A MODIFICATION OF THE GODUNOV DIFFERENCE SCHEME

N. Ya. Moiseev
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1986. Вып.3. С. 35-43.

      The paper considers the Godunov scheme modification which allows to increase smooth solution accuracy while maintaining such useful features as scheme conservatism and monotonicity.
      Increasing the result accuracies for smooth solutions is obtained by constructing a difference higher-order approximation scheme from the Godunov scheme and the monotonicity is maintained by using a hybrid scheme where weak and strong shock regions are calculated with the Godunov scheme while smooth solution regions use a higher-order approximation.
      This modification procedure is simple and generalizes to a multidimensional case in a natural way. Scheme capabilities are illustrated by solving test problems having exact solutions.