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
Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Numerical Simulation of High Mach Number Astrophysical Jets with Radiative Cooling
Journal of Scientific Computing
High-order well-balanced schemes and applications to non-equilibrium flow
Journal of Computational Physics
On maximum-principle-satisfying high order schemes for scalar conservation laws
Journal of Computational Physics
Journal of Computational Physics
Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations
Journal of Computational Physics
Positivity-preserving high order finite difference WENO schemes for compressible Euler equations
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Scientific Computing
Positivity-preserving Lagrangian scheme for multi-material compressible flow
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.47 |
In [16,17], we constructed uniformly high order accurate discontinuous Galerkin (DG) schemes which preserve positivity of density and pressure for the Euler equations of compressible gas dynamics with the ideal gas equation of state. The technique also applies to high order accurate finite volume schemes. For the Euler equations with various source terms (e.g., gravity and chemical reactions), it is more difficult to design high order schemes which do not produce negative density or pressure. In this paper, we first show that our framework to construct positivity-preserving high order schemes in [16,17] can also be applied to Euler equations with a general equation of state. Then we discuss an extension to Euler equations with source terms. Numerical tests of the third order Runge-Kutta DG (RKDG) method for Euler equations with different types of source terms are reported.