Extended Finite Volumes
Alfio Grillo (Politecnico di Torino, Italy)
Arne Nägel (Goethe Universität Frankfurt, Germany)
Gillian Queisser (Goethe Universität Frankfurt, Germany)
Gabriel Wittum (Goethe Universität Frankfurt, Germany)
Besides the extended finite element methods (X-FEM), extended discretizations are heavily used in connection with finite volume methods (X-FV). The proposed mini-symposium focuses on these methods, used particularly in Environmental Science and Computational Neuroscience.
Environmental Science: A leading subject involves the study of fluid flow and transport processes in hydrogeological porous media. Especially when the geometry and heterogeneity of computational domains reduce the efficiency of standard numerical methods, computational strategies should be developed to solve the large, highly non-linear, coupled partial differential equations modeling groundwater motion and heat and pollutant transport. Treatment of free surfaces, caused e.g. by rain, requires extended discretization schemes. Other applications are particulate flows with floating particles inside the fluid.
Computational Neuroscience: Topical subjects are the characterization of synaptic boutons, and the propagation of electrochemical signals in neurons. Extended Discretization Methods and faithful reconstructions of the geometry of nerve cells and synaptic regions allow for visualizing the phenomena occurring in the nervous system. This is the case for boutons, since their morphology influences their functionality, and nerve fibers, since their structure affects the propagation of signals throughout them. Moreover, particulate flows play a crucial role when treating vesicles floating in synaptic boutons with detailed resolution.
