An efficient dynamically adaptive mesh for potentially singular solutions

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Adaptivity with moving grids (2009, methodology): “…recent interesting work of Bank and Smith (1997), Beckett, Mackenzie and Robertson (2001a), Budd et al. (1996), Calhoun, Helzel and LeVeque (2008), Ceniceros and Hou (2001), Chacón and Lapenta (2006), Lapenta and Chacón (2006), Di, Li, Tang and Zhang (2005), Huang and Zhan (2004), Mackenzie…”
MULTISCALE FLOW SIMULATIONS USING PARTICLES (2005, methodology): “Similar to r-adaptive mesh-based methods (Ceniceros & Hou 2001), it is desirable to require enhanced resolution for vortex particles in areas of high shear.”
A Moving Mesh Finite Element Algorithm for Singular Problems in Two and Three Space Dimensions (2002, background): “Some useful applications based on various moving mesh techniques can be found in a number of papers, including [3, 11, 28, 31] for computational fluid dynamics, [12, 18] for computational geometry and [27] for simulations of the reactive flows.”
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws (2003, methodology): “In the past two decades, there has been important progress in developing mesh methods for PDEs, including the variational approach of Winslow [36], Brackbill [5], and Brackbill and Saltzman [6]; finite element methods by Miller and Miller [25] and Davis and Flaherty [11]; the moving mesh PDEs of Cao”