This volume collects the most important contributions from four minisymposia from ICIAM 2019. The papers highlight cutting-edge applications of Cartesian CFD methods and describe the employed algorithms and numerical schemes. An emphasis is laid on complex multi-physics applications like magnetohydrodynamics, combustion, aerodynamics with fluid-structure interaction, solved with various discretizations, e.g. finite difference, finite volume, multiresolution or lattice Boltzmann CFD schemes. Software design aspects and parallelization challenges are also considered. The book is addressed to graduate students and scientists in the fields of applied mathematics and computational engineering.

Ralf Deiterdingis currently Associate Professor in Fluid Dynamics at the University of Southampton. He graduated with a Master in Technomathematics from the Technical University of Clausthal and has obtained a PhD in Applied Mathematics and CFD from the Technical University Cottbus. His research focuses on the development and application of innovative high-resolution and multiscale simulation methods for CFD. He is the main author of the simulation frameworks AMROC and Virtual Test Facility.

Margarete Dominguesis senior researcher at the National Institute for Space Research (INPE), Brazil. She obtained her Master in Meteorology at INPE, and PhD degree in Applied Mathematics from the University of Campinas (UNICAMP), Brazil. Her research activities are focused on nonlinear analysis, multi-scale techniques and wavelets for scientific computing and their application to space flows and data, including space magnetohydrodynamics developments and multidimensional signal processing.

Kai Schneider is Professor of Mechanics and Applied Mathematics at Aix-Marseille University, Marseille, France. He obtained his Master and PhD degree from the University of Kaiserslautern, Germany, and his habilitation from the University Strasbourg, France. His research activities are focused on multiscale techniques and wavelets for scientific computing and their application to turbulent flows, including fluid-structure interaction, e.g. for insect flight, and magnetohydrodynamic turbulence.

Incompressible ows: Bergmann, M. et al., AMR enabled quadtree discretization of incompressible Navier-Stokes equations with moving boundaries.- Truong, H. et al., Fluid-structure interaction using volume penalization and mass-spring models with application to flapping bumblebee flight.- Kadri Harouna, S. and Perrier, V., No-slip and Free-slip divergence-free wavelets for the simulation of incompressible viscous flows.- Compressible and weakly compressible ows:  Péron, S., An immersed boundary method on Cartesian adaptive grids for the simulation of compressible flows.- Moreira Lopes, M., Magnetohydrodynamics adaptive solvers in the AMROC framework for space plasma applications.- Gkoudesnes, C. and Deiterding, R., Verification of the WALE large eddy simulation model for adaptive lattice Boltzmann methods implemented in the AMROC framework.