Brian T. Helenbrook

Bio: Brian T. Helenbrook is an academic researcher from Clarkson University. The author has contributed to research in topics: Multigrid method & Finite element method. The author has an hindex of 19, co-authored 96 publications receiving 1548 citations. Previous affiliations of Brian T. Helenbrook include Varian Semiconductor & Princeton University.

Mesh deformation using the biharmonic operator

Abstract: The use of the biharmonic operator for deforming a mesh in an arbitrary-Lagrangian-Eulerian simulation is investigated. The biharmonic operator has the advantage that two conditions can be specified on each boundary of the mesh. This allows both the position and the normal mesh spacing along a boundary to be controlled, which is important for two-fluid interfaces and periodic boundaries. At these boundaries, we can simultaneously fix the position of the boundary and ensure that the normal mesh spacing is continuous across the boundary. In addition, results for deforming surfaces show that greater surface deformation can be tolerated when using biharmonic equations compared to approaches using second-order partial differential equations. A final advantage is that with the biharmonic operator, the integrity of a grid in a moving boundary layer can be preserved as the boundary moves. The main disadvantage of the approach is its increased computational expense.

Testing of an automobile exhaust thermoelectric generator in a light truck

Abstract: Testing was conducted on a prototype automobile exhaust thermoelectric generator (AETEG) installed in a 1999 GMC Sierra pick-up truck. The system consisted of the generator, its power conditioning unit, and the interfaces to the test truck's engine coolant and exhaust systems. The objective of the test was to measure the AETEG's performance and its effect on the truck systems as well as to determine which factors are important for optimizing an AETEG design. Testing was performed in a dynamometer-equipped wind tunnel at Delphi Corporation's Harrison Thermal Systems Division in Lockport, New York. The first tests established the benchmark data set. Then the prototype AETEG was installed and three configurations of the system were tested in succession: the AETEG alone, the AETEG with portions of the exhaust pipes leading to it insulated, and the AETEG with insulated upstream exhaust pipes and with a pre-cooling heat exchanger operating to lower the inlet coolant temperature to the generator. Some of the important outcomes of the tests were: insulating the exhaust and lowering the coolant temperature had a significant positive effect on the power, parasitic losses resulting from the AETEG weight and the coolant pumping power were significant but manageable, and the increased exhaust flow resistance and the additional heat load from the AETEG were not significant effects.

Analysis of ``p''-Multigrid for Continuous and Discontinuous Finite Element Discretizations

Abstract: Analysis and numerical experiments examining the behavior and performance of p-multigrid (p = polynomial degree) for solving hp-finite element (FEM) discretizations are presented. We begin by demonstrating the mesh and order independent properties of p-multigrid when used to solve a C0 continuous FEM discretization of the Laplace equation. We then apply pmultigrid to both continuous and discontinuous FEM discretizations of the convection equation. Although 1D Fourier analysis predicts that mesh independent results should be possible for both discretizations, in 2D the results are sensitive to both the mesh resolution and the degree of polynomial approximation. Examining the solutions, we find that for both discretizations, the slowest converging mode is long-wavelength along the streamwise direction and short wavelength normal to this direction. Because of the isotropic coarsening of p-multigrid, this mode is not damped on coarse levels.

Dynamics and stability of thin liquid films

Abstract: The dynamics and stability of thin liquid films have fascinated scientists over many decades: the observations of regular wave patterns in film flows down a windowpane or along guttering, the patterning of dewetting droplets, and the fingering of viscous flows down a slope are all examples that are familiar in daily life. Thin film flows occur over a wide range of length scales and are central to numerous areas of engineering, geophysics, and biophysics; these include nanofluidics and microfluidics, coating flows, intensive processing, lava flows, dynamics of continental ice sheets, tear-film rupture, and surfactant replacement therapy. These flows have attracted considerable attention in the literature, which have resulted in many significant developments in experimental, analytical, and numerical research in this area. These include advances in understanding dewetting, thermocapillary- and surfactant-driven films, falling films and films flowing over structured, compliant, and rapidly rotating substrates, and evaporating films as well as those manipulated via use of electric fields to produce nanoscale patterns. These developments are reviewed in this paper and open problems and exciting research avenues in this thriving area of fluid mechanics are also highlighted.

Arbitrary Lagrangian–Eulerian Methods

Abstract: The aim of the present chapter is to provide an in-depth survey of arbitrary Lagrangian–Eulerian (ALE) methods, including both conceptual aspects of the mixed kinematical description and numerical implementation details. Applications are discussed in fluid dynamics, nonlinear solid mechanics and coupled problems describing fluid–structure interaction. The need for an adequate mesh-update strategy is underlined, and various automatic mesh-displacement prescription algorithms are reviewed. This includes mesh-regularization methods essentially based on geometrical concepts, as well as mesh-adaptation techniques aimed at optimizing the computational mesh according to some error indicator. Emphasis is then placed on particular issues related to the modeling of compressible and incompressible flow and nonlinear solid mechanics problems. This includes the treatment of convective terms in the conservation equations for mass, momentum, and energy, as well as a discussion of stress-update procedures for materials with history-dependent constitutive behavior. Keywords: ALE description; convective transport; finite elements; stabilization techniques; mesh regularization and adaptation; fluid dynamics; nonlinear solid mechanics; stress-update procedures; fluid–structure interaction