"Accuracy." . . "Computations." . . "Computational fluid dynamics." . . "Gas dynamics." . . . "In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially non-oscillatory) finite difference schemes of Liu, Osher and Chan 9. It was shown by Liu et al. that WENO schemes constructed from the r(th) order (in L(1) norm) ENO schemes are (r + 1)th order accurate. We propose a new way of measuring the smoothness of a numerical solution, emulating the idea of minimizing the total variation of the approximation, which results in a 5th order WENO scheme for the case r = 3, instead of the 4th order with the original."@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Efficient implementation of weighted ENO schemes"@en . "Efficient implementation of weighted ENO schemes" . . . . . . "Efficient Implementation of Weighted ENO Schemes"@en . . . . "Convergence." . . "Vector analysis." . . "Fluid Mechanics." . . "Pressure distribution." . . "Smoothing(mathematics)" . . "Finite difference theory." . . "Partial differential equations." . . "Shock waves." . . . . "Interpolation." . . "Euler equations." . . "Mathematical models." . . "Flow fields." . . "Nozzle gas flow." . . "Entropy." . . "Optimization." . . "One dimensional flow." . . "Weighting functions." . . "Essentially non-oscillatory schemes." . . "Approximation(mathematics)" . . "Euler equations of motion." . . "Numerical methods and procedures." . . "Polynomials." . . "Conservation laws." . . "Numerical Mathematics." . .