Cerebral autoregulation plays a key physiological role by limiting blood flow changes in the face of pressure fluctuations. Although the involved cellular processes are mechanically driven, the quantification of haemodynamic forces in in-vivo settings remains extremely difficult and uncertain. In this work, we propose a novel computational framework for evaluating the blood flow dynamics across networks of myogenically active cerebral arteries, which can modulate their muscular tone to stabilize flow (and perfusion pressure) as well as to limit vascular intramural stress. The introduced framework is built on contractile (myogenically active) vascular wall mechanics and blood flow dynamics models, which can be numerically coupled in either a weak or strong way. We investigate the time dependency of the vascular wall response to pressure changes at both single vessel and network levels. The robustness of the model was assessed by considering different types of inlet signals and numerical settings in an idealized vascular network formed by a middle cerebral artery and its three generations. For the vessel size and boundary conditions considered, weak coupling ensured accurate results with a lower computational cost. To complete the analysis, we evaluated the effect of an upstream pressure surge on the haemodynamics of the vascular network. This provided a clear quantitative picture of how pressure and flow are redistributed across each vessel generation upon inlet pressure changes. This work paves the way for future combined experimental-computational studies aiming to decipher cerebral autoregulation.
Finite element methods based on cut-cells are becoming increasingly popular because of their advantages over formulations based on body-fitted meshes for problems with moving interfaces. In such methods, the cells (or elements) which are cut by the interface between two different domains need to be integrated using special techniques in order to obtain optimal convergence rates and accurate fluxes across the interface. The adaptive integration technique in which the cells are recursively subdivided is one of the popular techniques for the numerical integration of cut-cells due to its advantages over tessellation, particularly for problems involving complex geometries in three dimensions. Although adaptive integration does not impose any limitations on the representation of the geometry of immersed solids as it requires only point location algorithms, it becomes computationally expensive for recovering optimal convergence rates. This paper presents a comprehensive assessment of the adaptive integration of cut-cells for applications in computational fluid dynamics and fluid-structure interaction. We assess the effect of the accuracy of integration of cut cells on convergence rates in velocity and pressure fields, and then on forces and displacements for fluid-structure interaction problems by studying several examples in two and three dimensions. By taking the computational cost and the accuracy of forces and displacements into account, we demonstrate that numerical results of acceptable accuracy for FSI problems involving laminar flows can be obtained with only fewer levels of refinement. In particular, we show that three levels of adaptive refinement are sufficient for obtaining force and displacement values of acceptable accuracy for laminar fluid-structure interaction problems.
Summary In the presence of strong added mass effects, partitioned solution strategies for incompressible fluid‐structure interaction are known to lack robustness and computational efficiency. A number of strategies have been proposed to address this challenge. However, these strategies are often complicated or restricted to certain problem classes and generally require intrusive modifications of existing software. In this work, the well‐known Dirichlet‐Neumann coupling is revisited and a new combined two‐field relaxation strategy is proposed. A family of efficient staggered schemes based crucially on a force predictor is formulated alongside the classical iterative approach. Both methodologies are rigorously analyzed on the basis of a linear model problem derived from a simplified fluid‐conveying elastic tube. The investigation suggests that both the robustness and the efficiency of a partitioned Dirichlet‐Neumann coupling scheme can be improved by a relatively small nonintrusive modification of a standard implementation. The relevance of the model problem analysis for finite element‐based computational fluid‐structure interaction is demonstrated in detail for a submerged cylinder subject to an external force.
Artificial Intelligence (AI) is now entering every sub-field of science, technology, engineering, arts, and management. Thanks to the hype and availability of research funds, it is being adapted in many fields without much thought. Computational Science and Engineering (CS&E) is one such sub-field. By highlighting some critical questions around the issues and challenges in adapting Machine Learning (ML) for CS&E, most of which are often overlooked in journal papers, this contribution hopes to offer some insights into the adaptation of ML for applications in CS\&E and related fields. This is a general-purpose article written for a general audience and researchers new to the fields of ML and/or CS\&E. This work focuses only on the forward problems in computational science and engineering. Some basic equations and MATLAB code are also provided to help the reader understand the basics.
Summary In this paper, we present novel techniques of using quadratic Bézier triangular and tetrahedral elements for elastostatic and implicit/explicit elastodynamic simulations involving nearly incompressible linear elastic materials. A simple linear mapping is proposed for developing finite element meshes with quadratic Bézier triangular/tetrahedral elements from the corresponding quadratic Lagrange elements that can be easily generated using the existing mesh generators. Numerical issues arising in the case of nearly incompressible materials are addressed using the consistent B ‐bar formulation, thus reducing the finite element formulation to one consisting only of displacements. The higher‐order spatial discretization and the nonnegative nature of Bernstein polynomials are shown to yield significant computational benefits. The optimal spatial convergence of the B ‐bar formulation for the quadratic triangular and tetrahedral elements is demonstrated by computing error norms in displacement and stresses. The applicability and computational efficiency of the proposed elements for elastodynamic simulations are demonstrated by studying several numerical examples involving real‐world geometries with complex features. Numerical results obtained with the standard linear triangular and tetrahedral elements are also presented for comparison.
Through fluid-structure interaction simulations, this study assesses the dynamic response characteristics of elastically mounted circular and square cylinders subjected to pulsating inflow conditions, providing valuable insights into the analysis and optimization of these systems. The main focus of the present work is on analyzing the effects of two factors: (i) the ratio of the oscillatory velocity component to the steady velocity component in pulsating flow (flow ratio) and (ii) the ratio of the oscillation frequency of pulsating flow to the natural frequency of the structure (frequency ratio). The simulation results for different parameters of interest are analysed using Fourier analysis and Poincaré maps of time series data, and contour plots of vorticity. For the circular cylinder, it is found that cylinder loses synchronization in lock-in as the flow and frequency ratios are increased. Three distinct vibration patterns of vortex-induced vibration are observed for selected combinations of flow and frequency ratios at a Reynolds number of 110 for circular cylinder. For the galloping of square cylinder at a Reynolds number of 250, it is found that the instability and nonlinearity of vortex shedding become more pronounced as the flow ratio increases.
Finite element methods based on cut-cells are becoming increasingly popular because of their advantages over formulations based on body-fitted meshes for problems with moving interfaces. In such methods, the cells (or elements) which are cut by the interface between two different domains need to be integrated using special techniques in order to obtain optimal convergence rates and accurate fluxes across the interface. The adaptive integration technique in which the cells are recursively subdivided is one of the popular techniques for the numerical integration of cut-cells due to its advantages over tessellation, particularly for problems involving complex geometries in three dimensions. Although adaptive integration does not impose any limitations on the representation of the geometry of immersed solids as it requires only point location algorithms, it becomes computationally expensive for recovering optimal convergence rates. This paper presents a comprehensive assessment of the adaptive integration of cut-cells for applications in computational fluid dynamics and fluid-structure interaction. We assess the effect of the accuracy of integration of cut cells on convergence rates in velocity and pressure fields, and then on forces and displacements for fluid-structure interaction problems by studying several examples in two and three dimensions. By taking the computational cost and the accuracy of forces and displacements into account, we demonstrate that numerical results of acceptable accuracy for FSI problems involving laminar flows can be obtained with only fewer levels of refinement. In particular, we show that three levels of adaptive refinement are sufficient for obtaining force and displacement values of acceptable accuracy for laminar fluid-structure interaction problems.