Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Journal of Computational Physics
Parallel, adaptive finite element methods for conservation laws
Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Adaptive multiresolution schemes for shock computations
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Accurate monotonicity-preserving schemes with Runge-Kutta time stepping
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Journal of Computational Physics
A problem-independent limiter for high-order Runge—Kutta discontinuous Galerkin methods
Journal of Computational Physics
Simple modifications of monotonicity-preserving limiters
Journal of Computational Physics
Conservative hybrid compact-WENO schemes for shock-turbulence interaction
Journal of Computational Physics
Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Journal of Computational Physics
Anti-diffusive flux corrections for high order finite difference WENO schemes
Journal of Computational Physics
SIAM Journal on Scientific Computing
High order Hybrid central-WENO finite difference scheme for conservation laws
Journal of Computational and Applied Mathematics
Adaptive Runge-Kutta discontinuous Galerkin methods using different indicators: One-dimensional case
Journal of Computational Physics
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
Hybrid Well-balanced WENO Schemes with Different Indicators for Shallow Water Equations
Journal of Scientific Computing
Hi-index | 31.45 |
A key idea in finite difference weighted essentially non-oscillatory (WENO) schemes is a combination of lower order fluxes to obtain a higher order approximation. The choice of the weight to each candidate stencil, which is a nonlinear function of the grid values, is crucial to the success of WENO schemes. For the system case, WENO schemes are based on local characteristic decompositions and flux splitting to avoid spurious oscillation. But the cost of computation of nonlinear weights and local characteristic decompositions is very high. In this paper, we investigate hybrid schemes of WENO schemes with high order up-wind linear schemes using different discontinuity indicators and explore the possibility in avoiding the local characteristic decompositions and the nonlinear weights for part of the procedure, hence reducing the cost but still maintaining non-oscillatory properties for problems with strong shocks. The idea is to identify discontinuity by an discontinuity indicator, then reconstruct numerical flux by WENO approximation in discontinuous regions and up-wind linear approximation in smooth regions. These indicators are mainly based on the troubled-cell indicators for discontinuous Galerkin (DG) method which are listed in the paper by Qiu and Shu (J. Qiu, C.-W. Shu, A comparison of troubled-cell indicators for Runge-Kutta discontinuous Galerkin methods using weighted essentially non-oscillatory limiters, SIAM Journal of Scientific Computing 27 (2005) 995-1013). The emphasis of the paper is on comparison of the performance of hybrid scheme using different indicators, with an objective of obtaining efficient and reliable indicators to obtain better performance of hybrid scheme to save computational cost. Detail numerical studies in one- and two-dimensional cases are performed, addressing the issues of efficiency (less CPU time and more accurate numerical solution), non-oscillatory property.