Well-Balanced High-Order Methods for Systems of Balance Laws

A family of well-balanced high-order numerical methods for 1d systems of balance laws is introduced. These methods are based on a reconstruction operator, i.e., an operator that, given the cell averages of a function, provides high-order approximations of the function at the cells. The key concept of well-balanced reconstruction operator is discussed. Burgers’ equation with a nonlinear source term is considered to illustrate the application of the methods.

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