George Green Medal 2024

George Green MedalThe George Green Medal was established by the University of Mississippi at Oxford, Mississippi, USA, and the Wessex Institute and is supported by Elsevier. It is in honour of the man who single-handedly set up the basis for the modern Boundary Element Method, among other notable achievements.

 

The Medal is awarded to those scientists who have carried out original work with practical applications in the field of Boundary Elements and other Mesh Reduction Methods, continuing in this manner to further develop the pioneering ideas of George Green. They are also persons of the highest integrity who, by sharing their knowledge, have helped to establish research groups all around the world. The Medal is given once a year and is presented during the BEM/MRM Conference.

George Green (1793-1841)

George Green was a self-taught genius who mysteriously delivered one of the most influential mathematics and physics works of all time. He educated himself in mathematics and self-published the work “An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism”. In his very first article, he derived Green’s first, second and third identities, forged the concept of Green’s function, and solved the problem of the electrical potential created by a single charge placed inside a spherical metal shell. The ideas of Green’s function forever changed the landscape of science, as many physics and mathematics problems have been solved using this technique. As Green died early, and his work was discovered only posthumously, it remains a mystery today how Green could produce such a masterpiece without the guidance of a great teacher or school and, in fact, without a formal education. Only recently, due to the advent of powerful computers, has it been possible to take full advantage of Green’s pioneering developments.

The George Green Medal 2024 will be presented on the occasion of the 47th International Conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM 47). The ceremony will take place during a special session, followed by a keynote address from the medal recipient, see below for details of the presentation. The exact date and time of the ceremony will be confirmed at a later stage.

2024 George Green Medal Recipient

Leopold Škerget, Ph.D., Professor Emeritus at the University of Maribor, Slovenia

Leopold Skerget

Leopold Škerget was a full professor at the Faculty of Mechanical Engineering at the University of Maribor, Slovenia, teaching courses in fluid mechanics, computational fluid dynamics, and transport phenomena. He also served as a professor of fluid mechanics at the Faculty of Mechanical Engineering at the University of Ljubljana, Slovenia, and as a professor at the Wessex Institute of Technology, Southampton, UK.

He was the vice-dean for research at the Faculty of Mechanical Engineering at the University of Maribor, head of the Department and Institute of Energy, Process, and Environmental Engineering, scientific advisor at the Turboinstitute, Ljubljana, National Coordinator of Slovenia for the field of mechanics and process engineering. He was a recipient of the prestigious Alexander von Humboldt Foundation scholarship and DAAD scholarship, Germany, as well as the Eminent Scientist Medal of Wessex Institute, Southampton, and the Zois Award for outstanding scientific achievements in the field of process and environmental engineering, Slovenia. He is one of the editors of the international journal Engineering Analysis with Boundary Elements.

He worked in the field of energy, process, and environmental engineering with a focus on numerical modeling and simulation of transport phenomena in solids and fluids. His research focused on the development and application of numerical approximation methods - computational fluid dynamics, e.g. finite element method (FEM) and boundary element method (BEM), for solving transport phenomena of laminar and turbulent fluid flow in machinery, devices, and environmental systems. As a visiting professor, he recently collaborated with the ITECONS Research Institute and the University of Coimbra, Portugal, on the development and application of reliable numerical tools for addressing nonlinear coupled problems of heat, moisture, and air transfer through porous multilayered building structures and green facades and roofs.

Leopold Škerget has published 183 scientific articles, authored 3 books and 12 chapters in scientific monographs, and delivered 30 invited lectures. He has led and participated in numerous research projects for industry.

Keynote Presentation

Green’s functions in the boundary element method for fluid dynamics

Abstract

The Navier-Stokes equations (NSEs) represent a dynamical system of coupled nonlinear partial differential equations (PDEs) that govern the general laminar and turbulent motion of a viscous compressible fluid. It is a mathematical model of the physical conservation laws of mass, momentum and energy for a control volume. The occurrence of small structures in turbulent flows prevents direct numerical simulation (DNS) of leading NSEs for general flow cases. Therefore, much attention is paid to simplified time-averaged governing equations, known as Reynolds-averaged Navier-Stokes equations (RANS) or large-eddy simulation (LES), in which the large-scale turbulent structures are explicitly captured by a numerical discretization model, while the effect of the structures is modeled at a small subgrid scale. The governing equations of transport phenomena in a fluid flow are generally diffusion-convection PDEs, the characteristics of which vary greatly from point to point in the flow domain due to the local values of the Reynolds or Peclet numbers, which physically represent the relationship between diffusion and convection. Consequently, the equations cannot be considered pure elliptic, parabolic, or hyperbolic, as they are of mixed type. Navier-Stokes equations can be written for primitive variables or for derivative ones. In particular, the velocity and vorticity variables approach has certain advantages when using the numerical boundary element method (BEM). The advantage of the formulation lies in the numerical separation of the kinematics and flow kinetics from the pressure calculation. For general viscous flow, the flow kinetics is given by a strongly nonlinear parabolic diffusion-convective vorticity PDE, whose physical-mathematical characteristics are successfully captured using diffusion or diffusion-convective Green’s functions. The kinematics of the fluid flow is governed by the elliptic Biot-Savart integral representation. Depending on the nature of the equation, there are various Green’s functions that cover the majority of transport phenomena, e.g. accumulation, diffusion, or both processes, namely diffusion and convection, resulting in different numerical solution schemes in terms of stability and accuracy. Since Green’s functions take into account only the linear part of the transport phenomenon, the physically based choice of the linear differential operator is essential for establishing a stable and accurate singular integral representation of the original differential transport equations.

Boundary-domain integral representations are usually developed from NSEs by the weighted residual technique or by using Green’s integral theorems. The corresponding algebraic equations obtained by discretizing the integral equations are relatively well-ordered matrix equations suitable for computer solution. The size of the matrices and the amount of computation required to solve these equations are generally considerable. This fact is due to the presence of different flow components with different length scales. In particular, the thickness of the boundary layer flow component is inversely proportional to the square root of the value of the flow Reynolds number. The discrete viscous parts of the flow domain, including the recirculation region and vortex wake, have length scales comparable to the characteristic length of the problem. The potential or irrotational part of the flow, which exists together with the viscous or rotational part of the external flow, has a length scale of infinity. Since the kinematic calculation of the velocity field can be restricted to the vorticity region only, the numerical solution can be restricted to the viscous region only.

Numerical solution of integral equations requires spatial and temporal discretization. A high-order spatial discretization is adopted, associated with a high-degree polynomial, which is used to approximate the solution. Complete Lagrangian 4-node continuous cubic boundary elements and complete Lagrangian 16-node continuous cubic interior cells are used. Time discretization is based on the constant variation of all field functions in a single time increment. A macroelement is used, resulting in sparse and diagonal block influence matrices similar to those in finite element (FEM) and finite volume (FVM) numerical methods.

Previous Laureates

Details of the previous George Green Medal presentations can be found in the conference reports listed below:

For further information about the George Green Medal please contact:

George Green Medal
Wessex Institute
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