A numerical method for systems of hyperbolic conservation laws with single stencil reconstructions (Q1344020)

A numerical method for systems of conservation laws related to the Godunov method and essentially non-oscillatory (ENO) schemes described by \textit{A. Harten, B. Engquist, St. Osher} and \textit{S. Chakravarthy} [J. Comput. Phys. 71, 231-303 (1987; Zbl 0652.65067)] is presented. The current method uses the same idea as in the original ENO schemes: Using an adaptive moving stencil of grid points to obtain smooth information about the solution with total minimal variation in a certain sense. The method requires only one evaluation of a Riemann problem per grid point and per time step which is comparable to the first-order Godunov method, while it produces solutions with significantly better resolution than results of the Godunov method. Numerical tests are calculated for the system of equations for gas dynamics.