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We present a new computational method by extending the Immersed Boundary (IB) method with a spectrally-accurate geometric model based on Radial Basis Function (RBF) interpolation of the Lagrangian structures. Our specific motivation is the…

Numerical Analysis · Mathematics 2015-05-27 Varun Shankar , Grady B. Wright , Robert M. Kirby , Aaron L. Fogelson

This paper presents an improved immersed moving boundary model (IBM) for solving complex fluid-particle interactions in a coupled lattice Boltzmann method (LBM) and an adhesive discrete element method (DEM), using the "partially saturated…

Soft Condensed Matter · Physics 2020-10-21 Wenwei Liu , Chuan-Yu Wu

There has been an increasing interest in developing efficient immersed boundary method (IBM) based on Cartesian grids, recently in the context of high-order methods. IBM based on volume penalization is a robust and easy to implement method…

Numerical Analysis · Mathematics 2021-07-22 Jiaqing Kou , Esteban Ferrer

This paper presents eigensolution and non-modal analyses for immersed boundary methods (IBMs) based on volume penalization for the linear advection equation. This approach is used to analyze the behavior of flux reconstruction (FR)…

Numerical Analysis · Mathematics 2021-11-09 Jiaqing Kou , Aurelio Hurtado-de-Mendoza , Saumitra Joshi , Soledad Le Clainche , Esteban Ferrer

A boundary thickening-based direct forcing (BTDF) immersed boundary (IB) method is proposed for fully resolved simulation of incompressible viscous flows laden with finite size particles. By slightly thickening the boundary thickness, the…

Computational Physics · Physics 2020-06-26 Maoqiang Jiang , Zhaohui Liu

The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto…

Numerical Analysis · Mathematics 2020-03-19 Ondrej Maxian , Charles S. Peskin

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

Computational modeling and simulation of fluid-structure interactions constitute a fundamental cornerstone for advancing aerospace engineering endeavors. This paper addresses the notion and implementation of the immersed boundary method for…

Computational Physics · Physics 2025-12-24 Longqing Ge , Qingdong Cai , Yonghao Zhang , Tianbai Xiao

Immersed boundary methods are extensively used for simulations of dynamic solid objects interacting with fluids due to their computational efficiency and modelling flexibility compared to body-fitted grid methods. However, thin geometries,…

Fluid Dynamics · Physics 2022-03-14 Marin Lauber , Gabriel D. Weymouth , Georges Limbert

We present a novel immersed boundary method that implements acoustic perturbation theory to model an acoustically levitated droplet. Instead of resolving sound waves numerically, our hybrid method solves acoustic scattering…

Soft Condensed Matter · Physics 2024-03-22 Jacqueline B. Sustiel , David G. Grier

We introduce a new implementation of the Immersed Boundary method in the finite-volume library OpenFOAM. The implementation is tailored to the simulation of temperature-dependent non-Newtonian polymeric flows in complex moving geometries,…

Numerical Analysis · Mathematics 2024-08-12 G. Negrini , N. Parolini , M. Verani

Immersed boundary-lattice Boltzmann method (IB-LBM) has been widely used for simulation of particle-laden flows recently. However, it was limited to small-scale simulations with no more than O(103) particles. Here, we expand IB-LBM for…

Computational Physics · Physics 2020-02-21 Maoqiang Jiang , Jing Li , Zhaohui Liu

We present an efficient and accurate immersed boundary (IB) finite element (FE) solver for numerically solving incompressible Navier--Stokes equations. Particular emphasis is given to internal flows with complex geometries (blood flow in…

Computational Engineering, Finance, and Science · Computer Science 2020-07-07 G. C. Bourantas , D. L. Lampropoulos , B. F. Zwick , V. C. Loukopoulos , A. Wittek , K. Miller

The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet for fluid problems it only achieves first-order spatial accuracy near embedded boundaries for the velocity field and…

Numerical Analysis · Mathematics 2017-03-08 David B. Stein , Robert D. Guy , Becca Thomases

We introduce a refined immersed boundary (IB) methodology that is better-than-first-order accurate in practice, while preserving key properties of "continuous-forcing" IB approaches that retain a singular source term in the governing…

Numerical Analysis · Mathematics 2026-05-01 Diederik Beckers , H. Jane Bae , Andres Goza

Strongly coupled immersed boundary (IB) methods solve the nonlinear fluid and structural equations of motion simultaneously for strongly enforcing the no-slip constraint on the body. Handling this constraint requires solving several large…

Fluid Dynamics · Physics 2021-03-12 Nirmal Jayaprasad Nair , Andres Goza

The immersed boundary method (IB) is an elegant way to fully couple the motion of a fluid and deformations of an immersed elastic structure. In that vein, the IB2d software allows for expedited explorations of fluid-structure interaction…

Fluid Dynamics · Physics 2018-09-19 Nicholas Battista , Christopher Strickland , Aaron Barrett , Laura Miller

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

There exists an increasing interest for using immersed boundary methods (IBMs) (Peskin 2000) to model moving objects in computational fluid dynamics. Indeed, this approach is particularly efficient, because the fluid mesh does not require…

Computational Physics · Physics 2019-04-04 Joel Beny , Jonas Latt

In this work, the Immersed Boundary Method (IBM) with feedback forcing introduced by Goldstein et al. (1993) and often referred in the literature as the Virtual Boundary Method (VBM), is addressed. The VBM has been extensively applied both…

Numerical Analysis · Mathematics 2021-10-25 Michele Girfoglio , Giovanni Stabile , Andrea Mola , Gianluigi Rozza