Publications

2024

1. AIAAJ

   Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Models

   Qiang Liu , and Nils Thuerey

   AIAA Journal, 2024

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   Leveraging neural networks as surrogate models for turbulence simulation is a topic of growing interest. At the same time, embodying the inherent uncertainty of simulations in the predictions of surrogate models remains very challenging. The present study makes a first attempt to use denoising diffusion probabilistic models (DDPMs) to train an uncertainty-aware surrogate model for turbulence simulations. Due to its prevalence, the simulation of flows around airfoils with various shapes, Reynolds numbers, and angles of attack is chosen as the learning objective. Our results show that DDPMs can successfully capture the whole distribution of solutions and, as a consequence, accurately estimate the uncertainty of the simulations. The performance of DDPMs is also compared with varying baselines in the form of Bayesian neura networks and heteroscedastic models. Experiments demonstrate that DDPMs outperformthe other methods regarding a variety of accuracy metrics. Besides, it offers the advantageof providing access to the complete distributions of uncertainties rather than providing a set of parameters. As such, it can yield realistic and detailed samples from the distribution of solutions.

   @article{airfoilDDPM2023,
     journal = {AIAA Journal},
     title = {Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Models},
     author = {Liu, Qiang and Thuerey, Nils},
     year = {2024},
     eprint = {2312.05320},
     archiveprefix = {arXiv},
     primaryclass = {physics.flu-dyn},
     arixv = {https://arxiv.org/abs/2312.05320},
     url = {https://arc.aiaa.org/doi/10.2514/1.J063440},
     doi = {10.2514/1.J063440},
     volume = {62},
     issue = {8},
     pages = {2192-2933},
   }

2. Arxiv

   ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks

   Qiang Liu , Mengyu Chu , and Nils Thuerey

   Arxiv preprint, 2024

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   The loss functions of many learning problems contain multiple additive terms that can disagree and yield conflicting update directions. For Physics-Informed Neural Networks (PINNs), loss terms on initial/boundary conditions and physics equations are particularly interesting as they are well-established as highly difficult tasks. To improve learning the challenging multi-objective task posed by PINNs, we propose the ConFIG method, which provides conflict-free updates by ensuring a positive dot product between the final update and each loss-specific gradient. It also maintains consistent optimization rates for all loss terms and dynamically adjusts gradient magnitudes based on conflict levels. We additionally leverage momentum to accelerate optimizations by alternating the back-propagation of different loss terms. The proposed method is evaluated across a range of challenging PINN scenarios, consistently showing superior performance and runtime compared to baseline methods. We also test the proposed method in a classic multi-task benchmark, where the ConFIG method likewise exhibits a highly promising performance.

   @article{ConFIG2024,
     journal = {Arxiv preprint},
     title = {ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks},
     author = {Liu, Qiang and Chu, Mengyu and Thuerey, Nils},
     year = {2024},
     eprint = {2408.11104},
     archiveprefix = {arXiv},
     primaryclass = {cs.LG},
     arixv = {https://arxiv.org/abs/2408.11104},
     url = {https://arxiv.org/abs/2408.11104},
     doi = {https://doi.org/10.48550/arXiv.2408.11104},
   }

2023

1. CJCM

   The effect of different interface capture methods on the simulation accuracy of droplet deformation under electric field

   Qiang Liu , and Jian Wu

   Chinese Journal of Computational Mechanics , 2023

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   Droplet’ s deformation under electric field is a basic research topic in Electrohydrodynamics.The accuracy of surface tension has a great influence on the simulation of droplet deformation.Based on the VOF model in OpenFOAM,we studied the effect of different phase update methods (MULES and isoAdvector algorithm) as well as different curvature calculation methods (phase fraction gradient and RDF function algorithm) on the simulation accuracy of droplet deformation under electric field.The results show that the isoAdvector algorithm requires lower mesh density than the MULES algorithm,but it generates higher error in surface tension calculation when coupled with phase fraction gradient algorithm.The simulation error of isoAdvector coupled RDF function algorithm is low,and it can deal with the droplet deformation both parallel and perpendicular to the electric field when using axisymmetric grids.The numerical results are in good agreement with the analytical solutions when using the isoAdvector coupled RDF function algorithm.

   @article{CJCM2022,
     title = {The effect of different interface capture methods on the simulation accuracy of droplet deformation under electric field},
     journal = {Chinese Journal of Computational Mechanics },
     volume = {40},
     issue = {6},
     pages = {979-984},
     year = {2023},
     doi = {10.7511/jslx20210519003},
     url = {https://doi.org/10.7511/jslx20210519003},
     author = {Liu, Qiang and Wu, Jian}
   }

2022

1. Fluid Drn. Res.

   Finite amplitude electro-thermo convection in a cubic box

   Yu-xing Peng , Qiang Liu , Zhong-xian Li , and Jian Wu

   Fluid Dynamics Research, Nov 2022

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   Three-dimensional electro-thermo-hydrodynamic (ETHD) flows of dielectric fluids driven by simultaneous Coulomb and buoyancy forces in a cubic box is numerically studied. The set of coupled equations associated with the ETHD phenomena are solved with the finite volume method. The code is first validated by comparing the numerically obtained linear critical values of the pure electro-convection and thermal convection with the previous studies. Then the neutral stability curve of the system is given and the finite amplitude instability thresholds with different Rayleigh numbers () are presented. It is found that along the neutral stability curve, the flow strength becomes weaker with the increase of and the decrease of electric Rayleigh number (T). Besides, the gap between the linear and nonlinear critical values expressed in terms of T decreases with the increase of . Primarily, the distributions of charge density, temperature and velocity fields with different governing parameters near neutral stability curve are presented. The temperature and charge density profiles near the linear and nonlinear critical values are given, showing that higher T results in wider charge void region and shorter distance between the charge void region’s lower boundary and injection electrode. Finally, the symmetries of the flow patterns along the neutral stability curve are also discussed briefly.

   @article{FDR,
     doi = {10.1088/1873-7005/ac9dbc },
     url = {https://dx.doi.org/10.1088/1873-7005/ac9dbc},
     year = {2022},
     month = nov,
     publisher = {IOP Publishing},
     volume = {54},
     number = {6},
     pages = {065501},
     author = {Peng, Yu-xing and Liu, Qiang and Li, Zhong-xian and Wu, Jian},
     title = {Finite amplitude electro-thermo convection in a cubic box},
     journal = {Fluid Dynamics Research}
   }

2. IJHFF

   Electrohydrodynamic conduction induced convection in a film with interface charge

   Qiang Liu , Zhonglin Du , and Jian Wu

   International Journal of Heat and Fluid Flow, Dec 2022

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   Film transportation driven by Electrohydrodynamic(EHD) conduction pumping has become a new prospect in many micro-scale industrial applications. This work numerically studied the electro-convection in a film induced by EHD conduction pumping. The effect of the interface charge on the heterocharge layer and the flow pattern has been carefully investigated. A 2-D geometry with flush electrodes situated at the bottom of a cavity was considered, and the EHD conduction flow was generated by both space charge and interface charge with the Onsager-Wien effect. Results show that the height of the heterocharge layer decreases due to the attraction by the interface charge. The interface charge also affects the flow pattern and contributes to the enhancement of the overall flow intensity. The average velocity of the flow field increases by 24.1% and the total kinetic energy increases by 44.1% within the parameters studied in this paper.

   @article{IJHFF2022,
     title = {Electrohydrodynamic conduction induced convection in a film with interface charge},
     journal = {International Journal of Heat and Fluid Flow},
     volume = {98},
     pages = {109063},
     year = {2022},
     month = dec,
     issn = {0142-727X},
     doi = {10.1016/j.ijheatfluidflow.2022.109063},
     url = {https://www.sciencedirect.com/science/article/pii/S0142727X2200131X},
     author = {Liu, Qiang and Du, Zhonglin and Wu, Jian},
     keywords = {EHD conduction pumping, Film flow, Interface charge, Heterocharge layer, Numerical simulation}
   }

3. Arxiv

   Direct numerical simulations of incompressible multiphase electrohydrodynamic flow with single-phase transportation schemes

   Qiang Liu , Jie Zhang , and Jian Wu

   Arxiv, Jul 2022

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   In the present study, two schemes named face discernment and flux correction are proposed to achieve single-phase transportation of free charge in multiphase electrohydrodynamic(EHD) problems. Many EHD phenomena occur between air and another liquid while the free charge can only be transported in the liquid phase through ohmic conduction and convection due to the poor conductivity of air. However, the charge may be leaked into the dielectric air during the simulation due to the asynchronous transportation between interface and free charge. To avoid this unphysical error, a face discernment method is designed to produce an accurate ohmic conduction of free charge by providing a superior physical properties distribution at the interface. Subsequently the flux correction method is developed to correct the advection flux of charge density to prevent ions crossing the interface. These two schemes are based on the Volume of Fluid (VOF) model and independent with the specific interface updating method. The performance of the proposed methods are carefully validated with several test cases. The algorithms are implemented as an OpenFOAM extension and are published as open source.

   @article{arxiv2022,
     title = {Direct numerical simulations of incompressible multiphase electrohydrodynamic flow with single-phase transportation schemes},
     author = {Liu, Qiang and Zhang, Jie and Wu, Jian},
     year = {2022},
     month = jul,
     eprint = {2207.08152},
     journal = {Arxiv},
     archiveprefix = {arXiv},
     primaryclass = {physics.flu-dyn},
     arixv = {https://arxiv.org/abs/2207.08152},
     url = {https://arxiv.org/abs/2207.08152},
     doi = {10.48550/arXiv.2207.08152}
   }

2021

1. IJMF

   Numerical modeling of solid-liquid phase change under the influence an external electric field

   R. Deepak Selvakumar , Qiang Liu , Luo Kang , Phillipe Traoré , and Jian Wu

   International Journal of Multiphase Flow, Mar 2021

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   Recent experimental results demonstrate that electric field can effectively decrease the melting time of dielectric Phase Change Materials (PCMs). In this study, a Finite-Volume Method (FVM) based numerical model for the solid-liquid phase change heat transfer of dielectric PCM under the influence of electric field is presented. Fully coupled governing equations of electric potential, charge transport, Navier–Stokes equations, and the energy equation are implemented in the finite-volume framework of OpenFOAM®. The numerical model is first validated against the analytical solutions for several test cases in the hydrostatic regime. Results from the numerical model exhibit good agreement with the analytical solutions. The numerical model presented in this work is capable of capturing the sudden step change in the charge density distribution and electric field due to the discontinuity of the physical properties at the interface. A numerical analysis of EHD assisted melting of a dielectric PCM inside a rectangular cavity is considered. Effects of electric Rayleigh number T and Stefan number St on the rate of melting are discussed. The transient evolution of the EHD assisted melting process which includes different flow stages is analyzed. It is found that the electric Rayleigh number T has a notable effect on the rate of melting and its influence is more pronounced at lower values of St. A maximum of 56.10% reduction in total melting time is achieved at T=3000 and St=0.01, for the flow configuration considered here.

   @article{JMF2021,
     title = {Numerical modeling of solid-liquid phase change under the influence an external electric field},
     journal = {International Journal of Multiphase Flow},
     volume = {136},
     pages = {103550},
     year = {2021},
     month = mar,
     issn = {0301-9322},
     doi = {https://doi.org/10.1016/j.ijmultiphaseflow.2020.103550},
     url = {https://www.sciencedirect.com/science/article/pii/S0301932220306613},
     author = {Selvakumar, R. Deepak and Liu, Qiang and Kang, Luo and Traoré, Phillipe and Wu, Jian},
     keywords = {Solid-Liquid phase change, Electrohydrodynamics, Heat transfer, Finite-Volume method, OpenFOAM®}
   }

2. Phys. Rev. E

   Numerical analysis of electrohydrodynamic instability in dielectric-liquid–gas flows subjected to unipolar injection

   Qiang Liu , Alberto T. Pérez , R. Deepak Selvakumar , Pengfei Yang , and Jian Wu

   Physical Review E, Dec 2021

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   In this work, the electrohydrodynamic instability induced by a unipolar charge injection is extended from a single-phase dielectric liquid to a two-phase system that consists of a liquid-air interface. A volume-of-fluid model-based two-phase solver was developed with simplified Maxwell equations implemented in the open-source platform OpenFOAM. The numerically obtained critical value for the linear stability matches well with the theoretical values. To highlight the effect of the slip boundary at interface, the deformation of the interface is ignored. A bifurcation diagram with hysteresis loop linking the linear and finite-amplitude criteria, which is Uf=0.059, was obtained in this situation. It is concluded that the lack of viscous effect at interface leads to a significant increase in the flow intensity, which is the reason for the smaller instability threshold in two-phase system. The presence of interface also changes the flow structure and results in a shear distribution of electric force, which may play an important role in the interface deformation.

   @article{PRE2021,
     title = {Numerical analysis of electrohydrodynamic instability in dielectric-liquid--gas flows subjected to unipolar injection},
     author = {Liu, Qiang and P\'erez, Alberto T. and Selvakumar, R. Deepak and Yang, Pengfei and Wu, Jian},
     journal = {Physical Review E},
     volume = {104},
     issue = {6},
     pages = {065109},
     numpages = {15},
     year = {2021},
     month = dec,
     publisher = {American Physical Society},
     doi = {10.1103/PhysRevE.104.065109},
     url = {https://link.aps.org/doi/10.1103/PhysRevE.104.065109},
   }

3. POF

   Numerical investigation on electrohydrodynamic conduction pumping with an external flow

   Zhonglin Du , Junyu Huang , Qiang Liu , R. Deepak Selvakumar , and Jian Wu

   Physics of Fluids, Dec 2021

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   As an advanced flow control and generation technology, electrohydrodynamic (EHD) pumping has received extensive attention in recent years. EHD conduction pumping is a type of EHD pumping that makes use of electric Coulomb force produced by an applied electric field and heterocharge layers formed near the electrodes in dielectric liquids. In this paper, we numerically investigated the flow characteristics of EHD conduction pumping with an external flow. A two-dimensional flushed electrode configuration with the external flow was considered. The coupled series of governing equations, which includes the charge conservation equations and the Poisson equation for the electric potential, are integrated into the finite-volume framework of the open-source OpenFOAM. The effects of external flow’s strength and flow direction on the heterocharge layers and the flow field are investigated. The strength of external flow is shown by the Reynolds number varying between 0 and 40. It is found that with the strong external flow, the structure of heterocharge layers is seriously deformed toward the downstream. In addition, the maximum velocity generated in the flow field of the co-current flow is greater than that of the countercurrent flow.

   @article{POF2021,
     author = {Du, Zhonglin and Huang, Junyu and Liu, Qiang and Deepak Selvakumar, R. and Wu, Jian},
     title = {{Numerical investigation on electrohydrodynamic conduction pumping with an external flow}},
     journal = {Physics of Fluids},
     volume = {33},
     number = {12},
     pages = {123609},
     year = {2021},
     month = dec,
     issn = {1070-6631},
     doi = {10.1063/5.0069462},
     url = {https://doi.org/10.1063/5.0069462},
   }