arXiv subjects

Weishuo Liu

Publications and source records attributed to Weishuo Liu.

4 recordsLinked to original sources

arXiv2026

Finite-time divergence of kinetic-energy fluctuations in a Schr\"odinger-induction flow

In this study, we use a constrained Schr\"odinger--induction system to investigate kinetic-energy fluctuations induced by a fluid singularity. Assuming the cited Navier--Stokes construction with zero initial velocity and its exact exterior profile, we construct a periodic trajectory from a constant normalized wave function and zero connection. The prescribed body force admits a smooth space--time extension across the normalized singular time $t=1$. In this construction, the probability density remains constant and the mean matter kinetic energy stays bounded, whereas the gauge-invariant kinetic-energy variance diverges. We prove a lower growth bound of order $(1-t)^{-1/2-5h}$, with $h$ fixed by the source construction, by integrating the fourth power of the complete velocity's magnitude over an exact exterior region where all oscillatory corrections vanish. After fixing a gauge with constant wave function, we identify a unique weak $L^2$ connection limit outside $L^4$ and construct its positive self-adjoint kinetic operator through the associated magnetic form. We further show that the normalized endpoint state belongs to the form domain but not the operator domain: its first kinetic spectral moment is finite, whereas its second is infinite. These results connect fluid concentration to a loss of kinetic-domain regularity and provide a dynamical benchmark for assessing the limits of mean-energy control in hydrodynamic wave formulations.

math.AP↗

arXiv2022

NNPred: A Predictor Library to Deploy Neural Networks in Computational Fluid Dynamics software

A neural-networks predictor library has been developed to deploy machine learning (ML) models into computational fluid dynamics (CFD) codes. The pointer-to-implementation strategy is adopted to isolate the implementation details in order to simplify the implementation to CFD solvers. The library provides simplified model-managing functions by encapsulating the TensorFlow C library, and it maintains self-belonging data containers to deal with data type casting and memory layouts in the input/output (I/O) functions interfacing with CFD solvers. On the language level, the library provides application programming interfaces (APIs) for C++ and Fortran, the two commonly used programming languages in the CFD community. High-level customized modules are developed for two open-source CFD codes, OpenFOAM and CFL3D, written with C++ and Fortran, respectively. The basic usage of the predictor is demonstrated in a simple data-driven heat transfer problem as the first tutorial case. Another tutorial case of modeling the effect of turbulence in channel flow using the library is implemented in both OpenFOAM and CFL3D codes. The developed ML predictor library provides a powerful tool for the deployment of ML models in CFD solvers.

physics.flu-dyn↗

arXiv2020

An Iterative Machine-Learning Framework for RANS Turbulence Modeling

Machine-learning (ML) techniques provide a new and encouraging perspective for constructing turbulence models for Reynolds-averaged Navier--Stokes (RANS) simulations. In this study, an iterative ML-RANS computational framework is proposed that combines an ML algorithm with transport equations of a conventional turbulence model. This framework maintains a consistent procedure for obtaining the input features of an ML model in both the training and predicting stages, ensuring a built-in reproducibility. The effective form of the closure term is discussed to determine suitable target variables for the ML algorithm, and the multi-valued problem of existing constitutive theory is studied to establish a proper regression system for ML algorithms. The developed ML model is trained under a cross-case strategy with data from turbulent channel flows at three Reynolds numbers and \textit{a posteriori} simulations of channel flows show that the framework is able to predict both the mean flow field and turbulent variables accurately. Interpolation tests for the channel flow show the proposed framework can reliably predict flow features that lie between the minimum and maximum Reynolds numbers associated with the training data. A further test related to the flow over periodic hills also demonstrates a better result than a traditional turbulence model, indicating a promising predictive capability of the developed ML model for separated flow even though the model is only trained with planar channel flow data.

physics.flu-dyn↗

arXiv2019

An Initial Attempt of Converged Machine-Learning Assisted Turbulence Modeling in RANS Simulations with Eddy-Viscosity Hypothesis

This work presents a converged framework of Machine-Learning Assisted Turbulence Modeling (MLATM). Our objective is to develop a turbulence model directly learning from high fidelity data (DNS/LES) with eddy-viscosity hypothesis induced. First, the target machine-learning quantity is discussed in order to avoid the ill-conditioning problem of RANS equations. Then, the novel framework to build the turbulence model using the prior estimation of traditional models is demonstrated. A close-loop computational chain is designed to ensure the convergence of result. Besides, reasonable non-dimensional variables are selected to predict the target learning variables and make the solver re-converge to DNS mean flow field. The MLATM is tested in incompressible turbulent channel flows, and it proved that the result converges well to DNS training data for both mean velocity and turbulence viscosity profiles.

physics.flu-dyn↗