An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation
Mathematics of Computation
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
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Sticky Particles and Scalar Conservation Laws
SIAM Journal on Numerical Analysis
Numerical Approximations of Pressureless and Isothermal Gas Dynamics
SIAM Journal on Numerical Analysis
A New Sticky Particle Method for Pressureless Gas Dynamics
SIAM Journal on Numerical Analysis
On maximum-principle-satisfying high order schemes for scalar conservation laws
Journal of Computational Physics
Journal of Computational Physics
An Eulerian Approach to the Analysis of Krause's Consensus Models
SIAM Journal on Control and Optimization
A minimum entropy principle of high order schemes for gas dynamics equations
Numerische Mathematik
| Hi-index | 31.45 |
In this paper, we apply discontinuous Galerkin (DG) methods to solve two model equations: Krause@?s consensus models and pressureless Euler equations. These two models are used to describe the collisions of particles, and the distributions can be identified as density functions. If the particles are placed at a single point, then the density function turns out to be a @d-function and is difficult to be well approximated numerically. In this paper, we use DG method to approximate such a singularity and demonstrate the good performance of the scheme. Since the density functions are always positive, we apply a positivity-preserving limiter to them. Moreover, for pressureless Euler equations, the velocity satisfies the maximum principle. We also construct special limiters to fulfill this requirement.