Front tracking for gas dynamics
Journal of Computational Physics
On front-tracking methods applied to hyperbolic systems of nonlinear conservation laws
SIAM Journal on Numerical Analysis
Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
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
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
ENO schemes with subcell resolution
Journal of Computational Physics
An artificial compression method for ENO schemes: the slope modification method
Journal of Computational Physics
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
The behavior of flux difference splitting schemes near slowly moving shock waves
Journal of Computational Physics
A treatment of discontinuities in shock-capturing finite difference methods
Journal of Computational Physics
A treatment of discontinuities for finite difference methods in the two-dimensional case
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
One-dimensional front tracking based on high resolution wave propagation methods
SIAM Journal on Scientific Computing
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
On postshock oscillations due to shock capturing schemes in unsteady flows
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Computational Considerations for the Simulation of Shock-Induced Sound
SIAM Journal on Scientific Computing
The Convergence Rate of Finite Difference Schemes in the Presence of Shocks
SIAM Journal on Numerical Analysis
The fast construction of extension velocities in level set methods
Journal of Computational Physics
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
The ghost fluid method for deflagration and detonation discontinuities
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
A level-set algorithm for tracking discontinuities in hyperbolic conservation laws
Journal of Computational Physics
Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method
Journal of Computational Physics
Elimination of First Order Errors in Shock Calculations
SIAM Journal on Numerical Analysis
The accuracy of the modified ghost fluid method for gas--gas Riemann problem
Applied Numerical Mathematics
Tracking discontinuities in hyperbolic conservation laws with spectral accuracy
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
Towards front-tracking based on conservation in two space dimensions III, tracking interfaces
Journal of Computational Physics
Hi-index | 0.02 |
A level set algorithm for tracking discontinuities in hyperbolic conservation laws is presented. The algorithm uses a simple finite difference approach, analogous to the method of lines scheme presented in [36]. The zero of a level set function is used to specify the location of the discontinuity. Since a level set function is used to describe the front location, no extra data structures are needed to keep track of the location of the discontinuity. Also, two solution states are used at all computational nodes, one corresponding to the “real” state, and one corresponding to a “ghost node” state, analogous to the “Ghost Fluid Method” of [12]. High order pointwise convergence was demonstrated for scalar linear and nonlinear conservation laws, even at discontinuities and in multiple dimensions in the first paper of this series [3]. The solutions here are compared to standard high order shock capturing schemes, when appropriate. This paper focuses on the issues involved in tracking discontinuities in systems of conservation laws. Examples will be presented of tracking contacts and hydrodynamic shocks in inert and chemically reacting compressible flow.