A class of implicit upwind schemes for Euler simulations with unstructured meshes
Journal of Computational Physics
Cell vertex algorithms for the compressible Navier-Stokes equations
Journal of Computational Physics
Finite volume approximation of elliptic problems and convergence of an approximate gradient
Applied Numerical Mathematics
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
A cell-centered diffusion scheme on two-dimensional unstructured meshes
Journal of Computational Physics
Journal of Computational Physics
Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes
Journal of Computational Physics
The Elastoplast Discontinuous Galerkin (EDG) method for the Navier-Stokes equations
Journal of Computational Physics
Hi-index | 31.46 |
The main approaches of discretising the viscous operator of fluid flow on hybrid meshes are analysed for accuracy, consistence, monotonicity and sensitivity to mesh quality. As none of these approaches is fully satisfactory, a novel method using an approximated finite-element approach is presented and analysed. The methods are compared for the linear heat equation and the Navier-Stokes equations. While the novel approximated finite-element method performs significantly better for the linear heat equation, a stabilised edge-based method performs equally well for the considered test-cases for the Navier-Stokes equations.