HIGH ORDER WELL-BALANCED SCHEMES BASED ON NUMERICAL RECONSTRUCTION OF THE EQUILIBRIUM VARIABLES

In this paper we deal with the problem of construction of well-balanced schemes for hyperbolic systems of balance laws. A method based on two sets of variables (conservative and equilibrium ones) is considered.(6) We propose a method for reconstruction of the equilibrium variables when the analytical mapping between the equilibrium variables and conservative ones is unknown. For model scalar equation well-balanced schemes of up to the fourth order are constructed. Numerical results shows the well-balanced properties and high order resolution of the schemes.