Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries
Journal of Computational Physics
Conservative multigrid methods for Cahn-Hilliard fluids
Journal of Computational Physics
Journal of Computational Physics
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
A level-set approach for simulations of flows with multiple moving contact lines with hysteresis
Journal of Computational Physics
An improved PLIC-VOF method for tracking thin fluid structures in incompressible two-phase flows
Journal of Computational Physics
Journal of Computational Physics
Advections with Significantly Reduced Dissipation and Diffusion
IEEE Transactions on Visualization and Computer Graphics
Journal of Computational Physics
Runge-Kutta-Chebyshev projection method
Journal of Computational Physics
Two-phase viscoelastic jetting
Journal of Computational Physics
An adaptive, formally second order accurate version of the immersed boundary method
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
FlowFixer: using BFECC for fluid simulation
NPH'05 Proceedings of the First Eurographics conference on Natural Phenomena
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In this method we present a fractional step discretization of the time-dependent incompressible Navier--Stokes equations. The method is based on a projection formulation in which we first solve diffusion--convection equations to predict intermediate velocities, which are then projected onto the space of divergence-free vector fields. Our treatment of the diffusion--convection step uses a specialized second-order upwind method for differencing the nonlinear convective terms that provides a robust treatment of these terms at a high Reynolds number. In contrast to conventional projection-type discretizations that impose a discrete form of the divergence-free constraint, we only approximately impose the constraint; i.e., the velocity field we compute is not exactly divergence-free. The approximate projection is computed using a conventional discretization of the Laplacian and the resulting linear system is solved using conventional multigrid methods. Numerical examples are presented to validate the second-order convergence of the method for Euler, finite Reynolds number, and Stokes flow. A second example illustrating the behavior of the algorithm on an unstable shear layer is also presented.