Jaroslav Hron - Profile on Academia.edu (original) (raw)

Papers by Jaroslav Hron

The 41st Annual SES Technical Meeting, 2004

In bioengineering applications problems of flow interacting with elastic solid are very common. W... more In bioengineering applications problems of flow interacting with elastic solid are very common. We formulate the problem of interaction between an incompressible fluid and an incompressible elastic material in the arbitrary Lagrangian-Eulerian formulation, including the possibility ...

Brain Sciences

Computational fluid dynamics (CFD) has grown as a tool to help understand the hemodynamic propert... more Computational fluid dynamics (CFD) has grown as a tool to help understand the hemodynamic properties related to the rupture of cerebral aneurysms. Few of these studies deal specifically with aneurysm growth and most only use a single time instance within the aneurysm growth history. The present retrospective study investigated four patient-specific aneurysms, once at initial diagnosis and then at follow-up, to analyze hemodynamic and morphological changes. Aneurysm geometries were segmented via the medical image processing software Mimics. The geometries were meshed and a computational fluid dynamics (CFD) analysis was performed using ANSYS. Results showed that major geometry bulk growth occurred in areas of low wall shear stress (WSS). Wall shape remodeling near neck impingement regions occurred in areas with large gradients of WSS and oscillatory shear index. This study found that growth occurred in areas where low WSS was accompanied by high velocity gradients between the aneurys...

$Research paper thumbnail of Tidal dissipation in Enceladus’ uneven, fractured ice shell$

Tidal dissipation in Enceladus’ uneven, fractured ice shell

Icarus

Astrobiology

We investigated the effect of variations in ice shell thickness and of the tiger stripe fractures... more We investigated the effect of variations in ice shell thickness and of the tiger stripe fractures crossing Enceladus' south polar terrain on the moon's tidal deformation by performing finite element calculations in three-dimensional geometry. The combination of thinning in the polar region and the presence of faults has a synergistic effect that leads to an increase of both the displacement and stress in the south polar terrain by an order of magnitude compared to that of the traditional model with a uniform shell thickness and without faults. Assuming a simplified conductive heat transfer and neglecting the heat sources below the ice shell, we computed the global heat budget of the ice shell. For the inelastic properties of the shell described by a Maxwell viscoelastic model, we show that unrealistically low average viscosity of the order of 10 13 Pa s is necessary for preserving the volume of the ocean, suggesting the important role of the heat sources in the deep interior. Similarly, low viscosity is required to predict the observed delay of the plume activity, which hints at other delaying mechanisms than just the viscoelasticity of the ice shell. The presence of faults results in large spatial and temporal heterogeneity of geysering activity compared to the traditional models without faults. Our model contributes to understanding the physical mechanisms that control the fault activity, and it provides potentially useful information for future missions that will sample the plume for evidence of life.

In this work we investigate a mathematical model for the description of the mechanical behavior o... more In this work we investigate a mathematical model for the description of the mechanical behavior of soft, hydrated tissues with signi cant perfusion. We set up and derive the mathematical description and balance laws using the continuum mixture theory as the theoretical framework. The constitutive relations suitable to describe perfused soft tissue and appropriate boundary conditions are discussed. We solve illustrative steady, one and two dimensional problems of di usion through nitely deformed slab, and develop an algorithm based on nite element method for nding approximate solution to the continuous, nonlinear, steady, two dimensional problem.

Introduction: Numerical Benchmarking of Fluid-Structure Interaction

Starting with a short introduction of the new nonconforming linear quadrilateral ˜ P1-finite elem... more Starting with a short introduction of the new nonconforming linear quadrilateral ˜ P1-finite element which has been recently proposed by Park ((13, 14)), we examine in detail the numerical behaviour of this element with special emphasis on the treatment of Dirichlet boundary conditions, efficient matrix assembly, solver aspects and the use as Stokes element in CFD. Furthermore, we compare the

We investigate a monolithic algorithm to solve the problem of time dependent interaction between ... more We investigate a monolithic algorithm to solve the problem of time dependent interaction between an incompressible viscous fluid and an elastic solid. The continuous formulation of the problem and its discretization is done in a monolithic way, treating the problem as one continuum. The Q2/P dis 1 finite elements are used for the discretization and an approximate Newton method with

A monolithic FEM/Multigrid solver for ALE formulation of fluid structure interaction with application in biomechanics

We investigate a new method of solving the problem of fluid-structure interaction of an incompres... more We investigate a new method of solving the problem of fluid-structure interaction of an incompressible elastic object in laminar incompressible viscous flow. Our proposed method is based on a fully implicit, monolithic formulation of the problem in the arbitrary Lagrangian-Eulerian framework. High order FEM is used to obtain the discrete approximation of the problem. In order to solve the resulting

In [13], we had performed numerical comparisons for different time stepping schemes for the incom... more In [13], we had performed numerical comparisons for different time stepping schemes for the incompressible Navier-Stokes equations. In this paper, we present the numerical analysis in the context of the Navier-Stokes equations for a new time-stepping θ-scheme which has been recently proposed by Glowinski [5]. Like the well-known classical Fractional-Step-θ-scheme which had been introduced by Glowinski [1], [4], too, and which is still one of the most popular time stepping schemes, with or without operator splitting techniques, this new scheme consists of 3 substeps with non-equidistant substepping to build one macro time step. However, in contrast to the Fractional-Step-θ-scheme, the second substep can be formulated as an extrapolation step for previously computed data only, and the two remaining substeps look like a Backward Euler step so that no expensive operator evaluations for the right hand side vector with older solutions, as for instance in the Crank-Nicolson scheme, have to...

The k ε − turbulence model and the VOF method of moving interface tracking have been used to gene... more The k ε − turbulence model and the VOF method of moving interface tracking have been used to generate the wave. By two-way iterative method ， the fluid structure interaction between wave and steel pipe pile platform has also been simulated numerically by using ANSYS Workbench. Taking the construction platform in deep waters of the Yangtze River Estuary as an example, the stress and deformation characteristics of the steel pipe pile platform under wave forces are analyzed in detail. As a resulted, it is suggested the platform piles should be arranged regularly and the connected node design of the platform structure should be strengthened to ensure the safety.

AJNR. American journal of neuroradiology, Jan 11, 2014

Rupture risk assessment for intracranial aneurysms remains challenging, and risk factors, includi... more Rupture risk assessment for intracranial aneurysms remains challenging, and risk factors, including wall shear stress, are discussed controversially. The primary purpose of the presented challenge was to determine how consistently aneurysm rupture status and rupture site could be identified on the basis of computational fluid dynamics. Two geometrically similar MCA aneurysms were selected, 1 ruptured, 1 unruptured. Participating computational fluid dynamics groups were blinded as to which case was ruptured. Participants were provided with digitally segmented lumen geometries and, for this phase of the challenge, were free to choose their own flow rates, blood rheologies, and so forth. Participants were asked to report which case had ruptured and the likely site of rupture. In parallel, lumen geometries were provided to a group of neurosurgeons for their predictions of rupture status and site. Of 26 participating computational fluid dynamics groups, 21 (81%) correctly identified the ...

Journal of Scientific Computing, 2006

In many numerical procedures one wishes to improve the basic approach either to improve efficienc... more In many numerical procedures one wishes to improve the basic approach either to improve efficiency or else to improve accuracy. Frequently this is based on an analysis of the properties of the discrete system being solved. Using a linear algebra approach one then improves the algorithm. We review methods that instead use a continuous analysis and properties of the differential equation rather than the algebraic system. We shall see that frequently one wishes to develop methods that destroy the physical significance of intermediate results. We present cases where this procedure works and others where it fails. Finally we present the opposite case where the physical intuition can be used to develop improved algorithms.

Numerical analysis for a new non-conforming linear finite element on quadrilaterals

Journal of Computational and Applied Mathematics, 2006

Starting with a short introduction of a new non-conforming linear quadrilateral View the MathML s... more Starting with a short introduction of a new non-conforming linear quadrilateral View the MathML source -finite element which has been recently proposed by Park [A study on locking phenomena in finite element methods, Ph.D. Thesis, Seoul National University, February 2002] and ...

Applied Numerical Mathematics, 2012

We present special finite element and multigrid techniques for solving prototypical cerebral aneu... more We present special finite element and multigrid techniques for solving prototypical cerebral aneurysm hemodynamics problems numerically. An arbitrary Lagrangian-Eulerian (ALE) formulation is employed for this fluid-structure interaction (FSI) application. We utilize the well-known high order finite element pair Q 2 P 1 for discretization in space to gain high accuracy and robustness and perform as time-stepping a fully implicit second order accurate time integrator. The resulting nonlinear discretized algebraic system is solved by an iterative Newton solver which approximates the Jacobian matrix by the divided difference approach, and the resulting linear system is solved by means of Krylov type and geometrical multigrid solvers with a Vanka-like smoother. The aim of this paper is to study the interaction of the elastic walls of an aneurysm with the geometrical shape of an implanted stent structure for prototypical 2D configurations. Preliminary results for the stent-assisted occlusion of a cerebral aneurysm and a qualitative analysis of the behavior of the elasticity of the walls vs. the geometrical details of the stent for prototypical flow situation are presented. Additionally, our approach is designed in such a way that complicated realistic constitutive relations for biomechanics applications for blood vessel simulations can be easily integrated.

Starting with a short introduction of the new nonconforming linear quadrilateral P1-finite eleme... more Starting with a short introduction of the new nonconforming linear quadrilateral P1-finite element which has been recently proposed by Park ([13, 14]), we examine in detail the numerical behaviour of this element with special emphasis on the treatment of Dirichlet boundary conditions, ...

Computational Fluid Dynamics of a Fatal Ruptured Anterior Communicating Artery Aneurysm

Journal of neurological surgery. Part A, Central European neurosurgery, 2017

Computational fluid dynamics (CFD) has been studied as a tool for the stratification of aneurysm ... more Computational fluid dynamics (CFD) has been studied as a tool for the stratification of aneurysm rupture risk. We performed CFD analysis in a patient operated on for a ruptured anterior communicating artery aneurysm. The point of rupture was identified during surgery. The aneurysm and blood vessels were segmented from computed tomography angiography to prepare a model for simulations. We found that the streamlines showed a concentrated inflow jet directed straight at the rupture point, and high wall shear stress was found at the point of rupture in the aneurysm sac. Thus specific local hemodynamics may be indicative of the aneurysm rupture site.

Characterization of solid-fluid mixtures

Nonlinear Analysis: Real World Applications, 2011

Suslov and Tran [3] recently revisited the study carried out by Hron et al. [1] and they on the b... more Suslov and Tran [3] recently revisited the study carried out by Hron et al. [1] and they on the basis of their analysis claim that some of conclusions concerning one specific example, amongst the many considered by Hron et al. [1], are not justified. They claim that the class of simple flows of fluids with pressure dependent viscosity considered by Hron et al. [1] do not allow multiple solutions, and that the inflection velocity profiles reported in Hron et al. [1] cannot exist. We have reexamined both papers, and we find that whether or not velocity profiles with inflection points exist depends on the class of functions to which the pressure belongs. If the pressure field is allowed to be discontinuous, which is in keeping with the class of functions to which pressure belongs to in the study of Hron et al. [1], such inflectional profiles are possible. However, if one requires the pressure field to be continuous then as Suslov and Tran [3] claim, such inflectional profiles are not possible. We provide a detailed explanation for this phenomenon that goes beyond the discussion presented in the paper by Suslov and Tran [3], and concerns subtle mathematical issues. Among other results we show that the solution with the inflectional profile is-interestingly-not a weak solution of the governing equations. Concerning the non-uniqueness of the solution, we show that if we explicitly-instead of assuming that constants are fixed by an unknown procedure-specify a procedure for fixing all the integration constants in the solution, for example by fixing the pressure at two points or fixing the pressure gradient and the pressure at one point, we get a unique solution to the problem, provided all relevant quantities are continuous. On the other hand, if we relax the assumption on continuity, we can get multiple solutions.

Numerical techniques for solving the problem of fluid-structure interaction with an elastic mater... more Numerical techniques for solving the problem of fluid-structure interaction with an elastic material in a laminar incompressible viscous flow are described. An Arbitrary Lagrangian-Eulerian (ALE) formulation is employed in a fully coupled monolithic way, considering the problem as one continuum. The mathematical description and the numerical schemes are designed in such a way that more complicated constitutive relations (and more