Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Computing interface motion in compressible gas dynamics
Journal of Computational Physics
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Reconstructing volume tracking
Journal of Computational Physics
The fast construction of extension velocities in level set methods
Journal of Computational Physics
An adaptive level set approach for incompressible two-phase flows
Journal of Computational Physics
SIAM Journal on Scientific Computing
Tree methods for moving interfaces
Journal of Computational Physics
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
A critical analysis of Rayleigh-Taylor growth rates
Journal of Computational Physics
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Enhancing scalability of parallel structured AMR calculations
ICS '03 Proceedings of the 17th annual international conference on Supercomputing
Interface conditions for wave propagation through mesh refinement boundaries
Journal of Computational Physics
Journal of Computational Physics
A conservative level set method for two phase flow
Journal of Computational Physics
A Lagrangian particle level set method
Journal of Computational Physics
On High Order Strong Stability Preserving Runge---Kutta and Multi Step Time Discretizations
Journal of Scientific Computing
A quadrature-free discontinuous Galerkin method for the level set equation
Journal of Computational Physics
Adaptive characteristics-based matching for compressible multifluid dynamics
Journal of Computational Physics
A fast and accurate semi-Lagrangian particle level set method
Computers and Structures
A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids
Journal of Computational Physics
Numerical prediction of interfacial instabilities: Sharp interface method (SIM)
Journal of Computational Physics
Differential equation based constrained reinitialization for level set methods
Journal of Computational Physics
Journal of Computational Physics
An accurate conservative level set/ghost fluid method for simulating turbulent atomization
Journal of Computational Physics
A front-tracking/ghost-fluid method for fluid interfaces in compressible flows
Journal of Computational Physics
An all-speed relaxation scheme for interface flows with surface tension
Journal of Computational Physics
The constrained reinitialization equation for level set methods
Journal of Computational Physics
An Eulerian method for multi-component problems in non-linear elasticity with sliding interfaces
Journal of Computational Physics
Journal of Computational Physics
An interface capturing method for the simulation of multi-phase compressible flows
Journal of Computational Physics
Marker Redistancing/Level Set Method for High-Fidelity Implicit Interface Tracking
SIAM Journal on Scientific Computing
A conservative level-set based method for compressible solid/fluid problems on fixed grids
Journal of Computational Physics
A hybrid level set-volume constraint method for incompressible two-phase flow
Journal of Computational Physics
A ghost fluid method for compressible reacting flows with phase change
Journal of Computational Physics
Eulerian adaptive finite-difference method for high-velocity impact and penetration problems
Journal of Computational Physics
Journal of Computational Physics
A new level set model for multimaterial flows
Journal of Computational Physics
Hi-index | 31.53 |
The interface-capturing-fidelity issue of the level set method is addressed wholly within the Eulerian framework. Our aim is for a practical and efficient way to realize the expected benefits of grid resolution and high order schemes. Based on a combination of structured adaptive mesh refinement (SAMR), rather than quad/octrees, and on high-order spatial discretization, rather than the use of Lagrangian particles, our method is tailored to compressible flows, while it provides a potentially useful alternative to the particle level set (PLS) for incompressible flows. Interesting salient features of our method include (a) avoidance of limiting (in treating the Hamiltonian of the level set equation), (b) anchoring the level set in a manner that ensures no drift and no spurious oscillations of the zero level during PDE-reinitialization, and (c) a non-linear tagging procedure for defining the neighborhood of the interface subject to mesh refinement. Numerous computational results on a set of benchmark problems (strongly deforming, stretching and tearing interfaces) demonstrate that with this approach, implemented up to 11th order accuracy, the level set method becomes essentially free of mass conservation errors and also free of parasitic interfacial oscillations, while it is still highly efficient, and convenient for 3D parallel implementation. In addition, demonstration of performance in fully-coupled simulations is presented for multimode Rayleigh-Taylor instability (low-Mach number regime) and shock-induced, bubble-collapse (highly compressible regime).