Semi-discrete central-upwind schemes with reduced dissipation for Hamilton–Jacobi equations

We introduce a new family of Godunov-type semi-discrete central schemes for multidimensional Hamilton–Jacobi equations. These schemes are a less dissipative generalization of the central-upwind schemes that have been recently proposed in Kurganov, Noelle and Petrova (2001, SIAM J. Sci. Comput., 23, pp. 707–740). We provide the details of the new family of methods in one, two, and three space dimensions, and then verify their expected low-dissipative property in a variety of examples.