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We propose a new formula for the nonlinear viscous numerical flux and extend the direct discontinuous Galerkin method with interface correction (DDGIC) of Liu and Yan (H. Liu, J. Yan, The direct discontinuous Galerkin (DDG) method for…

Numerical Analysis · Mathematics 2022-09-29 Mustafa E. Danis , Jue Yan

Artificial intelligence techniques are considered an effective means to accelerate flow field simulations. However, current deep learning methods struggle to achieve generalization to flow field resolutions while ensuring computational…

Fluid Dynamics · Physics 2024-05-15 Kuijun Zuo , Zhengyin Ye , Linyang Zhu , Xianxu Yuan , Weiwei Zhang

This work presents and compares efficient implementations of high-order discontinuous Galerkin methods: a modal matrix-free discontinuous Galerkin (DG) method, a hybridizable discontinuous Galerkin (HDG) method, and a primal formulation of…

Computational Physics · Physics 2018-12-14 Matteo Franciolini , Krzysztof Fidkowski , Andrea Crivellini

We propose a new family of high order staggered semi-implicit discontinuous Galerkin (DG) methods for the simulation of natural convection problems. Assuming small temperature fluctuations, the Boussinesq approximation is valid and the flow…

Computational Physics · Physics 2019-12-05 Saray Busto , Maurizio Tavelli , Walter Boscheri , Michael Dumbser

Classical Proper Orthogonal Decomposition (POD)-based Galerkin projection models of chaotic flows typically require a large number of modes as well as stabilization or closure terms to achieve adequate accuracy and long-term stability. We…

Computational Physics · Physics 2026-05-27 Anant Kumar , Oliver Morales , Rohit Deshmukh

We present a multiscale continuous Galerkin (MSCG) method for the fast and accurate stochastic simulation and optimization of time-harmonic wave propagation through photonic crystals. The MSCG method exploits repeated patterns in the…

Numerical Analysis · Mathematics 2020-04-30 Ferran Vidal-Codina , Joel Saa-Seoane , Ngoc-Cuong Nguyen , Jaime Peraire

Computationally efficient and accurate simulations of the flow over axisymmetric bodies of revolution (ABR) has been an important desideratum for engineering design. In this article the flow field over an ABR is predicted using machine…

Fluid Dynamics · Physics 2021-11-16 J P Panda , H V Warrior

We present discontinuous Galerkin (DG) methods for solving a first-order semi-linear hyperbolic system, which was originally proposed as a continuum model for a one-dimensional dimer lattice of topological resonators. We examine the…

Numerical Analysis · Mathematics 2023-05-23 Qiang Du , Huaiyu Li , Michael Weinstein , Lu Zhang

An evolutionary multi-objective aerodynamic design optimization method using the computational fluid dynamics (CFD) simulations incorporating deep neural network (DNN) to reduce the required computational time is proposed. In this approach,…

Fluid Dynamics · Physics 2023-05-01 Yukito Tsunoda , Akira Oyama

Computational fluid dynamics (CFD) is a powerful tool for modeling turbulent flow and is commonly used for urban microclimate simulations. However, traditional CFD methods are computationally intensive, requiring substantial hardware…

Deep learning techniques for improving fluid flow modelling have gained significant attention in recent years. Advanced deep learning techniques achieve great progress in rapidly predicting fluid flows without prior knowledge of the…

Atmospheric and Oceanic Physics · Physics 2020-04-22 M. Cheng , F. Fang , C. C. Pain , I. M. Navon

Diffusion model, the state-of-the-art generative machine learning architecture, has shown promising results airfoil inverse designs. In this study, we implemented and trained a series of diffusion models on three different airfoil geometry…

Fluid Dynamics · Physics 2026-01-26 Yingfan Geng , Jinhong Wang , Teng Cao

We propose a family of high-order local discontinuous Galerkin (LDG) methods, built on a parametric representation and coupled with a semi-implicit backward Euler time discretization, for isotropic and anisotropic curve-shortening flows.…

Numerical Analysis · Mathematics 2026-04-06 Xiuhui Guo , Wei Jiang , Chunmei Su

We investigate the numerical performance of a Discontinuous Galerkin (DG) hydrodynamics implementation when applied to the problem of driven, isothermal supersonic turbulence. While the high-order element-based spectral approach of DG is…

Instrumentation and Methods for Astrophysics · Physics 2024-10-03 Miha Cernetic , Volker Springel , Thomas Guillet , Rüdiger Pakmor

Real-time and accurate prediction of aerodynamic flow fields around airfoils is crucial for flow control and aerodynamic optimization. However, achieving this remains challenging due to the high computational costs and the non-linear nature…

Fluid Dynamics · Physics 2025-10-23 Chunyang Wang , Biyue Pan , Zhibo Dai , Yudi Cai , Yuhao Ma , Hao Zheng , Dixia Fan , Hui Xiang

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.…

Fluid Dynamics · Physics 2024-10-10 Qiang Liu , Nils Thuerey

Reduced order models (ROMs) are inexpensive surrogate models that reduce costs associated with many-query scenarios. Current methods for constructing entropy stable ROMs for nonlinear conservation laws utilize full order models (FOMs) based…

Numerical Analysis · Mathematics 2025-12-24 Ray Qu , Akil Narayan , Jesse Chan

An implicit high-order discontinuous Galerkin (DG) method is developed to find steady-state solution of rarefied gas flow described by the Boltzmann equation with full collision operator. In the physical space, velocity distribution…

Computational Physics · Physics 2019-01-08 Wei Su , Peng Wang , Yonghao Zhang , Lei Wu

In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…

Fluid Dynamics · Physics 2025-07-14 Yannick Gachnang , Vismay Churiwala

High-order accurate discontinuous Galerkin (DG) methods have emerged as powerful tools for solving partial differential equations such as the compressible Navier-Stokes equations due to their excellent dispersion-dissipation properties and…

Numerical Analysis · Mathematics 2025-11-12 Patrick Kopper , Anna Schwarz , Jens Keim , Andrea Beck