Vasilios Alexiades

Bio: Vasilios Alexiades is an academic researcher from University of Tennessee. The author has contributed to research in topics: Boundary value problem & Stefan problem. The author has an hindex of 18, co-authored 67 publications receiving 1719 citations. Previous affiliations of Vasilios Alexiades include Union Carbide & Michigan Technological University.

Mathematical Modeling Of Melting And Freezing Processes

Abstract: This reference book presents mathematical models of melting and solidification processes thare are key to the effective performance of latent heat thermal energy storage systems (LHTES), utilized in a wide range of heat transfer and industrial applications. Especially timely, this topic has spurred a growth in research into LHTES applications in energy conservation and utilization, space station power systems, and thermal protection of electronic equipment in hostile environments. Further, interest in mathematical modeling has increased dramatically with the spread of high-powered computers used in most industrial and academic settings. In two sections, the book first describes modeling of phase change processes and then describes applications for LHTES.

Super-time-stepping acceleration of explicit schemes for parabolic problems

Abstract: The goal of the paper is to bring to the attention of the computational community a long overlooked, very simple, acceleration method that impressively speeds up explicit time-stepping schemes, at essentially no extra cost. The authors explain the basis of the method, namely stabilization via wisely chosen inner steps (stages), justify it for linear problems, and spell out how simple it is to incorporate in any explicit code for parabolic problems. Finally, we demonstrate its performance on the (linear) heat equation as well as on the (non-linear) classical Stefan problem, by comparing it with standard implicit schemes (employing SOR or Newton iterations). The results show that super-time-stepping is more efficient than the implicit schemes in that it runs at least as fast, it is of comparable or better accuracy, and it is, of course, much easier to program (and to parallelize for distributed computing).

Resolving the controversy over tin and gallium melting in a rectangular cavity heated from the side

Abstract: commonly accepted answer to the problem in the scientific community. In this work, we summarize earlier works and present a grid-refinement study for several discretization schemes with emphasis on tin melting and some results for gallium melting. Simulations are carried out with the enthalpy method. The flow cell structure is analyzed in detail, while some results are provided for the heat transfer and the melting rate. Our results show that the multicellular structure is the correct numerical solution and that the flow structure has a strong influence on other features of the solution. We also provide a detailed discussion of earlier results in order to clarify important issues and bring a final answer to the controversy.

The role of mass removal mechanisms in the onset of ns-laser induced plasma formation

Abstract: The present study focuses on the role of mass removal mechanisms in ns-laser ablation. A copper sample is placed in argon, initially set at standard pressure and temperature. Calculations are performed for a 6 ns laser pulse with a wavelength of 532 nm and laser fluences up to 10 J/cm2. The transient behavior in and above the copper target is described by a hydrodynamic model. Transmission profiles and ablation depths are compared with experimental results and similar trends are found. Our calculations reveal an interesting self-inhibiting mechanism: volumetric mass removal in the supercritical region triggers plasma shielding and therefore stops proceeding. This self-limiting process indicates that volumetric mass removal does not necessarily result in large ablation depths.

A reference solution for phase change with convection

Abstract: A reference solutions for phase change involving convection in the melt is currently missing. In the present study, we focus on the problem of melting of pure tin in a square cavity heated from the side, which is used as a benchmark test problem. The mathematical model used for the simulations is based on the enthalpy formulation. Extensive numerical computations are performed with grids as fine as 800 × 800. The convergence of the numerical solution is demonstrated and its level assessed. Data values and plots are provided for use as a reference solution. Copyright © 2005 John Wiley & Sons, Ltd.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Review on thermal energy storage with phase change materials and applications

Abstract: The use of a latent heat storage system using phase change materials (PCMs) is an effective way of storing thermal energy and has the advantages of high-energy storage density and the isothermal nature of the storage process. PCMs have been widely used in latent heat thermal-storage systems for heat pumps, solar engineering, and spacecraft thermal control applications. The uses of PCMs for heating and cooling applications for buildings have been investigated within the past decade. There are large numbers of PCMs that melt and solidify at a wide range of temperatures, making them attractive in a number of applications. This paper also summarizes the investigation and analysis of the available thermal energy storage systems incorporating PCMs for use in different applications.

PLUTO: A Numerical Code for Computational Astrophysics

Abstract: We present a new numerical code, PLUTO, for the solution of hypersonic flows in 1, 2, and 3 spatial dimensions and different systems of coordinates. The code provides a multiphysics, multialgorithm modular environment particularly oriented toward the treatment of astrophysical flows in presence of discontinuities. Different hydrodynamic modules and algorithms may be independently selected to properly describe Newtonian, relativistic, MHD, or relativistic MHD fluids. The modular structure exploits a general framework for integrating a system of conservation laws, built on modern Godunov-type shock-capturing schemes. Although a plethora of numerical methods has been successfully developed over the past two decades, the vast majority shares a common discretization recipe, involving three general steps: a piecewise polynomial reconstruction followed by the solution of Riemann problems at zone interfaces and a final evolution stage. We have checked and validated the code against several benchmarks available in literature. Test problems in 1, 2, and 3 dimensions are discussed.

Quasilinear elliptic-parabolic differential equations

Abstract: The structure conditions are the ellipticity of a and the (weak) monotonicity of b, and b has to be a subgradient in case m > 1. First we treat the case that b is continuous, and later (Sect. 4) we include Stefan problems, that is, we allow b to have jumps. The special cases of an elliptic equation with time as parameter, that is, b(z)= 0, and the standard parabolic equation, that is, b(z)=z are included. Some special single equations of mixed elliptic and parabolic type are given in the following. The gas flow through a porous medium is described by the equation