Journal of Computational Physics
High-order semi-discrete central-upwind schemes for multi-dimensional Hamilton--Jacobi equations
Journal of Computational Physics
A central-constrained transport scheme for ideal magnetohydrodynamics
Journal of Computational Physics
Non-oscillatory central schemes for one- and two-dimensional MHD equations: I
Journal of Computational Physics
Central schemes on overlapping cells
Journal of Computational Physics
Staggered Finite Difference Schemes for Conservation Laws
Journal of Scientific Computing
A windowed Fourier pseudospectral method for hyperbolic conservation laws
Journal of Computational Physics
A lattice-Boltzmann relaxation scheme for coupled convection-radiation systems
Journal of Computational Physics
A new fourth-order non-oscillatory central scheme for hyperbolic conservation laws
Applied Numerical Mathematics
A central conservative scheme for general rectangular grids
Journal of Computational Physics
FORCE schemes on unstructured meshes I: Conservative hyperbolic systems
Journal of Computational Physics
Approximation error of the Lagrange reconstructing polynomial
Journal of Approximation Theory
Advances in Engineering Software
Alternating Evolution Schemes for Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
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A family of shock capturing schemes for the approximate solution of hyperbolic systems of conservation laws is presented. The schemes are based on a modified ENO reconstruction of pointwise values from cell averages and on approximate computation of the flux on cell boundaries. The use of a staggered grid avoids the need of a Riemann solver. The integral of the fluxes is computed by Simpson's rule. The approximation of the flux on the quadrature nodes is obtained by Runge--Kutta schemes with the aid of natural continuous extension (NCE). This choice gives great flexibility at low computational cost. Several tests are performed on the scalar equation and on systems. The numerical results confirm the expected accuracy and the high resolution properties of the schemes.