Applications of Optimal Transportation in the Natural Sciences

The aim of this workshop was to gather a mixed group of experts and young researchers from different areas of applied mathematics in which optimal transport plays a central role. Applications in one of the classical areas of natural sciences, like physics, chemistry and (mathematical) biology were the main focus of the workshop

The 1982 NASA/ASEE Summer Faculty Fellowship Program

A NASA/ASEE Summer Faculty Fellowship Research Program was conducted to further the professional knowledge of qualified engineering and science faculty members, to stimulate an exchange of ideas between participants and NASA, to enrich and refresh the research and teaching activities of participants' institutions, and to contribute to the research objectives of the NASA Centers

Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference

The 6th ECCOMAS Young Investigators Conference YIC2021 will take place from July 7th through 9th, 2021 at Universitat Politècnica de València, Spain. The main objective is to bring together in a relaxed environment young students, researchers and professors from all areas related with computational science and engineering, as in the previous YIC conferences series organized under the auspices of the European Community on Computational Methods in Applied Sciences (ECCOMAS). Participation of senior scientists sharing their knowledge and experience is thus critical for this event.YIC 2021 is organized at Universitat Politécnica de València by the Sociedad Española de Métodos Numéricos en Ingeniería (SEMNI) and the Sociedad Española de Matemática Aplicada (SEMA). It is promoted by the ECCOMAS.The main goal of the YIC 2021 conference is to provide a forum for presenting and discussing the current state-of-the-art achievements on Computational Methods and Applied Sciences,including theoretical models, numerical methods, algorithmic strategies and challenging engineering applications.Nadal Soriano, E.; Rodrigo Cardiel, C.; Martínez Casas, J. (2022). Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. https://doi.org/10.4995/YIC2021.2021.15320EDITORIA

Efficient upwind algorithms for solution of the Euler and Navier-stokes equations

An efficient three-dimensionasl tructured solver for the Euler and Navier-Stokese quations is developed based on a finite volume upwind algorithm using Roe fluxes. Multigrid and optimal smoothing multi-stage time stepping accelerate convergence. The accuracy of the new solver is demonstrated for inviscid flows in the range 0.675 :5M :5 25. A comparative grid convergence study for transonic turbulent flow about a wing is conducted with the present solver and a scalar dissipation central difference industrial design solver. The upwind solver demonstrates faster grid convergence than the central scheme, producing more consistent estimates of lift, drag and boundary layer parameters. In transonic viscous computations, the upwind scheme with convergence acceleration is over 20 times more efficient than without it. The ability of the upwind solver to compute viscous flows of comparable accuracy to scalar dissipation central schemes on grids of one-quarter the density make it a more accurate, cost effective alternative. In addition, an original convergencea cceleration method termed shock acceleration is proposed. The method is designed to reduce the errors caused by the shock wave singularity M -+ 1, based on a localized treatment of discontinuities. Acceleration models are formulated for an inhomogeneous PDE in one variable. Results for the Roe and Engquist-Osher schemes demonstrate an order of magnitude improvement in the rate of convergence. One of the acceleration models is extended to the quasi one-dimensiona Euler equations for duct flow. Results for this case d monstrate a marked increase in convergence with negligible loss in accuracy when the acceleration procedure is applied after the shock has settled in its final cell. Typically, the method saves up to 60% in computational expense. Significantly, the performance gain is entirely at the expense of the error modes associated with discrete shock structure. In view of the success achieved, further development of the method is proposed

An exact analysis of two-dimensional radiative transfer in an absorbing and emitting gray medium

The exact formulations for the radiative flux and the emissive power are presented for a two-dimensional, finite, planar, absorbing and emitting, gray medium in radiative equilibrium. Exact expressions are obtained for the medium subjected to the following types of boundary conditions: (1) cosine varying diffuse, (2) cosine varying collimated, (3) constant temperature strip, and (4) the strip illuminated by a uniform collimated flux. The solutions for the physically unrealistic cosine varying models are used to construct the solutions for the more practical finite strip models. The two-dimensional equations are reduced to one-dimensional equations by the method of separation of variables. This simplification is made possible by the cosine form of the boundary radiation. The corresponding equations for the semi-infinite medium are obtained from the equations for the finite optical thick medium by letting the optical thickness become infinite. The reduced one-dimensional equations are then solved exactly by techniques from one-dimensional radiative theory for the emissive power and radiative flux at the boundaries for both the finite and semi-infinite models. A wide range of exact numerical data is presented. The cosine varying collimated boundary condition generates functions which are analogous to the one-dimensional X- and Y-functions of Chandrasekhar for the finite model and the H-function of Chandrasekhar for the semi-infinite model. These generalized functions represent the dimensionless emissive power at the boundaries and appear in the radiative flux and emissive power at the boundaries for the cosine varying diffuse model as well as for both finite strip models. The generalized H-, X- and Y-functions are tabulated exactly for a wide range of numerical values. In addition to the generalized H-, X- and Y-functions, a function analogous to the exponential integral function is introduced. Generalized exponential integral functions of the first, second, and third order are defined and the recurrence formulas and series expansions are developed. The generalized exponential integral functions are tabulated for a wide range of numerical values --Abstract, pages ii-iii

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described