Construction of explicit and implicit symmetric tvd schemes and their applications
Journal of Computational Physics
Numerical experiments on the accuracy of ENO and modified ENO schemes
Journal of Scientific Computing
Triangle based adaptive stencils for the solution of hyperbolic conservation laws
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational Physics
A projection FEM for variable density incompressible flows
Journal of Computational Physics
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
High Order Fluctuation Schemes on Triangular Meshes
Journal of Scientific Computing
SIAM Journal on Numerical Analysis
Error estimate for finite volume scheme
Numerische Mathematik
$L^\infty$- and $L^2$-Error Estimates for a Finite Volume Approximation of Linear Advection
SIAM Journal on Numerical Analysis
An hybrid finite volume-finite element method for variable density incompressible flows
Journal of Computational Physics
Journal of Computational Physics
Monoslope and multislope MUSCL methods for unstructured meshes
Journal of Computational Physics
L ∞ stability of the MUSCL methods
Numerische Mathematik
Journal of Computational and Applied Mathematics
Positivity-preserving schemes for Euler equations: Sharp and practical CFL conditions
Journal of Computational Physics
Upwind-Difference Potentials Method for Patlak-Keller-Segel Chemotaxis Model
Journal of Scientific Computing
Hi-index | 31.45 |
This work is devoted to the design of multi-dimensional finite volume schemes for solving transport equations on unstructured grids. In the framework of MUSCL vertex-based methods we construct numerical fluxes such that the local maximum property is guaranteed under an explicit Courant-Friedrichs-Levy condition. The method can be naturally completed by adaptive local mesh refinements and it turns out that the mesh generation is less constrained than when using the competitive cell-centered methods. We illustrate the effectiveness of the scheme by simulating variable density incompressible viscous flows. Numerical simulations underline the theoretical predictions and succeed in the computation of high density ratio phenomena such as a water bubble falling in air.