Front tracking for gas dynamics
Journal of Computational Physics
Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
A treatment of discontinuities in shock-capturing finite difference methods
Journal of Computational Physics
A front-tracking method for viscous, incompressible, multi-fluid flows
Journal of Computational Physics
A treatment of discontinuities for finite difference methods in the two-dimensional case
Journal of Computational Physics
A shock tracking technique based on conservation in one space dimension
SIAM Journal on Numerical Analysis
Two-dimensional front tracking based on high resolution wave propagation methods
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Reconstructing volume tracking
Journal of Computational Physics
The point-set method: front-tracking without connectivity
Journal of Computational Physics
A level-set algorithm for tracking discontinuities in hyperbolic conservation laws
Journal of Computational Physics
A Boundary Condition Capturing Method for Multiphase Incompressible Flow
Journal of Scientific Computing
A front-tracking method for the computations of multiphase flow
Journal of Computational Physics
Toward Front Tracking Based on Conservation in Two Space Dimensions
SIAM Journal on Scientific Computing
Journal of Computational Physics
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Resolution of high order WENO schemes for complicated flow structures
Journal of Computational Physics
Journal of Scientific Computing
Conservative Front Tracking with Improved Accuracy
SIAM Journal on Numerical Analysis
A simple package for front tracking
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
Towards front-tracking based on conservation in two space dimensions III, tracking interfaces
Journal of Computational Physics
Hi-index | 31.46 |
In this paper, the second one in the series beginning with [D. Mao, Towards front tracking based on conservation in two space dimensions, SIAM J. Sci. Comput. 22 (1) (2000) 113-151], we study another important feature of our 2D conservative front-tracking method, i.e. discontinuity curves in two space dimensions are tracked in a 1D capturing fashion. The evolution of 2D discontinuity curves are locally described by 1D conservation laws with source terms, which are derived from the governing equations. The front-tracking in our method is then realized by numerically simulating these 1D conservation laws with source terms in a conservative fashion. In this paper, our 2D front-tracking method is described in details, which is Cartesian-grid-based, conservative and much simpler in algorithm than other 2D front-tracking methods. The discussion starts with the 1D case, which facilitates the following 2D discussion. Data structure of the numerical solutions and first- and second-order versions of our 2D front-tracking method are described. Finally, numerical examples for both scalar equations and the Euler system of gas dynamics in 2D are presented to show the efficiency and effectiveness of the method.