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The accuracy and stability of implicit CFD codes are frequently impaired by the decoupling between variables, which can ultimately lead to numerical divergence. Coupled solvers, which solve all the governing equations simultaneously, have…

Computational Physics · Physics 2019-09-24 Francisco Pimenta , Manuel A. Alves

This study proposes a novel adaptive finite volume-particle method (AFVPM) for accurate and efficient free surface flow simulations. The proposed AFVPM synergistically combines the Eulerian finite volume method (FVM) on unstructured meshes…

Computational Physics · Physics 2026-03-27 Jiawang Zhang , Fengxiang Zhao , Kun Xu

We present a computational framework for the simulation of blood flow with fully resolved red blood cells (RBCs) using a modular approach that consists of a lattice Boltzmann solver for the blood plasma, a novel finite element based solver…

Computational Physics · Physics 2019-08-28 Christos Kotsalos , Jonas Latt , Bastien Chopard

We extend the shifted boundary method (SBM) to the simulation of incompressible fluid flow using immersed octree meshes. Previous work on SBM for fluid flow primarily utilized two- or three-dimensional unstructured tetrahedral grids.…

This paper studies the characteristics and applicability of the CutFEM approach as the core of a robust topology optimization framework for 3D laminar incompressible flow and species transport problems at low Reynolds number (Re < 200).…

Optimization and Control · Mathematics 2017-02-09 Hernan Villanueva , Kurt Maute

Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical methods to solve fluid flows. The finite volume method (FVM) is an important one. In FVM, space is discretized to many grid cells. When the number of grid…

We consider a Leray model with a nonlinear differential low-pass filter for the simulation of incompressible fluid flow at moderately large Reynolds number (in the range of a few thousands) with under-refined meshes. For the implementation…

Numerical Analysis · Mathematics 2024-12-20 Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

The study of multiphase flows in porous media is fundamental to various fields, including oil recovery, CO2 sequestration, hydrogeology, and others. Accurate predictions of fluid behavior in these systems can enhance process efficiency…

Fluid Dynamics · Physics 2025-09-17 Roberto Lange , Gabriel M. Magalhães , Franciane F. Rocha , Hélio R. Neto

The gVOF package includes a complete and self-contained set of routines for volume of fluid initialization, interface reconstruction and fluid advection, which are used to implement several accurate and efficient geometric volume of fluid…

Computational Physics · Physics 2022-05-25 Joaquín López , Julio Hernández

In this paper, the Immersed Boundary Method (IBM) proposed by Pinelli is implemented for finite volume approximations of incompressible Navier-Stokes equations solutions in the open source toolbox OpenFOAM version 2.2. Solid obstacles are…

Fluid Dynamics · Physics 2016-09-15 E. Constant , C. Li , J. Favier , M. Meldi , P. Meliga , E. Serre

This work concerns the simulation of compressible multi-material fluid flows and follows the method FVCF-NIP described in the former paper Braeunig et al (Eur. J. Mech. B/Fluids, 2009). This Cell-centered Finite Volume method is totally…

Numerical Analysis · Mathematics 2010-10-26 Raphaël Loubère , Jean-Philippe Braeunig , Jean-Michel Ghidaglia

In this paper, two mesh-free CFD solvers for pore-scale fluid flow through porous media are considered, namely the Lattice Boltzmann Method with the two relaxation time collision term and the direct Navier-Stokes solver under the artificial…

Fluid Dynamics · Physics 2025-09-12 Dawid Strzelczyk , Miha Rot , Gregor Kosec , Maciej Matyka

We consider a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are respectively piecewise constant and affine. We use a projection…

Numerical Analysis · Mathematics 2007-05-23 Sebastien Zimmermann

In this paper, we present a class of finite volume schemes for incompressible flow problems. The unknowns are collocated at the center of the control volumes, and the stability of the schemes is obtained by adding to the mass balance…

Numerical Analysis · Mathematics 2020-03-13 R. Eymard , R. Herbin , J. -C Latché , B Piar

We develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media. Some of the methods developed using the framework are already known…

Numerical Analysis · Mathematics 2012-08-20 Lijian Jiang , Ilya D. Mishev

The capillary time-step constraint is the dominant limitation on the applicable time-step in many simulations of interfacial flows with surface tension and, consequently, governs the execution time of these simulations. We propose a…

Computational Physics · Physics 2022-03-10 Fabian Denner , Fabien Evrard , Berend van Wachem

This paper presents uniGasFoam, an open-source particle-based solver for multiscale rarefied gas flow simulations, which has been developed within the well-established OpenFOAM framework, and is an extension of the direct simulation Monte…

The Multiscale Finite Element Method (MsFEM) is developed in the vein of Crouzeix-Raviart element for solving viscous incompressible flows in genuine heterogeneous media. Such flows are relevant in many branches of engineering, often at…

Numerical Analysis · Mathematics 2014-04-11 Bagus Putra Muljadi , Jacek Narski , Alexei Lozinski , Pierre Degond

Fluid-Structure Interaction (FSI) can be investigated by means of non-linear Finite Element Models (FEM), suitable to capture large deflections of structural parts interacting with fluids, and Computational Fluid Dynamics (CFD). High…

In this paper a new hybrid semi-implicit finite volume / finite element (FV/FE) scheme is presented for the numerical solution of the compressible Euler and Navier-Stokes equations at all Mach numbers on unstructured staggered meshes in two…

Numerical Analysis · Mathematics 2023-01-23 Saray Busto , Laura Río-Martín , María Elena Vázquez-Cendón , Michael Dumbser