Gaussian process emulation of particle method for estimating free-surface heights

Abstract

This paper presents the development of a statistical emulator to estimate free-surface heights with less computational time than a particle method. Particle methods can simulate free-surface flow problems by solving Navier-Stokes and continuity equations, but they require more computational time as the number of particles becomes greater in computational domains. Accordingly, it is not pragmatic to conduct statistical analysis of free-surface problems with respect to a variety of initial conditions by particle methods. In the place of the simulation methods, statistical emulators can estimate predictive values in these problems with less computational time. In this study, we apply a Gaussian process for designing a statistical emulator of the Explicit Moving Particle Simulation (EMPS) method and predict free-surface heights in dam break problems. Once it is developed based on a dataset made from only one simulation run of a dam break problem, the Gaussian process emulator is able to approximate these heights in other dam break problems. By measuring the coefficient of determination, root mean squared error, and mean absolute error, we evaluate the accuracy of emulated free-surface heights in dam break problems where the shapes of water columns are distinct from the original shape at the initial condition. We alter the initial lengths in the x-direction and the initial heights in the z-direction remaining the same initial width in the y-direction. Consequently, in terms of the computational speed and the accuracy, it is demonstrated that we can adopt the Gaussian process emulator as a replacement of the EMPS simulator especially when free-surface flow analysis is repeatedly conducted with different initial conditions.

Keywords

• collapse of water columns
• computational speed
• explicit moving particle simulation (emps) method
• gaussian process regression
• initial conditions
• numerical analysis
• statistical emulator