Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Numerical experiments on the accuracy of ENO and modified ENO schemes
Journal of Scientific Computing
Accurate monotone cubic interpolation
SIAM Journal on Numerical Analysis
Numerical solution of the Riemann problem for two-dimensional gas dynamics
SIAM Journal on Scientific Computing
Local piecewise hyperbolic reconstruction of numerical fluxes for nonlinear scalar conservation laws
SIAM Journal on Scientific Computing
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A well-behaved TVD limiter for high-resolution calculations of unsteady flow
Journal of Computational Physics
Accurate monotonicity-preserving schemes with Runge-Kutta time stepping
Journal of Computational Physics
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Comparison of Several Difference Schemes on 1D and 2D Test Problems for the Euler Equations
SIAM Journal on Scientific Computing
Non-uniform convergence of finite volume schemes for Riemann problems of ideal magnetohydrodynamics
Journal of Computational Physics
High order WENO schemes: investigations on non-uniform converges for MHD Riemann problems
Journal of Computational Physics
Limiter-Free Third Order Logarithmic Reconstruction
SIAM Journal on Scientific Computing
A Class of Extended Limiters Applied to Piecewise Hyperbolic Methods
SIAM Journal on Scientific Computing
Design principles for bounded higher-order convection schemes - a unified approach
Journal of Computational Physics
High-order conservative finite difference GLM-MHD schemes for cell-centered MHD
Journal of Computational Physics
Development of an improved spatial reconstruction technique for the HLL method and its applications
Journal of Computational Physics
Parallel, grid-adaptive approaches for relativistic hydro and magnetohydrodynamics
Journal of Computational Physics
Multi-dimensional limiting for high-order schemes including turbulence and combustion
Journal of Computational Physics
The multi-dimensional limiters for solving hyperbolic conservation laws on unstructured grids
Journal of Computational Physics
Hi-index | 31.47 |
We consider finite volume methods for the numerical solution of conservation laws. In order to achieve high-order accurate numerical approximation to non-linear smooth functions, we introduce a new class of limiter functions for the spatial reconstruction of hyperbolic equations. We therefore employ and generalize the idea of double-logarithmic reconstruction of Artebrant and Schroll [R. Artebrant, H.J. Schroll, Limiter-free third order logarithmic reconstruction, SIAM J. Sci. Comput. 28 (2006) 359-381]. The result is a class of efficient third-order schemes with a compact three-point stencil. The interface values between two neighboring cells are obtained by a single limiter function. The limiter belongs to a family of functions, which are based upon a non-polynomial and non-linear reconstruction function. The new methods handle discontinuities as well as local extrema within the standard semi-discrete TVD-MUSCL framework using only a local three-point stencil and an explicit TVD Runge-Kutta time-marching scheme. The shape-preserving properties of the reconstruction are significantly improved, resulting in sharp, accurate and symmetric shock capturing. Smearing, clipping and squaring effects of classical second-order limiters are completely avoided. Computational efficiency is enhanced due to large allowable Courant numbers (CFL@?1.6), as indicated by the von Neumann stability analysis. Numerical experiments for a variety of hyperbolic partial differential equations, such as Euler equations and ideal magneto-hydrodynamic equations, confirm a significant improvement of shock resolution, high accuracy for smooth functions and computational efficiency.