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We investigate the steady self-propelled motion of a rigid body immersed in a three-dimensional incompressible viscous fluid governed by the Navier-Stokes equations. The analysis is performed in a body-fixed reference frame, so that the…

Analysis of PDEs · Mathematics 2026-01-01 Sarka Necasova , Arnab Roy , Ana Leonor Silvestre

The paper develops a method for the numerical simulation of a free-surface flow of incompressible viscous fluid around a streamlined body. The body is a rigid stationary construction partially submerged in the fluid. The application we are…

A variety of numerical methods exist for the study of deformable particles in dense suspensions. None of the standard tools, however, currently include volume-changing objects such as oscillating microbubbles in three-dimensional periodic…

Biological Physics · Physics 2017-08-14 Achim Guckenberger , Stephan Gekle

A simple, yet efficient procedure to solve quasistatic problems of special linear visco-elastic solids at small strains with equal rheological response in all tensorial components, utilizing boundary element method (BEM), is introduced.…

Numerical Analysis · Mathematics 2014-02-27 C. G. Panagiotopoulos , V. Mantic , T. Roubicek

This paper deals with a new solid-fluid coupling algorithm between a rigid body and an unsteady compressible fluid flow, using an Embedded Boundary method. The coupling with a rigid body is a first step towards the coupling with a Discrete…

Numerical Analysis · Mathematics 2016-12-01 Laurent Monasse , Virginie Daru , Christian Mariotti , Serge Piperno , Christian Tenaud

We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are…

Numerical Analysis · Mathematics 2020-01-08 Hong Xiao , Eky Febrianto , Qiaoling Zhang , Fehmi Cirak

In this paper we propose a new diffuse interface model for the numerical simulation of inviscid compressible flows around fixed and moving solid bodies of arbitrary shape. The solids are assumed to be moving rigid bodies, without any…

Numerical Analysis · Mathematics 2020-03-27 Friedemann Kemm , Elena Gaburro , Ferdinand Thein , Michael Dumbser

We present a moving control volume (CV) approach to computing hydrodynamic forces and torques on complex geometries. The method requires surface and volumetric integrals over a simple and regular Cartesian box that moves with an arbitrary…

Numerical Analysis · Mathematics 2017-09-13 Nishant Nangia , Hans Johansen , Neelesh A. Patankar , Amneet Pal Singh Bhalla

In this work a finite element simulation of the motion of a rigid body in a fluid, with free surface, is described. A completely general referential description (of which both Lagrangian and Eulerian descriptions are special cases) of an…

Fluid Dynamics · Physics 2015-06-26 S. J. Childs , B. D. Reddy

Two methods for solid body representation in flow simulations available in the Pencil Code are the immersed boundary method and overset grids. These methods are quite different in terms of computational cost, flexibility and numerical…

Computational Physics · Physics 2018-11-20 Jørgen R. Aarnes , Tai Jin , Chaoli Mao , Nils E. L. Haugen , Kun Luo , Helge I. Andersson

An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied…

Fluid Dynamics · Physics 2013-01-22 Alessandro Iafrati

Modeling and direct numerical simulation of particle-laden flows have a tremendous variety of applications in science and engineering across a vast spectrum of scales from pollution dispersion in the atmosphere, to fluidization in the…

We investigate a projection-based reduced-order model of the steady incompressible Navier-Stokes equations for moderate Reynolds numbers. In particular, we construct an "embedded" reduced basis space, by applying proper orthogonal…

Numerical Analysis · Mathematics 2020-08-26 Efthymios N. Karatzas , Giovanni Stabile , Leo Nouveau , Guglielmo Scovazzi , Gianluigi Rozza

We consider a Navier-Stokes fluid-plate interaction (FSI) system which describes the evolutions of the fluid contained within a 3D cavity, as it interacts with a deformable elastic membrane on the ``free" upper boundary of the cavity. These…

Analysis of PDEs · Mathematics 2025-07-04 Pelin G. Geredeli , Quyuan Lin , Dylan Mcknight , Mohammad Mahabubur Rahman

We present a characterization of the forcing and the sub-filter scale terms produced in the volume-filtering immersed boundary (VF-IB) method by Dave et al, JCP, 2023. The process of volume-filtering produces bodyforces in the form of…

Numerical Analysis · Mathematics 2024-07-16 Dave Himanshu , Herrmann Marcus , Brady Peter , M. Houssem Kasbaoui

This work proposes a new stabilized $P_1\times P_0$ finite element method for solving the incompressible Navier--Stokes equations. The numerical scheme is based on a reduced Bernardi--Raugel element with statically condensed face bubbles…

Numerical Analysis · Mathematics 2023-04-06 Yuwen Li , Ludmil Zikatanov

We study the immersed boundary problem in 2-D. It models a 1-D elastic closed string immersed and moving in a fluid that fills the entire plane, where the fluid motion is governed by the 2-D incompressible Navier-Stokes equation with a…

Analysis of PDEs · Mathematics 2025-12-17 Jiajun Tong , Dongyi Wei

We present a reduced order method (ROM) based on proper orthogonal decomposition (POD) for the viscous Burgers' equation and the incompressible Navier-Stokes equations discretized using an implicit-explicit hybrid discontinuous…

Numerical Analysis · Mathematics 2020-04-21 Guosheng Fu , Zhu Wang

In this work we consider how surface-adherent bacterial biofilm communities respond in flowing systems. We simulate the fluid-structure interaction and separation process using the immersed boundary method. In these simulations we model and…

Numerical Analysis · Mathematics 2013-02-18 Jason F. Hammond , Elizabeth J. Stewart , John G. Younger , Michael J. Solomon , David M. Bortz

This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook…

Computational Physics · Physics 2021-09-21 Suhas S. Jain , Michael C. Adler , Jacob R. West , Ali Mani , Parviz Moin , Sanjiva K. Lele