High-Order Central Schemes for Hyperbolic Systems of Conservation Laws

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Abstract
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.