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
Journal of Computational Physics
An interface tracking method for hyperbolic systems of conservation laws
Applied Numerical Mathematics
A fast level set method for propagating interfaces
Journal of Computational Physics
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Three-Dimensional Front Tracking
SIAM Journal on Scientific Computing
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
A boundary condition capturing method for Poisson's equation on irregular domains
Journal of Computational Physics
A numerical method for two-phase flow consisting of separate compressible and incompressible regions
Journal of Computational Physics
A Boundary Condition Capturing Method for Multiphase Incompressible Flow
Journal of Scientific Computing
Computations of compressible multifluids
Journal of Computational Physics
A boundary condition capturing method for incompressible flame discontinuities
Journal of Computational Physics
Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method
Journal of Computational Physics
Ghost fluid method for strong shock impacting on material interface
Journal of Computational Physics
Conservative Front Tracking with Improved Accuracy
SIAM Journal on Numerical Analysis
The ghost fluid method for compressible gas-water simulation
Journal of Computational Physics
A Real Ghost Fluid Method for the Simulation of Multimedium Compressible Flow
SIAM Journal on Scientific Computing
Journal of Computational Physics
A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations
Journal of Computational Physics
An adaptive ghost fluid finite volume method for compressible gas-water simulations
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
Journal of Computational Physics
Anti-diffusion interface sharpening technique for two-phase compressible flow simulations
Journal of Computational Physics
Hi-index | 31.46 |
The high-order accurate Runge-Kutta discontinuous Galerkin (RKDG) method is applied to the simulation of compressible multi-medium flow, generalizing the interface treating method given in Chertock et al. (2008) [9]. In mixed cells, where the interface is located, Riemann problems are solved to define the states on both sides of the interface. The input states to the Riemann problem are obtained by extrapolation to the cell boundary from solution polynomials in the neighbors of the mixed cell. The level set equation is solved by using a high-order accurate RKDG method for Hamilton-Jacobi equations, resulting in a unified DG solver for the coupled problem. The method is conservative if we include the states in the mixed cells, which are however not used in the updating of the numerical solution in other cells. The states in the mixed cells are plotted to better evaluate the conservation errors, manifested by overshoots/undershoots when compared with states in neighboring cells. These overshoots/undershoots in mixed cells are problem dependent and change with time. Numerical examples show that the results of our scheme compare well with other methods for one and two-dimensional problems. In particular, the algorithm can capture well complex flow features of the one-dimensional shock entropy wave interaction problem and two-dimensional shock-bubble interaction problem.