculation method called (c) RF-SDS. While other methods obtain clean pressure time series with a time step of 0.0004 seconds, reducing the time step further results in pressure oscillations. However, the method proposed in our laboratory can calculate pressure with a similar level of accuracy regardless of the time step. This allows for high-precision simulation of fluid behavior without the need to fine-tune the time step.
In this manner, our laboratory is dedicated to advancing the accuracy of Computational Fluid Dynamics, particularly particle-based simulation methods, for strongly nonlinear free-surface flows.
Reference: Iida, T., & Yokoyama, Y. (2022). Convergence-improved source term of pressure Poisson equation for moving particle semi-implicit. Applied Ocean Research, 124, 103189.
Contact person: Takahito Iida
