Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume comprises the second part of the proceedings of the 10th International Conference on Finite Volumes for Complex Applications, FVCA, held in Strasbourg, France, during October 30 to November 3, 2023. The Finite Volume method, and several of its variants, is a spatial discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods are also built to preserve some properties of the continuous equations, including maximum principles, dissipativity, monotone decay of the free energy, asymptotic stability, or stationary solutions. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. In recent years, the efficient implementation of these methods in numerical software packages, more specifically to be used in supercomputers, has drawn some attention. The first volume contains all invited papers, as well as the contributed papers focusing on finite volume schemes for elliptic and parabolic problems. They include structure-preserving schemes, convergence proofs, and error estimates for problems governed by elliptic and parabolic partial differential equations. This volume is focused on finite volume methods for hyperbolic and related problems, such as methods compatible with the low Mach number limit or able to exactly preserve steady solutions, the development and analysis of high order methods, or the discretization of kinetic equations.

Mathematics. --- Engineering mathematics. --- Engineering --- Mathematical and Computational Engineering Applications. --- Data processing. --- Finite volume method.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

We hope that among these chapters you will find a topic which will raise your interest and engage you to further investigate a problem and build on the presented work. This book could serve either as a textbook or as a practical guide. It includes a wide variety of concepts in FVM, result of the efforts of scientists from all over the world. However, just to help you, all book chapters are systemized in three general groups: New techniques and algorithms in FVM; Solution of particular problems through FVM and Application of FVM in medicine and engineering. This book is for everyone who wants to grow, to improve and to investigate.

Engineering design. --- Finite volume method. --- Numerical analysis --- Design, Engineering --- Engineering --- Industrial design --- Strains and stresses --- Design --- Computer modelling & simulation

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Phase change materials (PCMs) are of high interest in thermal storage and thermal management applications for the earth and for space environments. Nevertheless, their functionality is intrinsically attached to phase change processes, which, from experience, it is known that they are computationally challenging. The present project arises with the intention to give a numerical solution to this problematic.

A solver based on the enthalpy-porosity technique, capable to deal with diffusive-convective phase change has been adapted for OpenFOAM 4.1. For the implementation of the enthalpy technique, the work of Voller Mushy has been closely followed, and a detailed explanation of the equations employed and the assumptions that support them is given. Furthermore, the numerical approach is also specified, with a close attention to the discretization process based on the Finite Volume Method (FVM). The solver algorithm is provided with a deep explanation of its implementation in OpenFOAM. Furthermore, an analysis of the convergence of the numerical solution is provided.

Moreover, the works of several authors, have been employed to help in some aspects of the implementation and validation of the solver. As part of this validation, the controversial case of the melting of pure Gallium in a rectangular cavity is computed with the OpenFOAM solver. The author gives some discussion about the results obtained and compares them with the existing literature in order to assess the accuracy of the mathematical model employed.

The last part of the project employs the customize solver to analyze the thermal behaviour of a PCM during melting. Three different cases are proposed and tested for two different geometries: one under gravity conditions, where natural convection is part of the heat transfer process, and another two independent of gravity or proper of micro-gravity environments: a pure conductive case and a case with Bénard-Marangoni convection.

Enthalpy-porosity technique --- OpenFOAM solver --- Finite Volume Method --- PCMs --- Marangoni Convection --- Melting of Gallium --- Ingénierie, informatique & technologie > Ingénierie aérospatiale

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Finite volume method. --- Meshfree methods (Numerical analysis) --- Gridless methods (Numerical analysis) --- Meshfree discretization techniques (Numerical analysis) --- Meshless methods (Numerical analysis) --- Numerical analysis

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book on numerical methods for singular perturbation problems - in particular, stationary reaction-convection-diffusion problems exhibiting layer behaviour is devoted to the construction and analysis of layer-adapted meshes underlying these numerical methods. A classification and a survey of layer-adapted meshes for reaction-convection-diffusion problems are included. This structured and comprehensive account of current ideas in the numerical analysis for various methods on layer-adapted meshes is addressed to researchers in finite element theory and perturbation problems. Finite differences, finite elements and finite volumes are all covered.

Reaction-diffusion equations --- Finite volume method --- Mathematics --- Engineering & Applied Sciences --- Applied Mathematics --- Calculus --- Mathematical Theory --- Physical Sciences & Mathematics --- Reaction-diffusion equations. --- Finite volume method. --- Diffusion-reaction equations --- Equations, Reaction-diffusion --- Mathematics. --- Differential equations. --- Partial differential equations. --- Numerical analysis. --- Numerical Analysis. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Mathematical analysis --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Math --- Science --- Numerical analysis --- Differential equations, Parabolic --- Differential Equations. --- Differential equations, partial.