English
Related papers

Related papers: An explicit divergence-free DG method for incompre…

200 papers

We propose a model for the coupling of flow and transport equations with porous membrane-type conditions on part of the boundary. The governing equations consist of the incompressible Navier--Stokes equations coupled with an…

Numerical Analysis · Mathematics 2025-10-07 Arbaz Khan , David Mora , Ricardo Ruíz-Baier , Jesus Vellojin

In this paper, we propose and analyze a high-order finite volume method for the Poisson problem based on the reduced discontinuous Galerkin (RDG) space. The main idea is to employ the RDG space as the trial space and the piecewise constant…

Numerical Analysis · Mathematics 2025-12-11 Wenbo Hu , Yinhua Xia

This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing…

Fluid Dynamics · Physics 2024-05-31 Matteo Zancanaro , Valentin Nkana Ngan , Giovanni Stabile , Gianluigi Rozza

In this article we present a novel staggered semi-implicit hybrid finite-volume/finite-element (FV/FE) method for the resolution of weakly compressible flows in two and three space dimensions. The pressure-based methodology introduced in…

Numerical Analysis · Mathematics 2020-06-16 A. Bermúdez , S. Busto , M. Dumbser , J. L. Ferrín , L. Saavedra , M. E. Vázquez-Cendón

In this paper, authors focus effort on improving the conventional discrete velocity method (DVM) into a multiscale scheme in finite volume framework for gas flow in all flow regimes. Unlike the typical multiscale kinetic methods unified…

Computational Physics · Physics 2020-03-24 Ruifeng Yuan , Sha Liu , Chengwen Zhong

The present paper deals with the numerical solution of the incompressible Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods for discretization in space. For DG methods applied to the dual splitting projection…

Numerical Analysis · Mathematics 2017-10-25 Niklas Fehn , Wolfgang A. Wall , Martin Kronbichler

Implicit constitutive theory provides a very general framework for fluid flow models, including both Newtonian and generalized Newtonian fluids, where the Cauchy stress tensor and the rate of strain tensor are assumed to be related by an…

Numerical Analysis · Mathematics 2019-02-22 Endre Süli , Tabea Tscherpel

The space-time adaptive ADER finite element DG method with a posteriori correction technique of solutions on subcells by the finite-volume ADER-WENO limiter was used to simulate non-stationary compressible multicomponent reactive flows. The…

Fluid Dynamics · Physics 2024-09-17 I. S Popov

The paper introduces a finite element method for the incompressible Navier--Stokes equations posed on a closed surface $\Gamma\subset\R^3$. The method needs a shape regular tetrahedra mesh in $\mathbb{R}^3$ to discretize equations on the…

Numerical Analysis · Mathematics 2019-03-27 Maxim A. Olshanskii , Vladimir Yushutin

This paper proposes and analyzes a class of weak Galerkin (WG) finite element methods for stationary natural convection problems in two and three dimensions. We use piecewise polynomials of degrees k, k-1, and k(k>=1) for the velocity,…

Numerical Analysis · Mathematics 2019-03-25 Han Yihui , Xie Xiaoping

In this paper we propose a novel arbitrary high order accurate semi-implicit space-time DG method for the solution of the three-dimensional incompressible Navier-Stokes equations on staggered unstructured curved tetrahedral meshes. As…

Numerical Analysis · Mathematics 2016-06-22 Maurizio Tavelli , Michael Dumbser

We propose to augment standard grid-based fluid solvers with pointwise divergence-free velocity interpolation, thereby ensuring exact incompressibility down to the sub-cell level. Our method takes as input a discretely divergence-free…

Graphics · Computer Science 2023-11-28 Jumyung Chang , Ruben Partono , Vinicius C. Azevedo , Christopher Batty

In this study we have developed a flexible and efficient numerical scheme for the simulation of three-dimensional incompressible flows in spherical coordinates. The main idea, inspired by a similar strategy as (Verzicco, R., Orlandi, P.,…

Fluid Dynamics · Physics 2020-10-28 L. Santelli , P. Orlandi , R. Verzicco

We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The…

Numerical Analysis · Mathematics 2024-11-25 Biswajit Khara , Robert Dyja , Kumar Saurabh , Anupam Sharma , Baskar Ganapathysubramanian

An interior penalty DG method is proposed for the steady-state linear partial differential equations of nonnegative characteristic form, suitable for mixed second-order elliptic-parabolic and first-order hyperbolic equations. Due to the…

Numerical Analysis · Mathematics 2025-03-21 Zhijie Du , Huoyuan Duan , Roger C E Tan , Yuanhong Wei

In this paper, we consider the Stokes problem with Dirichlet boundary conditions and the constant kinematic viscosity $\nu$ in an axis-aligned domain $\Omega$. We decouple the velocity $\bm u$ and pressure $p$ by deriving a novel biharmonic…

Numerical Analysis · Mathematics 2025-06-17 Qiwei Feng , Bin Han , Michael Neilan

We introduce a new multimesh finite element method for direct numerical simulation of incompressible particulate flows. The proposed approach falls into the category of overlapping domain decomposition / Chimera / overset grid meshes. In…

Numerical Analysis · Mathematics 2025-07-01 Raphael Münster , Otto Mierka , Dmitri Kuzmin , Stefan Turek

This paper presents a new method to approximate the time-dependent convection-diffusion equations using conforming finite element methods, ensuring that the discrete solution respects the physical bounds imposed by the differential…

Numerical Analysis · Mathematics 2025-03-06 Abdolreza Amiri , Gabriel R. Barrenechea , Tristan Pryer

We present a Discontinuous Galerkin (DG) solver for the compressible Navier-Stokes system, designed for applications of technological and industrial interest in the subsonic region. More precisely, this work aims to exploit the…

Numerical Analysis · Mathematics 2025-08-26 Spiros Zafeiris , Emmanuil H. Georgoulis , George Papadakis

Learning-based models for fluid dynamics often operate in unconstrained function spaces, leading to physically inadmissible, unstable simulations. While penalty-based methods offer soft regularization, they provide no structural guarantees,…

Machine Learning · Computer Science 2026-03-26 Xigui Li , Hongwei Zhang , Ruoxi Jiang , Deshu Chen , Chensen Lin , Limei Han , Yuan Qi , Xin Guo , Yuan Cheng