Xueqin Liu | Search arXiv

arXiv2026

A deterministic Fokker--Planck/lattice-Boltzmann micro--macro solver for dilute Hookean polymer solutions

Deterministic micro--macro simulation of polymer solutions requires the coupled evolution and spatial transport of a configuration distribution, together with the conversion of its moments into macroscopic stress and feedback to the flow. We develop a Fokker--Planck/lattice-Boltzmann solver for this coupling in two-dimensional dilute Hookean polymer solutions. The solver represents the distribution on the unbounded configuration space by Hermite coefficient fields, advances local configuration dynamics and physical-space transport in separate steps, and recovers Kramers stress from the second moment to achieve two-way coupling with a purified two-relaxation-time lattice-Boltzmann flow solver. To assess whether this configuration description recovers the corresponding macroscopic response, we use the exact second-moment closure of the continuous Hookean model as a macroscopic reference for comparison with analytical and independently discretized macroscopic solutions. The calculations reproduce velocity overshoot and damped oscillations in start-up Poiseuille flow, with velocity profiles approaching the analytical start-up transient under grid refinement; in four-roll flow with spatially nonuniform extension and stress feedback, the maximum full-domain relative differences in velocity and polymer stress are approximately $0.0309\%$ and $3.84\%$, respectively, over the tested Weissenberg numbers at corresponding sampling times. These comparisons support the solver's ability to recover the Hookean macroscopic response from configuration-distribution evolution. Further calculations of wall-bounded recirculation and open cross-slot flow exhibit the corresponding conformation responses and symmetric and asymmetric flow states, extending this deterministic micro--macro method to viscoelastic flows under different boundary constraints.

physics.flu-dyn↗

arXiv2024

Forecasting Day-Ahead Electricity Prices in the Integrated Single Electricity Market: Addressing Volatility with Comparative Machine Learning Methods

This paper undertakes a comprehensive investigation of electricity price forecasting methods, focused on the Irish Integrated Single Electricity Market, particularly on changes during recent periods of high volatility. The primary objective of this research is to evaluate and compare the performance of various forecasting models, ranging from traditional machine learning models to more complex neural networks, as well as the impact of different lengths of training periods. The performance metrics, mean absolute error, root mean square error, and relative mean absolute error, are utilized to assess and compare the accuracy of each model. A comprehensive set of input features was investigated and selected from data recorded between October 2018 and September 2022. The paper demonstrates that the daily EU Natural Gas price is a more useful feature for electricity price forecasting in Ireland than the daily Henry Hub Natural Gas price. This study also shows that the correlation of features to the day-ahead market price has changed in recent years. The price of natural gas on the day and the amount of wind energy on the grid that hour are significantly more important than any other features. More specifically speaking, the input fuel for electricity has become a more important driver of the price of it, than the total generation or demand. In addition, it can be seen that System Non-Synchronous Penetration (SNSP) is highly correlated with the day-ahead market price, and that renewables are pushing down the price of electricity.

cs.LG↗