A spectral method with subcell resolution for shock wave calculations
The authors report a spectral method for the numerical solution of hyperbolic partial differential equations assuming that if discontinuous solutions occur they can be represented as the sum of a step function and a smooth function. The latter is then approximated by a series to eliminate the Gibbs phenomenon. By adding the step function to the series one obtains an accurate approximation to the solution at any given time. In this way improvements on some recently published results are reported. The method is tested on three classical problems of fluid mechanics -- the scalar wave equation, Burgers' equation and the Euler equations in gas dynamics. The accuracy of the method is illustrated by numerical examples.
scientific article; zbMATH DE number 937359