Toward the ultimate conservative scheme: following the quest
Journal of Computational Physics
Residual Distribution Schemes for Conservation Laws via Adaptive Quadrature
SIAM Journal on Scientific Computing
UNIFICATION OF SOME ADVECTION SCHEMES IN TWO DIMENSIONS
UNIFICATION OF SOME ADVECTION SCHEMES IN TWO DIMENSIONS
Journal of Computational Physics
High Order Fluctuation Schemes on Triangular Meshes
Journal of Scientific Computing
Residual distribution for general time-dependent conservation laws
Journal of Computational Physics
Essentially non-oscillatory Residual Distribution schemes for hyperbolic problems
Journal of Computational Physics
Discontinuous fluctuation distribution
Journal of Computational Physics
Goal-oriented mesh adaptation for flux-limited approximations to steady hyperbolic problems
Journal of Computational and Applied Mathematics
Linearity-preserving flux correction and convergence acceleration for constrained Galerkin schemes
Journal of Computational and Applied Mathematics
Hi-index | 31.45 |
This paper addresses the issue of constructing non-oscillatory, higher than second order, fluctuation splitting methods on unstructured triangular meshes. It highlights the reasons why existing approaches fail and proposes a procedure which can be applied to any high order fluctuation splitting scheme to impose positivity on it. Its success is demonstrated through application to a series of linear and nonlinear scalar problems, using a pseudo-time-stepping technique to reach steady state solutions on two-dimensional unstructured meshes.