Natural continuous extensions of Runge-Kutta formulas
Mathematics of Computation
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
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Numerical experiments on the accuracy of ENO and modified ENO schemes
Journal of Scientific Computing
A numerical study of the convergence properties of ENO schemes
Journal of Scientific Computing
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Applied Numerical Mathematics - Special issue on time integration
Journal of Computational Physics
SIAM Journal on Numerical Analysis
High-Order Central Schemes for Hyperbolic Systems of Conservation Laws
SIAM Journal on Scientific Computing
Journal of Computational Physics
New high-resolution semi-discrete central schemes for Hamilton-Jacobi equations
Journal of Computational Physics
A Third-Order Semidiscrete Central Scheme for Conservation Laws and Convection-Diffusion Equations
SIAM Journal on Scientific Computing
Compact Central WENO Schemes for Multidimensional Conservation Laws
SIAM Journal on Scientific Computing
A Fourth-Order Central WENO Scheme for Multidimensional Hyperbolic Systems of Conservation Laws
SIAM Journal on Scientific Computing
Central Schemes for Balance Laws of Relaxation Type
SIAM Journal on Numerical Analysis
Additive Runge-Kutta schemes for convection-diffusion-reaction equations
Applied Numerical Mathematics
Journal of Computational Physics
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
High-Order Central WENO Schemes for Multidimensional Hamilton--Jacobi Equations
SIAM Journal on Numerical Analysis
Central Runge--Kutta Schemes for Conservation Laws
SIAM Journal on Scientific Computing
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Overlapping Yee FDTD Method on Nonorthogonal Grids
Journal of Scientific Computing
A fourth-order divergence-free method for MHD flows
Journal of Computational Physics
A Central Discontinuous Galerkin Method for Hamilton-Jacobi Equations
Journal of Scientific Computing
Journal of Computational and Applied Mathematics
Alternating Evolution Schemes for Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations
Journal of Computational Physics
Hi-index | 31.47 |
Nessyahu and Tadmor's central scheme [J. Comput. Phys. 87 (1990)] has the benefit of not using Riemann solvers for solving hyperbolic conservation laws. But the staggered averaging causes large dissipation when the time step size is small compared to the mesh size. The recent work of Kurganov and Tadmor [J. Comput. Phys. 160 (2000)] overcomes this problem by using a variable control volume and results in semi-discrete and fully discrete non-staggered schemes. Motivated by this work, we introduce overlapping cell averages of the solution at the same discrete time level, and develop a simple alternative technique to control the O(1/@Dt) dependence of the dissipation. The semi-discrete form of the central scheme can also be obtained to which the TVD Runge-Kutta time discretization methods of Shu and Osher [J. Comput. Phys. 77 (1988)] or other stable and sufficiently accurate ODE solvers can be applied. This technique is essentially independent of the reconstruction and the shape of the mesh. The overlapping cell representation of the solution also opens new possibilities for reconstructions. Generally speaking, more compact reconstruction can be achieved. In the following, schemes of up to fifth order in 1D and third order in 2D have been developed. We demonstrate through numerical examples that by combining two classes of the overlapping cells in the reconstruction we can achieve higher resolution.