Proceedings, MSVSCC 2015

The Virginia Modeling, Analysis and Simulation Center (VMASC) of Old Dominion University hosted the 2015 Modeling, Simulation, & Visualization Student capstone Conference on April 16th. The Capstone Conference features students in Modeling and Simulation, undergraduates and graduate degree programs, and fields from many colleges and/or universities. Students present their research to an audience of fellow students, faculty, judges, and other distinguished guests. For the students, these presentations afford them the opportunity to impart their innovative research to members of the M&S community from academic, industry, and government backgrounds. Also participating in the conference are faculty and judges who have volunteered their time to impart direct support to their students’ research, facilitate the various conference tracks, serve as judges for each of the tracks, and provide overall assistance to this conference. 2015 marks the ninth year of the VMASC Capstone Conference for Modeling, Simulation and Visualization. This year our conference attracted a number of fine student written papers and presentations, resulting in a total of 51 research works that were presented. This year’s conference had record attendance thanks to the support from the various different departments at Old Dominion University, other local Universities, and the United States Military Academy, at West Point. We greatly appreciated all of the work and energy that has gone into this year’s conference, it truly was a highly collaborative effort that has resulted in a very successful symposium for the M&S community and all of those involved. Below you will find a brief summary of the best papers and best presentations with some simple statistics of the overall conference contribution. Followed by that is a table of contents that breaks down by conference track category with a copy of each included body of work. Thank you again for your time and your contribution as this conference is designed to continuously evolve and adapt to better suit the authors and M&S supporters. Dr.Yuzhong Shen Graduate Program Director, MSVE Capstone Conference Chair John ShullGraduate Student, MSVE Capstone Conference Student Chai

Proceedings, MSVSCC 2016

Proceedings of the 10th Annual Modeling, Simulation & Visualization Student Capstone Conference held on April 14, 2016 at VMASC in Suffolk, Virginia

Ahlfors circle maps and total reality: from Riemann to Rohlin

This is a prejudiced survey on the Ahlfors (extremal) function and the weaker {\it circle maps} (Garabedian-Schiffer's translation of "Kreisabbildung"), i.e. those (branched) maps effecting the conformal representation upon the disc of a {\it compact bordered Riemann surface}. The theory in question has some well-known intersection with real algebraic geometry, especially Klein's ortho-symmetric curves via the paradigm of {\it total reality}. This leads to a gallery of pictures quite pleasant to visit of which we have attempted to trace the simplest representatives. This drifted us toward some electrodynamic motions along real circuits of dividing curves perhaps reminiscent of Kepler's planetary motions along ellipses. The ultimate origin of circle maps is of course to be traced back to Riemann's Thesis 1851 as well as his 1857 Nachlass. Apart from an abrupt claim by Teichm\"uller 1941 that everything is to be found in Klein (what we failed to assess on printed evidence), the pivotal contribution belongs to Ahlfors 1950 supplying an existence-proof of circle maps, as well as an analysis of an allied function-theoretic extremal problem. Works by Yamada 1978--2001, Gouma 1998 and Coppens 2011 suggest sharper degree controls than available in Ahlfors' era. Accordingly, our partisan belief is that much remains to be clarified regarding the foundation and optimal control of Ahlfors circle maps. The game of sharp estimation may look narrow-minded "Absch\"atzungsmathematik" alike, yet the philosophical outcome is as usual to contemplate how conformal and algebraic geometry are fighting together for the soul of Riemann surfaces. A second part explores the connection with Hilbert's 16th as envisioned by Rohlin 1978.Comment: 675 pages, 199 figures; extended version of the former text (v.1) by including now Rohlin's theory (v.2

Meshless methods for Maxwell’s equations with applications to magnetotelluric modelling and inversion

The first part of thesis presents new meshless methods for solving time harmonic electromagnetic fields in closed two- or three-dimensional volumes containing heterogeneous materials. This new methods will be used to simulate magnetotelluric experiments, when an Earth conductivity model is given in advanced. Normally, classical approximation methods like finite elements or finite differences are used to solve this task. The algorithms here in this thesis, only need an unstructured point sampling in the modelling domain for the discretization and is able to gain a solution for the partial differential equation without a fixed mesh or grid. This is advantageous when complex model geometries have to be described, because no adapted mesh or grid need to be generated. The meshless methods, described here in this thesis, use a direct discretization technique in combination with a generalized approximation method. This allows to formulate the partial differential equations in terms of linear functionals, which can be approximated and directly form the discretization. For the two-dimensional magnetotelluric problem, a second-order accurate algorithm to solve the partial differential equations was developed and tested with several example calculations. The accuracy of the new meshless methods was compared to analytical solutions, and it was found, that a better accuracy can be achieved with less degrees of freedoms compared to previously published results. For the three-dimensional case, a meshless formulation was given and numerical calculations show the ability of the scheme to handle models with heterogeneous conductivity structures. In the second part of this thesis, the newly developed two-dimensional simulation method will be used in an inversion scheme. Here, the task is to recover the unknown Earth conductivity model with the help of data gained from a magnetotelluric experiment. Due to the previously developed meshless approximation algorithm, some numerical tasks during the inversion can be simplified by reusing the discretization defined on the point sampling from the forward simulation. The newly developed meshless inversion algorithm will be tested with synthetic data to reconstruct known conductivity anomalies. It can be shown, that the inverse algorithm produces correct results, even in the presence of topography

Software for Exascale Computing - SPPEXA 2016-2019

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest

The Fifth Symposium on Numerical and Physical Aspects of Aerodynamic Flows

This volume contains the papers presented at the Fifth Symposium on Numerical and Physical Aspects of Aerodynamic Flows, held at the California State University, Long Beach, from 13 to 15 January 1992. The symposium, like its immediate predecessors, considers the calculation of flows of relevance to aircraft, ships, and missiles with emphasis on the solution of two-dimensional unsteady and three-dimensional equations

Immersed boundary method for cavitating and biological flows

The aim of the present work is the development of a computational tool to ease the numerical simulation of cavitating flows in domains of complex topology or with arbitrary moving boundaries. Within the framework of Computational Fluid Dynamics(CFD), an Immersed Boundary (IB) Method has been developed. According to the IB methodology, the grid that discretises the computational domain does not need to conform to the geometry and the solid boundaries are modelled on a fixed canonical grid by alternations of the governing equations in their vicinity. This modelling strategy is beneficial in terms of both computational cost and numerical solution. The grid generation, which is a complex and time consuming process, is simplified as a regular canonical grid, non-conformal to the boundaries, can be used. In addition, when moving boundaries are present, a conformal grid would need to adapt or deform following the motion of boundaries, which would increase the computational cost of the simulations in the first case and affect the solution in the latter case; the use of IB method alleviates these issues. The developed method follows the direct-forcing approach, which simply adds to the governing equations a source term to account for the body force acting on the fluid. The simplicity of the method makes it suitable for complex flow regimes, including phase change, strong shocks and compressibility effects, as well as Fluid Structure Interaction (FSI). Since cavitation dynamics regard a wide range of applications of engineering interest, from hydraulic machines to novel therapeutic techniques, the method is designed to be applicable in a wide range of flow regimes. Turbulent modelling and flow induced motion has been taken into account. The method has been successfully applied to cavitating and incompressible cases where conventional techniques are not easily or at all applicable. The shock-wave interaction with material interfaces is studied via the high-speed impact of a solid projectile on a water jet, which has been studied only experimentally before and only qualitative observations existed. The numerical investigation with the proposed methodology unveiled rich information regarding the physics of the impact, the resulting shock formation, cavitation development and interface instabilities initiation. Moreover, the methodology was applied on the thoroughly studied pulsatile flow through a bi leaflet Mechanical Heart Valve, to provide additional information regarding shear stress development. The methodology aids an experimental campaign employing novel shear stress measuring techniques, carried out by our collaborators. The research work and the developed method described in the present Thesis, intend to set the foundations for more elaborate numerical investigations of highly complex problems of Fluid Dynamics