This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Followingare chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

This review covers Verification, Validation, Confirmation and related subjects for computational fluid dynamics (CFD), including error taxonomies, error estimation and banding, convergence rates, surrogate estimators, nonlinear dynamics, and error estimation for grid adaptation vs Quantification of Uncertainty.

/pdf/quantification-of-uncertainty-in-computational-fluid-3imbkhwf41.pdf

Quantification of uncertainty in computational fluid dynamics

Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques

	This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization

	An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques



	
		Will provide you with the knowledge required to develop and understand modern flow simulation codes
	
		Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics
	
		Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques

Computational Fluid Dynamics: Principles and Applications Ed. 3

Aircraft wings are a compromise that allows the aircraft to fly at a range of flight conditions, but the performance at each condition is sub-optimal. The ability of a wing surface to change its geometry during flight has interested researchers and designers over the years as this reduces the design compromises required. Morphing is the short form for metamorphose; however, there is neither an exact definition nor an agreement between the researchers about the type or the extent of the geometrical changes necessary to qualify an aircraft for the title ‘shape morphing.’ Geometrical parameters that can be affected by morphing solutions can be categorized into: planform alteration (span, sweep, and chord), out-of-plane transformation (twist, dihedral/gull, and span-wise bending), and airfoil adjustment (camber and thickness). Changing the wing shape or geometry is not new. Historically, morphing solutions always led to penalties in terms of cost, complexity, or weight, although in certain circumstances, thes...

A Review of Morphing Aircraft

https://www.scorec.rpi.edu/REPORTS/2006-22.pdf

Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries

In this paper a one-dimensional model of a vascular network based on space-time variables is investigated. Although the one-dimensional system has been more widely studied using a space-frequency decomposition, the space-time formulation offers a more direct physical interpretation of the dynamics of the system. The objective of the paper is to highlight how the space-time representation of the linear and nonlinear one-dimensional system can be theoretically and numerically modelled. In deriving the governing equations from first principles, the assumptions involved in constructing the system in terms of area-mass flux (A,Q), area-velocity (A,u), pressure-velocity (p,u) and pressure-mass flux(p,Q) variables are discussed. For the nonlinear hyperbolic system expressed in terms of the (A,u) variables the extension of the single-vessel model to a network of vessels is achieved using a characteristic decomposition combined with conservation of mass and total pressure. The more widely studied linearised system is also discussed where conservation of static pressure, instead of total pressure, is enforced in the extension to a network. Consideration of the linearised system also allows for the derivation of a reflection coefficient analogous to the approach adopted in acoustics and surface waves. The derivation of the fundamental equations in conservative and characteristic variables provides the basic information for many numerical approaches. In the current work the linear and nonlinear systems have been solved using a spectral/hp element spatial discretisation with a discontinuous Galerkin formulation and a second-order Adams-Bashforth time-integration scheme. The numerical scheme is then applied to a model arterial network of the human vascular system previously studied by Wang and Parker (To appear in J. Biomech. (2004)). Using this numerical model the role of nonlinearity is also considered by comparison of the linearised and nonlinearised results. Similar to previous work only secondary contributions are observed from the nonlinear effects under physiological conditions in the systemic system. Finally, the effect of the reflection coefficient on reversal of the flow waveform in the parent vessel of a bifurcation is considered for a system with a low terminal resistance as observed in vessels such as the umbilical arteries.

/pdf/one-dimensional-modelling-of-a-vascular-network-in-space-50c22v2hd3.pdf

One-dimensional modelling of a vascular network in space-time variables

Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements

http://spiral.imperial.ac.uk/bitstream/10044/1/613/1/Modelling%20the%20circle%20of%20Willis.pdf

Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows

We numerically investigate a one-dimensional model of blood flow in human arteries using both a discontinuous Galerkin and a Taylor-Galerkin formulation. The derivation of the model and the numerical schemes are detailed and applied to two model numerical experiments. We first study the effect of an intervention, such the implantation of a vascular prosthesis (e.g. a stent), which leads to an abrupt variation of the mechanical characteristics of an artery. We then discuss the simulation of the propagation of pressure and velocity waveforms in the human arterial tree using a simplified model consisting of the 55 main arteries

/pdf/computational-modelling-of-1d-blood-flow-with-variable-1e4b07e7et.pdf

Computational modelling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system

The effects of free-surface proximity on the flow field around tidal stream turbines are modelled using actuator disc theory. Theoretical results are presented for a blocked configuration of tidal stream turbines such as a linear array that account for the proximity of the free surface and the seabed. The theoretical results are compared to open channel flow experimental results in which the flow field has been simulated using a porous disc and strip. These results are complemented by more detailed measurements of the performance of a model horizontal-axis turbine carried out in a water flume and a wind tunnel. The two sets of experiments represent highly blocked and effectively unblocked cases, respectively. The theoretical model of the effects of free-surface proximity provides a blockage correction for axial induction that can be incorporated in blade element momentum codes. The performance predictions obtained with such a code are in good agreement with the experimental results for C P and C T at low tip-speed ratios. The agreement weakens with increasing tip-speed ratio, as the wake of turbine enters a reversed flow state. A correction following the philosophy of Maskell is applied to C T in this region, which provides a better agreement.

Joaquim Peiró

Papers

One-dimensional modelling of a vascular network in space-time variables

Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements

Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows

Computational modelling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system

A free-surface and blockage correction for tidal turbines