arXiv subjects

Ebrahim M. Kolahdouz

Publications and source records attributed to Ebrahim M. Kolahdouz.

12 recordsLinked to original sources

arXiv2025

Improving the robustness of the immersed interface method through regularized velocity reconstruction

Robust, broadly applicable fluid-structure interaction (FSI) algorithms remain a challenge for computational mechanics. In previous work, we introduced an immersed interface method (IIM) for discrete surfaces and an extension based on an immersed Lagrangia-Eulerian (ILE) coupling strategy for modeling FSI involving complex geometries. The ability of the method to sharply resolve stress discontinuities induced by singular immersed boundary forces in the presence of low-regularity geometrical representations makes it a compelling choice for three-dimensional modeling of complex geometries in diverse engineering applications. Although the IIM we previously introduced offers many desirable advantages, it also imposes a restrictive mesh factor ratio, requiring the surface mesh to be coarser than the fluid grid to ensure stability. This is because when the mesh factor ratio constraint is not satisfied, parts of the structure motion are not controlled by the discrete FSI system. This constraint can significantly increase computational costs, particularly in applications involving multiscale geometries with highly localized complexity or fine-scale features. To address this limitation, we devise a stabilization strategy for the velocity restriction operator inspired by Tikhonov regularization. This study demonstrates that using a stabilized velocity restriction operator in IIM enables a broader range of structure-to-fluid grid-size ratios without compromising accuracy or altering the flow dynamics. This advancement significantly broadens the applicability of the method to real-world FSI problems involving complex geometries and dynamic conditions, offering a robust and practical solution.

physics.comp-ph↗

arXiv2025

An Immersed Interface Method for Incompressible Flows and Geometries with Sharp Features

The immersed interface method (IIM) for models of fluid flow and fluid-structure interaction imposes jump conditions that capture stress discontinuities generated by forces that are concentrated along immersed boundaries. Most prior work using the IIM for fluid dynamic applications has focused on smooth interfaces, but boundaries with sharp features such as corners and edges can appear in practical analyses, particularly on engineered structures. The present study builds on our work to integrate finite element-type representations of interface geometries with the IIM. Initial realizations of this approach used a continuous Galerkin (CG) finite element discretization for the boundary, but as we show herein, these approaches generate large errors near sharp geometrical features. To overcome this difficulty, this study introduces an IIM approach using discontinuous Galerkin (DG) representation of the jump conditions. Numerical examples explore the impacts of different interface representations on accuracy for both smooth and sharp boundaries, particularly flows interacting with fixed interface configurations. We demonstrate that using a DG approach provides accuracy that is comparable to the CG method for smooth cases. Further, we identify a time step size restriction for the CG representation that is directly related to the sharpness of the geometry. In contrast, time step size restrictions imposed by DG representations are demonstrated to be insensitive to the presence of sharp features.

math.NA↗

arXiv2023

A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

This paper introduces a sharp-interface approach to simulating fluid-structure interaction involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. We use a penalty method involving two representations of the fluid-structure interface. These two representations are connected by approximate Lagrange multiplier forces that impose kinematic interface conditions. This approach also enables the use of multi-rate time stepping, which allows us to take different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method for discrete surfaces to impose stress jump conditions along complex interfaces. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures for cases in which part of the solid boundary does not contact the incompressible fluid. Comparisons are made with computational and experimental benchmarks. We also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a cylindrical blood clot in an inferior vena cava filter.

math.NA↗

arXiv2022

An Immersed Interface Method for Discrete Surfaces

Fluid-structure systems occur in a range of scientific and engineering applications. The immersed boundary(IB) method is a widely recognized and effective modeling paradigm for simulating fluid-structure interaction(FSI) in such systems, but a difficulty of the IB formulation is that the pressure and viscous stress are generally discontinuous at the interface. The conventional IB method regularizes these discontinuities, which typically yields low-order accuracy at these interfaces. The immersed interface method(IIM) is an IB-like approach to FSI that sharply imposes stress jump conditions, enabling higher-order accuracy, but prior applications of the IIM have been largely restricted to methods that rely on smooth representations of the interface geometry. This paper introduces an IIM that uses only a C0 representation of the interface,such as those provided by standard nodal Lagrangian FE methods. Verification examples for models with prescribed motion demonstrate that the method sharply resolves stress discontinuities along the IB while avoiding the need for analytic information of the interface geometry. We demonstrate that only the lowest-order jump conditions for the pressure and velocity gradient are required to realize global 2nd-order accuracy. Specifically,we show 2nd-order global convergence rate along with nearly 2nd-order local convergence in the Eulerian velocity, and between 1st-and 2nd-order global convergence rates along with 1st-order local convergence for the Eulerian pressure. We also show 2nd-order local convergence in the interfacial displacement and velocity along with 1st-order local convergence in the fluid traction. As a demonstration of the method's ability to tackle complex geometries,this approach is also used to simulate flow in an anatomical model of the inferior vena cava.

math.NA↗

arXiv2021

A sharp interface Lagrangian-Eulerian method for rigid-body fluid-structure interaction

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 test cases along with large-scale models of biomedical FSI. The numerical approach developed herein, which we refer to as an immersed Lagrangian-Eulerian method, integrates aspects of partitioned and immersed FSI formulations by solving separate momentum equations for the fluid and solid subdomains, as in a partitioned formulation, while also using non-conforming discretizations of the dynamic fluid and structure regions, as in an immersed formulation. A Dirichlet-Neumann coupling scheme is used, in which the motion of the immersed solid is driven by fluid traction forces evaluated along the fluid-structure interface, and the motion of the fluid along that interface is constrained to match the solid velocity and thereby satisfy the no-slip condition. To develop a practical numerical method, we adopt a penalty approach that approximately imposes the no-slip condition along the fluid-structure interface. Our fluid-structure interaction scheme relies on an immersed interface method for discrete geometries, which enables the accurate determination of both velocities and stresses along complex fluid-structure interfaces. Unlike commonly used partitioned FSI methods, which can suffer from so-called added mass effect instabilities, our methodology retains stability for test cases involving extremely small, nearly equal, equal, and large solid-fluid density ratios without requiring subiterations or complex handling of the pressure. Biomedical FSI demonstration cases are also presented including the dynamics of a bileaflet mechanical heart valve in a pulse duplicator, and transport of blood clots in a patient-averaged anatomical model of the inferior vena cava.

math.NA↗

arXiv2020

An immersed interface-lattice Boltzmann method for fluid-structure interaction

An immersed interface-lattice Boltzmann method (II-LBM) is developed for modelling fluid-structure systems. The key element of this approach is the determination of the jump conditions that are satisfied by the distribution functions within the framework of the lattice Boltzmann method when forces are imposed along a surface immersed in an incompressible fluid. In this initial II-LBM, the discontinuity related to the normal portion of the interfacial force is sharply resolved by imposing the relevant jump conditions using an approach that is analogous to imposing the corresponding pressure jump condition in the incompressible Navier-Stokes equations. We show that the jump conditions for the distribution functions are the same in both single-relaxation-time and multi-relaxation-time LBM formulations. Tangential forces are treated using the immersed boundary-lattice Boltzmann method (IB-LBM). The performance of the II-LBM method is compared to both the direct forcing IB-LBM for rigid-body fluid-structure interaction, and the classical IB-LBM for elastic interfaces. Higher order accuracy is observed with the II-LBM as compared to the IB-LBM for selected benchmark problems. Because the jump conditions of the distribution function also satisfy the continuity of the velocity field across the interface, the error in the velocity field is much smaller for the II-LBM than the IB-LBM. The II-LBM is also demonstrated to provide superior volume conservation when simulating flexible boundaries.

physics.comp-ph↗

arXiv2017

Image-based immersed boundary model of the aortic root

Each year, approximately 300,000 heart valve repair or replacement procedures are performed worldwide, including approximately 70,000 aortic valve replacement surgeries in the United States alone. This paper describes progress in constructing anatomically and physiologically realistic immersed boundary (IB) models of the dynamics of the aortic root and ascending aorta. This work builds on earlier IB models of fluid-structure interaction (FSI) in the aortic root, which previously achieved realistic hemodynamics over multiple cardiac cycles, but which also were limited to simplified aortic geometries and idealized descriptions of the biomechanics of the aortic valve cusps. By contrast, the model described herein uses an anatomical geometry reconstructed from patient-specific computed tomography angiography (CTA) data, and employs a description of the elasticity of the aortic valve leaflets based on a fiber-reinforced constitutive model fit to experimental tensile test data. Numerical tests show that the model is able to resolve the leaflet biomechanics in diastole and early systole at practical grid spacings. The model is also used to examine differences in the mechanics and fluid dynamics yielded by fresh valve leaflets and glutaraldehyde-fixed leaflets similar to those used in bioprosthetic heart valves. Although there are large differences in the leaflet deformations during diastole, the differences in the open configurations of the valve models are relatively small, and nearly identical hemodynamics are obtained in all cases considered.

physics.med-ph↗

arXiv2016

Level Set Jet Schemes for Stiff Advection Equations: The SemiJet Method

Many interfacial phenomena in physical and biological systems are dominated by high order geometric quantities such as curvature. Here a semi-implicit method is combined with a level set jet scheme to handle stiff nonlinear advection problems. The new method offers an improvement over the semi-implicit gradient augmented level set method previously introduced by requiring only one smoothing step when updating the level set jet function while still preserving the underlying methods higher accuracy. Sample results demonstrate that accuracy is not sacrificed while strict time step restrictions can be avoided.

math.NA↗

arXiv2015

Dynamics of Three-Dimensional Vesicles in DC Electric fields

A numerical and systematic parameter study of three-dimensional vesicle electrohydrodynamics is presented to investigate the effects of different fluid and membrane properties. The dynamics of vesicles in the presence of DC electric fields is considered, both in the presence and absence of linear shear flow. For suspended vesicles it is shown that the conductivity ratio and viscosity ratio between the interior and exterior fluids, as well as the vesicle membrane capacitance, substantially affect the minimum electric field strength required to induce a full Prolate-Oblate-Prolate transition.In addition, there exists a critical electric field strength above which a vesicle will no longer tumble when exposed to linear shear flow.

cond-mat.soft↗

arXiv2014

Electrohydrodynamics of Three-Dimensional Vesicles: A Numerical Approach

A three-dimensional numerical model of vesicle electrohydrodynamics in the presence of DC electric fields is presented. The vesicle membrane is modeled as a thin capacitive interface through the use of a semi-implicit level set Jet scheme. The enclosed volume and surface area are conserved both locally and globally by a new Navier-Stokes projection method. The electric field calculations explicitly take into account the capacitive interface by an implicit Immersed Interface Method formulation, which calculates the electric potential field and the trans-membrane potential simultaneously. The results match well with previously published experimental, analytic and two-dimensional computational works.

cond-mat.soft↗

arXiv2014

A numerical model for the trans-membrane voltage of vesicles

The Immersed Interface Method is employed to solve the time-varying electric field equations around a three-dimensional vesicle. To achieve second-order accuracy the implicit jump conditions for the electric potential, up to the second normal derivative, are derived. The trans-membrane potential is determined implicitly as part of the algorithm. The method is compared to an analytic solution based on spherical harmonics and verifies the second-order accuracy of the underlying discretization even in the presence of solution discontinuities. A sample result for an elliptic interface is also presented.

cond-mat.soft↗

arXiv2012

The Semi Implicit Gradient Augmented Level Set Method

Here a semi-implicit formulation of the gradient augmented level set method is presented. By tracking both the level set and it's gradient accurate subgrid information is provided,leading to highly accurate descriptions of a moving interface. The result is a hybrid Lagrangian-Eulerian method that may be easily applied in two or three dimensions. The new approach allows for the investigation of interfaces evolving by mean curvature and by the intrinsic Laplacian of the curvature. In this work the algorithm, convergence and accuracy results are presented. Several numerical experiments in both two and three dimensions demonstrate the stability of the scheme.

math.NA↗