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Mixtures of fluids and granular sediments play an important role in many industrial, geotechnical, and aerospace engineering problems, from waste management and transportation (liquid--sediment mixtures) to dust kick-up below helicopter…

Computational Engineering, Finance, and Science · Computer Science 2021-07-07 Aaron S. Baumgarten , Benjamin L. S. Couchman , Ken Kamrin

We present a collision model for phase-resolved Direct Numerical Simulations of sediment transport that couple the fluid and particles by the Immersed Boundary Method. Typically, a contact model for these types of simulations comprises a…

Fluid Dynamics · Physics 2017-04-18 Edward Biegert , Bernhard Vowinckel , Eckart Meiburg

Dirac-delta distributions are often crucial components of the solid-fluid coupling operators in immersed solution methods for fluid-structure interaction (FSI) problems. This is certainly so for methods like the Immersed Boundary Method…

Numerical Analysis · Mathematics 2013-02-06 Luca Heltai , Francesco Costanzo

The peridynamic theory brings advantages in dealing with discontinuities, dynamic loading, and non-locality. The integro-differential formulation of peridynamics poses challenges to numerical solutions of complicated and practical problems.…

Numerical Analysis · Mathematics 2021-06-01 Xue Liang , Linjuan Wang , Jifeng Xu , Jianxiang Wang

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

A volume penalization-based immersed boundary technique is developed and thoroughly validated for fluid flow problems, specifically flow over bluff bodies. The proposed algorithm has been implemented in an Open Source Field Operation and…

Fluid Dynamics · Physics 2023-09-19 Prashant Kumar , Vivek Kumar , Di Chen , Yosuke Hasegawa

This study presents an adaptive coupling peridynamic least-square minimization with the finite element method (PDLSM-FEM) for fracture analysis. The presented method utilizes the PDLSM modeling discontinuities while maximizing the FEM…

Numerical Analysis · Mathematics 2022-06-22 Qibang Liu , X. J. Xin , Jeff Ma

This paper presents a method for modelling interfacial mass transfer in Interface Capturing simulations of two-phase flow with phase change. The model enables mechanistic prediction of the local rate of phase change at the vapour-liquid…

Fluid Dynamics · Physics 2021-08-25 G. Giustini , R. I. Issa , M. J. Bluck

Partition of unity methods (PUM) are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Different physical models can exist within a PUM scheme for handling problems with zones of…

Computational Engineering, Finance, and Science · Computer Science 2023-02-06 Matthias Birner , Patrick Diehl , Robert Lipton , Marc Alexander Schweitzer

The aim of this paper is to provide a survey of the state of the art in the finite element approach to the Immersed Boundary Method (FE-IBM) which has been investigated by the authors during the last decade. In a unified setting, we present…

Numerical Analysis · Mathematics 2014-07-22 Daniele Boffi , Lucia Gastaldi

Partition of unity methods (PUM) are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Within the PUM global-local enrichment scheme [1, 2] different physical models can exist to…

Computational Engineering, Finance, and Science · Computer Science 2024-05-06 Matthias Birner , Patrick Diehl , Robert Lipton , Marc Alexander Schweitzer

We introduce a coupled system of PDEs for the modeling of the fluid-fluid and fluid-solid interaction in a poroelastic material with a single static fracture. The fluid flow in the fracture is modeled by a lower-dimensional Darcy equation,…

Numerical Analysis · Mathematics 2016-08-15 Katja K. Hanowski , Oliver Sander

Hydro-mechanical processes in rough fractures are highly non-linear and govern productivity and associated risks in a wide range of reservoir engineering problems. To enable high-resolution simulations of hydro-mechanical processes in…

The interaction of multiple fluids through a heterogeneous pore space leads to complex pore-scale flow dynamics, such as intermittent pathway flow. The non-local nature of these dynamics, and the size of the 4D datasets acquired to capture…

Accurate and efficient simulation of fluid-structure interaction (FSI) problems remains a central challenge in computational physics. High-order discontinuous Galerkin (DG) methods offer low numerical errors and excellent scalability on…

Fluid Dynamics · Physics 2025-12-08 Yingjie Xia , Stefano Colombo , David Huergo , Jiaqing Kou , Yuting Dai , Esteban Ferrer

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

Domain decomposition has been shown to be a computationally efficient distributed method for solving large scale entropic optimal transport problems. However, a naive implementation of the algorithm can freeze in the limit of very fine…

Numerical Analysis · Mathematics 2025-03-28 Ismael Medina , Bernhard Schmitzer

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

In this paper, we explore osmotic transport by means of molecular dynamics (MD) simulations. We first consider osmosis through a membrane, and investigate the reflection coefficient of an imperfectly semi-permeable membrane, in the dilute…

Mesoscale and Nanoscale Physics · Physics 2017-05-18 Hiroaki Yoshida , Sophie Marbach , Lydéric Bocquet

Numerical simulation of moving immersed solid bodies in fluids is now practiced routinely following pioneering work of Peskin and co-workers on immersed boundary method (IBM), Glowinski and co-workers on fictitious domain method (FDM), and…

Numerical Analysis · Mathematics 2024-02-26 Amneet Pal Singh Bhalla , Neelesh A. Patankar