Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
A fast level set method for propagating interfaces
Journal of Computational Physics
Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
On absorbing boundary conditions for linearized Euler equations by a perfectly matched layer
Journal of Computational Physics
A mathematical analysis of the PML method
Journal of Computational Physics
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Absorbing PML boundary layers for wave-like equations
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Practical animation of liquids
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
A Stable, perfectly matched layer for linearized Euler equations in unslit physical variables
Journal of Computational Physics
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Stability of perfectly matched layers, group velocities and anisotropic waves
Journal of Computational Physics
Perfectly Matched Layers for the Convected Helmholtz Equation
SIAM Journal on Numerical Analysis
ACM SIGGRAPH 2005 Papers
Dynamic Tubular Grid: An Efficient Data Structure and Algorithms for High Resolution Level Sets
Journal of Scientific Computing
Out-of-core and compressed level set methods
ACM Transactions on Graphics (TOG)
Journal of Computational Physics
Journal of Computational Physics
Non-reflective boundary conditions for incompressible free surface fluids
SIGGRAPH 2009: Talks
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Synthesizing waves from animated height fields
ACM Transactions on Graphics (TOG)
A new grid structure for domain extension
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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This article presents a novel nonreflective boundary condition for the free surface incompressible Euler and Navier-Stokes equations. Boundaries of this type are very useful when, for example, simulating water flow around a ship moving over a wide ocean. Normally waves generated by the ship will reflect off of the boundaries of the simulation domain and as these reflected waves return towards the ship they will cause undesired interference patterns. By employing a Perfectly Matched Layer (PML) approach we have derived a boundary condition that absorbs incoming waves and thus efficiently prevents these undesired wave reflections. To solve the resulting boundary equations we present a fast and stable algorithm based on the stable fluids approach. Through numerical experiments we then show that our boundaries are significantly more effective than simpler reflection preventing techniques. We also provide a thorough analysis of the parameters involved in our boundary formulation and show how they effect wave absorption efficiency.