Oleg V. Vasilyev

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Two mathematical approaches are combined to calculate high Reynolds number in-compressible fluid-structure interaction: a wavelet method to dynamically adapt the computational grid to flow intermittency and obstacle motion, and Brinkman penalization to enforce solid boundaries of arbitrary complexity. We also implement a wavelet-based multilevel solver for(More)
To simulate flows around solid obstacles of complex geometries, various immersed boundary methods had been developed. Their main advantage is the efficient implementation for stationary or moving solid boundaries of arbitrary complexity on fixed non-body conformal Cartesian grids. The Brinkman penalization method was proposed for incompressible viscous(More)
Dynamically adaptive numerical methods have been developed to efficiently solve differential equations whose solutions are intermittent in both space and time. These methods combine an adjustable time step with a spatial grid that adapts to spatial intermittency at a fixed time. The same time step is used for all spatial locations and all scales: this(More)
a r t i c l e i n f o a b s t r a c t In order to introduce solid obstacles into flows, several different methods are used, including volume penalization methods which prescribe appropriate boundary conditions by applying local forcing to the constitutive equations. One well known method is Brinkman penalization, which models solid obstacles as porous(More)
a r t i c l e i n f o a b s t r a c t Dynamic load balancing Wavelets Lifting scheme Second generation wavelets Adaptive grid Multiresolution Multilevel method Multigrid method Numerical method Partial differential equations Elliptic problem A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is(More)
a r t i c l e i n f o a b s t r a c t This paper presents an integrated approach for modeling several ocean test problems on adaptive grids using novel boundary techniques. The adaptive wavelet collocation method solves the governing equations on temporally and spatially varying meshes, which allows higher effective resolution to be obtained with less(More)