Assessment of immersed boundary methods for hypersonic flows with gas–surface interactions

The efficacy of immersed boundary (IB) methods with adaptive mesh refinement (AMR) techniques is assessed in the context of atmospheric entry applications, including effects of chemical nonequilibrium (CNE) and gas–surface interactions (GSI). We scrutinize a conservative cut-cell IB method and two non-conservative IB methods, comparing their...

Theory and Applications of Differential Equation Methods for Graph-based Learning

A large number of modern learning problems involve working with highly interrelated and interconnected data. Graph-based learning is an emerging technique for approaching such problems, by representing this data as a graph (a.k.a. a network). That is, the points of data are represented by the vertices of the graph, and then the edges linking...

A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains

We introduce a mimetic dual-field discretization which conserves mass, kinetic energy and helicity for three-dimensional incompressible Navier-Stokes equations. The discretization makes use of a conservative dual-field mixed weak formulation where two evolution equations of velocity are employed and dual representations of the solution are...