Weakly differentiable functions
Weakly differentiable functions
An approximate linearized Riemann solver for a two-fluid model
Journal of Computational Physics
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Journal of Computational Physics
A multiphase Godunov method for compressbile multifluid and multiphase flows
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
SIAM Journal on Numerical Analysis
Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Space-time discontinuous Galerkin discretization of rotating shallow water equations
Journal of Computational Physics
HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow
Journal of Computational Physics
Space-time discontinuous Galerkin finite element method for two-fluid flows
Journal of Computational Physics
A Simple Extension of the Osher Riemann Solver to Non-conservative Hyperbolic Systems
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.47 |
We present space- and space-time discontinuous Galerkin finite element (DGFEM) formulations for systems containing nonconservative products, such as occur in dispersed multiphase flow equations. The main criterium we pose on the weak formulation is that if the system of nonconservative partial differential equations can be transformed into conservative form, then the formulation must reduce to that for conservative systems. Standard DGFEM formulations cannot be applied to nonconservative systems of partial differential equations. We therefore introduce the theory of weak solutions for nonconservative products into the DGFEM formulation leading to the new question how to define the path connecting left and right states across a discontinuity. The effect of different paths on the numerical solution is investigated and found to be small. We also introduce a new numerical flux that is able to deal with nonconservative products. Our scheme is applied to two different systems of partial differential equations. First, we consider the shallow water equations, where topography leads to nonconservative products, in which the known, possibly discontinuous, topography is formally taken as an unknown in the system. Second, we consider a simplification of a depth-averaged two-phase flow model which contains more intrinsic nonconservative products.