The finite volume method in its various variants is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation. It has been used successfully in many applications including fluid dynamics, magnetohydrodynamics, structural analysis, nuclear physics, and semiconductor theory. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties including maximum principles, dissipativity, monotone decay of the free energy, or asymptotic stability.
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.
The goal of the symposium is to bring together mathematicians, physicists, and engineers interested in physically motivated discretizations. Contributions to the further advancement of the theoretical understanding of suitable finite volume, finite element, discontinuous Galerkin and other discretization schemes, and the exploration of new application fields for them are welcome.
- Preservation of physical properties on the discrete level
- Physically consistent coupling between discretizations for different processes
- Convergence, stability, and error analysis
- Connections to other discretization methods
- Relationship between grids and discretization schemes
- Complex geometries and adaptivity
- Shock waves and other flow discontinuities
- New and existing schemes and their limitations
- Bottlenecks in the solution of large scale problems
- Atmosphere and ocean modeling
- Chemical engineering and combustion
- Energy generation and storage
- Semiconductors and electrochemistry
- Porous media