Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries
Journal of Computational Physics
Adaptive low Mach number simulations of nuclear flame microphysics
Journal of Computational Physics
High-resolution methods for two-component fluid flow problem with moving interface
Mathematics and Computers in Simulation - Special issue: Mathematical modeling of ecological systems
An unsplit, cell-centered Godunov method for ideal MHD
Journal of Computational Physics
Stability of approximate projection methods on cell-centered grids
Journal of Computational Physics
A coupled quadrilateral grid level set projection method applied to ink jet simulation
Journal of Computational Physics
Journal of Computational Physics
Runge-Kutta-Chebyshev projection method
Journal of Computational Physics
Two-phase viscoelastic jetting
Journal of Computational Physics
Unconditionally stable discretizations of the immersed boundary equations
Journal of Computational Physics
An adaptive, formally second order accurate version of the immersed boundary method
Journal of Computational Physics
Journal of Computational Physics
An accurate adaptive solver for surface-tension-driven interfacial flows
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
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The use of approximate projection methods for modeling low Mach number flows avoids many of the numerical complications associated with exact projection methods, but introduces additional design choices in developing a robust algorithm. In this paper we first explore these design choices in the setting of inviscid incompressible flow using several computational examples. We then develop a framework for analyzing the behavior of the different design variations and use that analysis to explain the features observed in the computations. As part of this work we introduce a new variation of the approximate projection algorithm that combines the advantages of several of the previous versions.