Date of this Version
Journal of Computational Physics 265 (2014) 211–220.
In this note we generalize our previous treatment of the discretizations of geometric conservation laws on steady grids (Vinokur and Yee, 2000) to general time dependent grids. The commutative property of mixed difference operators is generalized to apply to time metrics and Jacobians. Our treatment uses half the number of terms as those used in a recent paper by Abe et al. (2012). We also derive the proper temporal discretizations of both Runge–Kutta and linear multistep methods to satisfy the commutativity property for higher than first order.