Adaptive wavelet algorithms for solving problems of hydro- and gas dynamics on Cartesian grids
Modern problems of fluid and gas mechanics are closely related to mathematical modeling of various physical processes and calculation of flows in areas with complex spatial geometry, which may depend on time. The investigated modes in such problems are characterized by a strong heterogeneity of the spatiotemporal scales. Their resolution requires detailed grids with high spatial resolution. The use of homogeneous grids leads to significant computational costs. Therefore, the idea arises of introducing local dynamic adaptation of the grid in order to increase the accuracy of numerical modeling, taking into account the structure of the solution, within the limits of available computing resources. The book outlines a new computing technology for solving problems of this type. It is based on a combination of the idea of multiscale in describing the flow of a medium with the free boundary method. The multiscale description of the flow is achieved using wavelet analysis. The free boundary method makes it possible to effectively implement internal boundary conditions on non-conformal locally adaptive Cartesian grids.