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We present an explicit divergence-free DG method for incompressible flow based on velocity formulation only. A globally divergence-free finite element space is used for the velocity field, and the pressure field is eliminated from the…

Numerical Analysis · Mathematics 2018-12-26 Guosheng Fu

We introduce a collection of benchmark problems in 2D and 3D (geometry description and boundary conditions), including simple cases with known analytic solution, classical experimental setups, and complex geometries with fabricated…

Computational Engineering, Finance, and Science · Computer Science 2021-12-13 Zizhou Huang , Teseo Schneider , Minchen Li , Chenfanfu Jiang , Denis Zorin , Daniele Panozzo

We perform numerical analysis of a nonlinear gradient flow, which can be regarded as a parabolic minimal surface problem or a regularised total variation flow, using the gradient discretisation method (GDM). GDM is a unified convergence…

Numerical Analysis · Mathematics 2026-04-21 Jerome Droniou , Kim-Ngan Le , Huateng Zhu

Combining machine learning (ML) with computational fluid dynamics (CFD) opens many possibilities for improving simulations of technical and natural systems. However, CFD+ML algorithms require exchange of data, synchronization, and…

Machine Learning · Computer Science 2024-06-25 Tomislav Maric , Mohammed Elwardi Fadeli , Alessandro Rigazzi , Andrew Shao , Andre Weiner

Hybrid methods for simulating rarefied gas flows reduce computational cost by coupling a particle-based model, typically the direct simulation Monte Carlo (DSMC) method, to a continuum-based solver, i.e. a computational fluid dynamics (CFD)…

Fluid Dynamics · Physics 2026-04-28 Arshad Kamal , Arun K. Chinnappan , James R. Kermode , Duncan A. Lockerby

We propose a fourth order Navier-Stokes solver based on the immersed interface method (IIM), for flow problems with stationary and one-way coupled moving boundaries and interfaces. Our algorithm employs a Runge-Kutta-based projection method…

Fluid Dynamics · Physics 2025-08-22 Xinjie Ji , Changxiao Nigel Shen , Wim M. van Rees

In this work we propose and analyze a novel Hybrid High-Order discretization of a class of (linear and) nonlinear elasticity models in the small deformation regime which are of common use in solid mechanics. The proposed method is valid in…

Numerical Analysis · Mathematics 2017-07-10 Michele Botti , Daniele Di Pietro , Pierre Sochala

We develop a variational multiscale proper orthogonal decomposition reduced-order model for turbulent incompressible Navier-Stokes equations. The error analysis of the full discretization of the model is presented. All error contributions…

Numerical Analysis · Mathematics 2013-06-03 Traian Iliescu , Zhu Wang

Computer simulation is an important tool for scientific progress, especially when lab experiments are either extremely costly and difficult or lack the required resolution. However, all of the simulation methods come with limitations. In…

Fluid Dynamics · Physics 2023-08-04 Edward R. Smith , Panagiotis E. Theodorakis

Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by…

Fluid Dynamics · Physics 2025-04-01 Xinjie Ji , James Gabbard , Wim M. van Rees

This work presents a high-fidelity computational fluid dynamics (CFD) and data-driven modeling framework for assembly-level flow characterization in a four-loop pressurized water reactor (PWR). A full lower-plenum and core-inlet domain was…

In this work, a new discretization approach for coupled free and porous-medium flows is introduced, which uses a finite volume staggered-grid method for the discretization of the Navier-Stokes equations in the free-flow subdomain, while a…

Numerical Analysis · Mathematics 2021-12-22 Martin Schneider , Dennis Gläser , Kilian Weishaupt , Edward Coltman , Bernd Flemisch , Rainer Helmig

M2C (Multiphysics Modeling and Computation) is an open-source software for simulating multi-material fluid flows and fluid-structure interactions under extreme conditions, such as high pressures, high temperatures, shock waves, and large…

Fluid Dynamics · Physics 2025-08-25 Xuning Zhao , Wentao Ma , Shafquat Islam , Aditya Narkhede , Kevin Wang

In this work, fourth-order compact block-centered finite difference (CBCFD) schemes combined with the Crank-Nicolson discretization are constructed and analyzed for solving parabolic integro-differential type non-Fickian flows in…

Analysis of PDEs · Mathematics 2022-07-05 Xuan Zhao , Ziyan Li , Xiaoli Li

Diffusion models (DMs) create samples from a data distribution by starting from random noise and iteratively solving a reverse-time ordinary differential equation (ODE). Because each step in the iterative solution requires an expensive…

Machine Learning · Computer Science 2025-02-25 Eric Frankel , Sitan Chen , Jerry Li , Pang Wei Koh , Lillian J. Ratliff , Sewoong Oh

This work presents a non-linear extension of the high-order discretisation framework based on the Variational Multiscale (VMS) method previously introduced for steady linear problems. We build on the concept of an optimal projector defined…

Numerical Analysis · Mathematics 2025-12-22 Suyash Shrestha , Marc Gerritsma , Gonzalo Rubio , Steven Hulshoff , Esteban Ferrer

Data-driven methods demonstrate considerable potential for accelerating the inherently expensive computational fluid dynamics (CFD) solvers. Nevertheless, pure machine-learning surrogate models face challenges in ensuring physical…

Fluid Dynamics · Physics 2024-09-12 Clément Caron , Philippe Lauret , Alain Bastide

Background: Chronic rhinosinusitis (CRS) is a prevalent and disruptive disease. Medical management including nasal steroid sprays is the primary treatment modality. Computational fluid dynamics (CFD) has been used to characterize sinonasal…

High-fidelity scale-resolving simulations of turbulent flows quickly become prohibitively expensive, especially at high Reynolds numbers. As a remedy, we may use multifidelity models (MFM) to construct predictive models for flow quantities…

Fluid Dynamics · Physics 2023-06-14 Saleh Rezaeiravesh , Timofey Mukha , Philipp Schlatter

Computational Fluid Dynamics (CFD) serves as a powerful tool for simulating fluid flow across diverse industries. High-resolution CFD simulations offer valuable insights into fluid behavior and flow patterns, aiding in optimizing design…