Spectral/hp element methods: recent developments, applications, and perspectives

The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate C0-continuous expansions. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed

The Appearance of Endothelium in Small Arteries After Treatment with 5-Fluorouracil. An Electron Microscopic Study of Late Effects in Rabbits

Cardiotoxicity is an unexplained toxic manifestation of 5-fluorouracil (5-FU). Its possible mechanism could be a direct cytotoxic effect on the vascular endothelium. We have tested this hypothesis in an experimental study in rabbits, using scanning and transmission electron microscopic evaluation of endothelium in small arteries (the central artery of the ear). The perfusion fixation method at physiological pressure and temperature was used. Both local and systemic effects of 5-FU on endothelium were studied 1, 3, 7, 14 and 30 days after in vivo treatment with 5-FU. Fifteen rabbits were used and five additional animals served as controls. The following parameters were evaluated: vessel wall and endothelial cell contraction, cell oedema, cytolysis, occurrence of denuded areas, platelet adhesion/aggregation and fibrin formation. For the description of each parameter, a scale of negative points (0.0-3.0) was used. We found severe cell damage with accompanying thrombus formation. The findings support the hypothesis that the thrombogenic effect of 5-FU, secondary to its direct cytotoxic effect on endothelium, is the pathophysiological mechanism behind 5-FU cardiotoxicity

The Influence of 5-Fluorouracil on the Endothelium in Small Arteries. An Electron Microscopic Study in Rabbits

5-Fluorouracil (5-FU) is a widely used antineoplastic agent. 5-FU induced cardiotoxicity is a still relatively unknown side-effect of this drug. This phenomenon could be due to a direct cytotoxic effect on the endothelial cells. We tested this hypothesis in an experimental study in rabbits, by scanning or transmission electron microscopic evaluation of endothelium in small arteries (the central artery of the ear) after in vivo treatment with 5-FU. Both local and systemic effects of 5-FU on endothelium were studied 15, 30, 60 and 120 minutes after intra-arterial or intraperitoneal treatment. Perfusion fixation at physiological pressure and temperature was used in order to minimize damage to the endothelium during the preparation procedure. Eighteen rabbits weighing 2.5-3.0 kg were used, and 6 animals served as controls. The following parameters were evaluated: vessel wall and endothelial cell contraction, cell edema, cytolysis, occurrence of denuded areas, platelet adhesion/aggregation and fibrin formation. For the description of each parameter a scale of negative points was used. Irreversible cell damage was observed in 5-FU treated animals: disruption of the endothelial sheet and patchy exposure of the subendothelium, sometimes as a focus for thrombus formation. Our findings support the hypothesis that the thrombogenic effect of 5-FU secondary to its direct cytotoxic effect on endothelium might be one of the pathophysiological mechanisms behind 5-FU induced cardiotoxicity

A Blind Comparative Study of Focused Wave Interactions with a Fixed FPSO-like Structure (CCP-WSI Blind Test Series 1)

Results from Blind Test Series 1, part of the Collaborative ComputationalProject in Wave Structure Interaction (CCP-WSI), are presented. Partici-pants, with a range of numerical methods, simulate blindly the interactionbetween a fixed structure and focused waves ranging in steepness and di-rection. Numerical results are compared against corresponding physicaldata. The predictive capability of each method is assessed based on pres-sure and run-up measurements. In general, all methods perform well inthe cases considered, however, there is notable variation in the results(even between similar methods). Recommendations are made for appro-priate considerations and analysis in future comparative studies

Highly Accurate Experimental Heave Decay Tests with a Floating Sphere: A Public Benchmark Dataset for Model Validation of Fluid-Structure Interaction

Highly accurate and precise heave decay tests on a sphere with a diameter of 300 mm were completed in a meticulously designed test setup in the wave basin in the Ocean and Coastal Engineering Laboratory at Aalborg University, Denmark. The tests were dedicated to providing a rigorous benchmark dataset for numerical model validation. The sphere was ballasted to half submergence, thereby floating with the waterline at the equator when at rest in calm water. Heave decay tests were conducted, wherein the sphere was held stationary and dropped from three drop heights: a small drop height, which can be considered a linear case, a moderately nonlinear case, and a highly nonlinear case with a drop height from a position where the whole sphere was initially above the water. The precision of the heave decay time series was calculated from random and systematic standard uncertainties. At a 95% confidence level, uncertainties were found to be very low-on average only about 0.3% of the respective drop heights. Physical parameters of the test setup and associated uncertainties were quantified. A test case was formulated that closely represents the physical tests, enabling the reader to do his/her own numerical tests. The paper includes a comparison of the physical test results to the results from several independent numerical models based on linear potential flow, fully nonlinear potential flow, and the Reynolds-averaged Navier-Stokes (RANS) equations. A high correlation between physical and numerical test results is shown. The physical test results are very suitable for numerical model validation and are public as a benchmark dataset

A Comparative Study on the Nonlinear Interaction Between a Focusing Wave and Cylinder Using State-of-the-art Solvers: Part A

This paper presents ISOPE’s 2020 comparative study on the interaction between focused waves and a fixed cylinder. The paper discusses the qualitative and quantitative comparisons between 20 different numerical solvers from various universities across the world for a fixed cylinder. The moving cylinder cases are reported in a companion paper as part B (Agarwal, Saincher, et al., 2021). The numerical solvers presented in this paper are the recent state of the art in the field, mostly developed in-house by various academic institutes. The majority of the participants used hybrid modeling (i.e., a combination of potential flow and Navier–Stokes solvers). The qualitative comparisons based on the wave probe and pressure probe time histories and spectral components between laminar, turbulent, and potential flow solvers are presented in this paper. Furthermore, the quantitative error analyses based on the overall relative error in peak and phase shifts in the wave probe and pressure probe of all the 20 different solvers are reported. The quantitative errors with respect to different spectral component energy levels (i.e., in primary, sub-, and superharmonic regions) capturing capability are reported. Thus, the paper discusses the maximum, minimum, and median relative errors present in recent solvers as regards application to industrial problems rather than attempting to find the best solver. Furthermore, recommendations are drawn based on the analysis