Kenneth E. Jansen

A generalized-α method for integrating the filtered Navier-Stokes equations with a stabilized finite element method

A generalized-a method is developed and analyzed for linear, first-order systems. The method is then extended to the filtered Navier-Stokes equations within the context of a stabilized finite element method. The formulation is studied through the application to laminar flow past a circular cylinder and turbulent flow past a long, transverse groove. The method is formulated to obtain a second-order accurate family of time integrators whose high frequency amplification factor is the sole free parameter. Such an approach allows the replication of midpoint rule (zero damping), Gears method (maximal damping), or anything in between.

Patient-specific modeling of blood flow and pressure in human coronary arteries.

Coronary flow is different from the flow in other parts of the arterial system because it is influenced by the contraction and relaxation of the heart. To model coronary flow realistically, the compressive force of the heart acting on the coronary vessels needs to be included. In this study, we developed a method that predicts coronary flow and pressure of three-dimensional epicardial coronary arteries by considering models of the heart and arterial system and the interactions between the two models. For each coronary outlet, a lumped parameter coronary vascular bed model was assigned to represent the impedance of the downstream coronary vascular networks absent in the computational domain. The intramyocardial pressure was represented with either the left or right ventricular pressure depending on the location of the coronary arteries. The left and right ventricular pressure were solved from the lumped parameter heart models coupled to a closed loop system comprising a three-dimensional model of the aorta, three-element Windkessel models of the rest of the systemic circulation and the pulmonary circulation, and lumped parameter models for the left and right sides of the heart. The computed coronary flow and pressure and the aortic flow and pressure waveforms were realistic as compared to literature data.

A stabilized finite element method for the incompressible Navier–Stokes equations using a hierarchical basis

Stabilized finite element methods have been shown to yield robust, accurate numerical solutions to both the compressible and incompressible Navier-Stokes equations for laminar and turbulent flows. The present work focuses on the application of higher-order, hierarchical basis functions to the incompressible Navier-Stokes equations using a stabilized finite element method. It is shown on a variety of problems that the most cost-effective simulations (in terms of CPU time, memory, and disk storage) can be obtained using higher-order basis functions when compared with the traditional linear basis. In addition, algorithms will be presented for the efficient implementation of these methods within the traditional finite element data structures

On Coupling a Lumped Parameter Heart Model and a Three-Dimensional Finite Element Aorta Model

Aortic flow and pressure result from the interactions between the heart and arterial system. In this work, we considered these interactions by utilizing a lumped parameter heart model as an inflow boundary condition for three-dimensional finite element simulations of aortic blood flow and vessel wall dynamics. The ventricular pressure–volume behavior of the lumped parameter heart model is approximated using a time varying elastance function scaled from a normalized elastance function. When the aortic valve is open, the coupled multidomain method is used to strongly couple the lumped parameter heart model and three-dimensional arterial models and compute ventricular volume, ventricular pressure, aortic flow, and aortic pressure. The shape of the velocity profiles of the inlet boundary and the outlet boundaries that experience retrograde flow are constrained to achieve a robust algorithm. When the aortic valve is closed, the inflow boundary condition is switched to a zero velocity Dirichlet condition. With this method, we obtain physiologically realistic aortic flow and pressure waveforms. We demonstrate this method in a patient-specific model of a normal human thoracic aorta under rest and exercise conditions and an aortic coarctation model under pre- and post-interventions.

Outflow boundary conditions for 3D simulations of non-periodic blood flow and pressure fields in deformable arteries

The simulation of blood flow and pressure in arteries requires outflow boundary conditions that incorporate models of downstream domains. We previously described a coupled multidomain method to couple analytical models of the downstream domains with 3D numerical models of the upstream vasculature. This prior work either included pure resistance boundary conditions or impedance boundary conditions based on assumed periodicity of the solution. However, flow and pressure in arteries are not necessarily periodic in time due to heart rate variability, respiration, complex transitional flow or acute physiological changes. We present herein an approach for prescribing lumped parameter outflow boundary conditions that accommodate transient phenomena. We have applied this method to compute haemodynamic quantities in different physiologically relevant cardiovascular models, including patient-specific examples, to study non-periodic flow phenomena often observed in normal subjects and in patients with acquired or congenital cardiovascular disease. The relevance of using boundary conditions that accommodate transient phenomena compared with boundary conditions that assume periodicity of the solution is discussed.

Large-eddy simulation on unstructured deforming meshes : towards reciprocating IC engines

A variable explicit/implicit characteristics-based advection scheme that is second-order accurate in space and time has been developed recently for unstructured deforming meshes (O’Rourke PJ, Sahota MS. A variable explicit/implicit numerical method for calculating advection on unstructured meshes. J Comput Phys 1998;142:312–45). To explore the suitability of this methodology for large-eddy simulation (LES) in reciprocating internal combustion engines, three subgrid-scale turbulence models have been implemented: a constant-coefficient Smagorinsky model, a dynamic Smagorinsky model for flows having one or more directions of statistical homogeneity, and a Lagrangian dynamic Smagorinsky model for flows having no spatial or temporal homogeneity (Meneveau C, Lund TS, Cabot WH. A Lagrangian dynamic subgrid-scale model of turbulence. J Fluid Mech 1996;319:353–85). Quantitative results are presented for three canonical flows (decaying homogeneous isotropic turbulence, non-solenoidal linear strains of homogeneous turbulence, planar channel flow) and for a simplified piston-cylinder assembly with moving piston and fixed central valve. Computations are compared to experimental measurements, to direct-numerical simulation data, and to rapid-distortion theory where appropriate. Generally satisfactory evolution of first, second, and some higher order moments is found. Computed mean and rms velocity profiles for the piston-cylinder configuration show better agreement with measurements than Reynolds-averaged turbulence models. These results demonstrate the suitability of this methodology for engineering LES, and the feasibility of LES for computing IC engine flows.

The ParaView Coprocessing Library: A scalable, general purpose in situ visualization library

As high performance computing approaches exascale, CPU capability far outpaces disk write speed, and in situ visualization becomes an essential part of an analysts workflow. In this paper, we describe the ParaView Coprocessing Library, a framework for in situ visualization and analysis coprocessing. We describe how coprocessing algorithms (building on many from VTK) can be linked and executed directly from within a scientific simulation or other applications that need visualization and analysis. We also describe how the ParaView Coprocessing Library can write out partially processed, compressed, or extracted data readable by a traditional visualization application for interactive post-processing. Finally, we will demonstrate the librarys scalability in a number of real-world scenarios.

A better consistency for low-order stabilized finite element methods

Abstract The standard implementation of stabilized finite element methods with a piece-wise function space of order lower than the highest derivative present in the partial differential equation often suffers from a weak consistency that can lead to reduced accuracy. The popularity of these low-order elements motivates the development of a new stabilization operator which globally reconstructs the derivatives not present in the local element function space. This new method is seen to engender a stronger consistency leading to better convergence and improved accuracy. Applications to the Navier—Stokes equations are given which illustrate the improvement at a negligible additional cost.

A stabilized finite element method for computing turbulence

Abstract For many flows, Reynold-averaged Navier—Stokes simulation (RANSS) techniques do not give an acceptable description of the flow. In these cases a more detailed simulation of the turbulence is required. One such detailed simulation technique, large-eddy simulation (LES) has matured to the point of application to complex flows. Historically, these simulations have been carried out with structured grids which suffer from two major difficulties: the extension to higher Reynolds numbers leads to an impractical number of grid points, and most real world flows are rather difficult to represent geometrically with structured grids. Unstructured-grid methods offer a release from both of these constraints. Herein, we describe the development and validation of a massively parallel, stabilized finite element method for LES.

Three-dimensional interactions between a finite-span synthetic jet and a crossflow

A complementary experimental and numerical investigation was performed to study the three-dimensional flow structures and interactions of a finite-span synthetic jet in a crossflow at a chord-based Reynolds number of 100,000 and a 0° angle of attack. Six blowing ratios in the range of 0.2–1.2 were considered. Experiments were conducted on a finite wing with a cross-sectional profile of NACA 4421, where particle-image velocimetry data were collected at the centre jet. To complement the experiments, three-dimensional numerical simulations were performed, where the numerical set-up matched not only the physical parameters (e.g. free stream) but also the physical dimensions (e.g. orientation and location of the jet. For the low blowing ratio cases, spatial non-uniformities developed, due to the finite span of the slit, which led to the formation of small and organized secondary structures or a streak-like pattern in the mean flow. On the other hand, for the high blowing ratio range, turbulent vortical structures were dominant, leading to larger spanwise structures, with a larger spanwise wavelength. Moreover, the phase-locked flow fields exhibited a train of counter-rotating coherent vortices that lifted off the surface as they advected downstream. In the mid-blowing ratio range, combined features of the low range (near the slit) and high range (in downstream locations) were found, where a pair of counter-rotating vortices issued in the same jet cycle collided with each other. In all cases, the spanwise extent of the secondary coherent structures reduced with downstream distance with a larger decrease at higher blowing ratios. Similar observations were made in earlier studies on finite-span synthetic jets in quiescent conditions.