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The immersed boundary method is a mathematical formulation and numerical method for solving fluid-structure interaction problems. For many biological problems, such as models that include the cell membrane, the immersed structure is a…

Numerical Analysis · Mathematics 2018-06-07 Ondrej Maxian , Andrew T. Kassen , Wanda Strychalski

This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…

Analysis of PDEs · Mathematics 2024-10-31 Rômulo Damasclin Chaves dos Santos , Jorge Henrique de Oliveira Sales

We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modelled by generalised Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelisable…

Fluid Dynamics · Physics 2019-09-17 Knut Sverdrup , Ann Almgren , Nikolaos Nikiforakis

We prove that uniform accuracy of almost second order can be achieved with a finite difference method applied to Navier-Stokes flow at low Reynolds number with a moving boundary, or interface, creating jumps in the velocity gradient and…

Numerical Analysis · Mathematics 2016-07-27 J. Thomas Beale

This work outlines a new multi-physics-compatible immersed rigid body method for Eulerian finite-volume simulations. To achieve this, rigid bodies are represented as a diffuse scalar field and an interface seeding method is employed to…

Computational Physics · Physics 2022-03-15 Tim Wallis , Philip Barton , Nikolaos Nikiforakis

We develop a framework for analyzing the momentum balance of laminar particle-laden flows based on immersed boundary methods, which solve the Navier-Stokes equations and resolve the particle surfaces. This framework differs from previous…

Fluid Dynamics · Physics 2018-06-04 E. Biegert , B. Vowinckel , E. Meiburg

This work focuses on the development of a new incompressible solver, incompressibleFoam, within OpenFOAM and integrating several numerical methods within the same framework. Two momentum interpolation (NCMI/CMI) methods are implemented, two…

Fluid Dynamics · Physics 2025-06-26 Paulin Ferro , Pierre-Etienne Meiller , Paul Landel , Carla Landrodie , Marc Pescheux

The immersed boundary (IB) method is a widely used approach to simulating fluid-structure interaction (FSI). Although explicit versions of the IB method can suffer from severe time step size restrictions, these methods remain popular…

Numerical Analysis · Mathematics 2016-12-08 Amneet Pal Singh Bhalla , Matthew G. Knepley , Mark F. Adams , Robert D. Guy , Boyce E. Griffith

We present an exponentially convergent semi-implicit meshless algorithm for the solution of Navier-Stokes equations in complex domains. The algorithm discretizes partial derivatives at scattered points using radial basis functions as…

Numerical Analysis · Mathematics 2021-06-15 Shantanu Shahane , Surya Pratap Vanka

Our paper proposes an innovative approach for modeling Fluid-Structure Interaction (FSI). Our method combines both traditional monolithic and partitioned approaches, creating a hybrid solution that facilitates FSI. At each time iteration,…

Numerical Analysis · Mathematics 2024-01-15 R. Nemer , A. Larcher , E. Hachem

This paper presents an efficient high-order sharp-interface method for solving the three-dimensional (3D) Poisson equation with Dirichlet boundary conditions on a nonuniform Cartesian grid with irregular domain boundaries. The new approach…

Computational Physics · Physics 2024-12-20 Shirzad Hosseinverdi , Hermann F. Fasel

This paper presents a novel finite volume mooring line model based on the geometrically exact Simo-Reissner beam model for analysing the interaction between a floating rigid body and its mooring lines. The coupled numerical model is…

Numerical Analysis · Mathematics 2026-01-21 Amirhossein Taran , Seevani Bali , Zeljko Tukovic , Vikram Pakrashi , Philip Cardiff

This work extends, to moving geometries, the immersed boundary method based on volume penalization and selective frequency damping approach [J. Kou, E. Ferrer, A combined volume penalization/selective frequency damping approach for immersed…

Fluid Dynamics · Physics 2024-01-10 Jiaqing Kou , Esteban Ferrer

We consider an efficient preconditioner for boundary integral equation (BIE) formulations of the two-dimensional Stokes equations in porous media. While BIEs are well-suited for resolving the complex porous geometry, they lead to a dense…

Numerical Analysis · Mathematics 2016-09-16 Pieter Coulier , Bryan Quaife , Eric Darve

We present a framework for Large Eddy Simulations (LES) with Immersed Boundaries (IBs) to simulate high Reynolds number flows over complex walls. In this approach, which we call Immersed Boundary-Modeled LES (IBMLES), we volume-filter the…

Fluid Dynamics · Physics 2025-11-03 Morrison Rickard , M. Houssem Kasbaoui

A hybrid sharp-interface immersed-boundary/front-tracking (IB/FT) method is developed for interface-resolved simulation of evaporating droplets in incompressible multiphase flows. A one-field formulation is used to solve the flow, species…

Fluid Dynamics · Physics 2025-10-30 Faraz Salimnezhad , Hasret Turkeri , Iskender Gokalp , Metin Muradoglu

In the present work, we propose a novel hybrid explicit jump immersed interface approach in conjunction with a higher order compact (HOC) scheme for simulating transient complex flows governed by the streamfunction-vorticity…

Numerical Analysis · Mathematics 2022-09-13 Raghav Singhal , Jiten C Kalita

Recently, physics informed neural networks (PINNs) have been explored extensively for solving various forward and inverse problems and facilitating querying applications in fluid mechanics applications. However, work on PINNs for unsteady…

Fluid Dynamics · Physics 2024-02-28 Rahul Sundar , Dipanjan Majumdar , Didier Lucor , Sunetra Sarkar

Continuum solvent models have become a standard technique in the context of electronic structure calculations, yet, no implementations have been reported capable to perform molecular dynamics at solid-liquid interfaces. We propose here such…

Chemical Physics · Physics 2015-05-13 Veronica M. Sanchez , Mariela Sued , Damian A. Scherlis

This paper introduces a sharp interface method to simulate fluid-structure interaction (FSI) involving rigid bodies immersed in viscous incompressible fluids. The capabilities of this methodology are demonstrated for a range of benchmark…